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Patent US4195338 - Computer typesetting
This invention relates to apparatus and methods suitable for directing automatic typesetting and display systems. More particularly this invention relates to such apparatus and methods in a system
including a programmed data processor. Still more particularly, the present invention relates to data processing apparatus and methods for generating images for use in printing mathematical formulas
and materials including other than linear text.
Recent improvements in printing and typesetting technology have greatly increased the efficiency of setting type for straight linear text, e.g., newspaper text, phone directories, and the like. These
improvements, which largely flow from the use of high speed data processors, include techniques for realizing such features as automatic character generation, and justification and hyphenation of
linear text. Many of these features are realized in non-impact printing systems not requiring the explicit operation of typesetting. See, for example, M. V. Mathews and J. E. Miller, "Computer
Editing, Typesetting, and Image Generation", AFIPS 1965 FJCC Proceedings, Vol. 27, Part 1, pp. 389-398, Spartan Books, Washington, D.C., 1965; F. Park, "The Printed Word", International Science and
Technology, Vol. 8, No. 2, pp. 103-109, July 1965 and U.S. Pat. Nos. 3,422,419 and 3,490,004, issued Jan. 14, 1969 to M. V. Mathews et al and Jan. 13, 1970 to R. F. Ross, respectively. Nevertheless,
in keeping with much common usage, the present description will proceed with the operation of character positioning characterized as "typesetting".
It is understandable that the emphasis for early efforts in computer typesetting would be in connection with the commonly-occurring, relatively simple linear textual materials. A substantial
percentage of modern printing, however, is directed to areas involving the mathematical and other sciences. In these and related fields the preferred method of printed communication often requires
the typesetting of a large number of mathematical and other formulas. The automation of typesetting for these more specialized mathematical and related symbols has been considerably less advanced
than for linear text material.
Efforts to overcome the difficulties implicit in computer-aided printing of mathematical formulas have been in two principal directions. The first of these involves the interpretation of the formulas
in a basically mathematical sense. That is, it is the mathematical and logical meaning of operations which are treated as controlling in the determination of the placing, spacing and relative
positioning of the symbols involved. Thus, for example, in the system described in W. A. Martin, "Symbolic Mathematical Laboratory", Ph.D. Thesis, MIT, January, 1967, the basic internal
representation of a formula is in terms of its mathematical content, and a display is generated completely automatically from this basic internal representation. The computer program automatically
does such things as choose the style and size of parentheses and divide a formula in two if the formula is too long to fit on a single line. The formula division is based on the identification of the
mathematical significance of the operators, e.g., a search for an equality sign is made and the position of it used to determine the point of division. Since the display program in this system is
completely automatic (given the representation of the formula's mathematical content), it has no provision for the user to insert spaces where he feels they will improve the appearance of the formula
or equation. Neither has it a provision for the user to select among various mathematically equivalent representations, e.g., the radical sign is not used, so that √(expression) is always represented
by (expression) ^1/2 ; multiplication is always represented explicitly, so that A(α+βγ) would be represented as A·(α+β·γ), and the minus sign is not used as a binary relation so that a-b would be
represented as a+(-1)·b. It should be noted that the mathematical meaning of the expression is maintained, although the esthetic characteristics of the printed representation are largely not
This brings us to the second area of endeavor in the computerized typesetting of mathematical formulas, namely the positioning of the mathematical symbols in an expression in accordance with their
appearance, as distinguished from their mathematical significance alone. It should be understood, of course, in connection with this latter area of interest that the mathematical integrity of the
expression must be maintained as well. Some examples of previous work on the problem of improving the esthetic aspects of typesetting mathematical formulas by computer will now be described.
In M. Klerer and F. Grossman "Further Advances in Two-Dimensional Input-Output by Teletype Terminals", AFIPS 1967 FJCC Proceedings, Vol. 31, pp. 675, 687, Thompson Books, Washington, D.C. 1967, for
example, there are described techniques for use in connection with a project to publish a table of integrals whose accuracy has been checked by computer programs. The integral is input to the
computer program by typing it in a stylized two dimensional format. The program controlled computer then modifies the spacing between symbols thereby removing excessive gaps, centering numerators and
denominators and breaking a formula in half if it is too long to fit on one line.
The J. H. Kuney, et al, "Computerized Typesetting of Complex Scientific Material", AFIPS 1966 FJCC Proceedings, Vol. 29, pp. 149-156, Spartan Books, Washington, D.C., 1966, there is described a
system for typesetting mathematical equations that is based on the use of macros. This system is intended to be used for typesetting mathematical equations and other materials as well, e.g., this
same system can be used to typeset tabular data. Hence this prior art system does not make use of the recursive structure inherent in mathematical equations. For that reason, that system requires a
considerable amount of typing to input a mathematical formula and depends much more on the judgment of the typist in determining the spacing of the symbols in a formula.
The present invention provides methods and apparatus which fall generally into the second category described above. These techniques permit the easy assembly of computer input data while at the same
time providing highly efficient and flexible storage and retrieval characteristics.
Briefly stated, in accordance with one typical embodiment of the present invention, there is provided means for generating an input tape or other input representation expressing the esthetic
preferences of a typesetter (within the limits of the correct mathematical interpretation). This input representation is conveniently arranged to take advantage of the recursive structure inherent in
mathematical equations. This input representation is then advantageously interpreted by a programmed digital computer. In the computer, the input information is arranged and stored in a hierarchical
tree structure. Further means in the form of a specially programmed processor are provided for interpreting and retrieving this stored information from memory. In this connection, a self-consistent
set of so-called "concatenation points" are advantageously associated with each character or symbol to be typeset. This specially programmed processor, in accordance with a "local positional
algorithm", then generates the commands necessary to generate a sequence of position signals. In particular, this algorithm is used to determine the relative positioning between a given symbol and
those symbols that are "adjacent" this given symbol (as the "y" and the "+" are "adjacent" to the "X" in the expression X^y-2 +W).
In effecting the positioning, the programmed computer treats the stored signal representing the symbols as abstract objects associated with respective sets of signals representing concatenation
points. These objects are then selectively connected together at appropriate concatenation points to form successively larger objects. The method steps for connecting, i.e., the rules for selecting
and joining the concatenation points, are completely specified by the computer program and are more completely described below. These steps include performing individually well-known computer
operations such as comparison, table look-up, conditional branching and the like.
The position signals are then applied to a cathode ray tube or other display device and the resulting image photographed (or otherwise reproduced) in a now-standard manner. This photograph then
serves the same purpose as photographic images generated in the prior art. That is, the photographic image is used to generate an etched plate or other more durable reproduction surface.
Other features of the present invention will appear in the detailed description below taken in connection with the accompanying drawings wherein:
FIG. 1 illustrates a computer typesetting system incorporating the present invention.
FIG. 2 shows a typical arrangement of program storage in the system of FIG. 1.
FIG. 3 illustrates the tree structure used in storing formula information in one embodiment of the present invention.
FIG. 4 illustrates the concept of concatenation points in connection with typical mathematical formula symbols.
FIGS. 5A-C illustrate the process of concatenating successive symbols along a line.
FIGS. 6A-C illustrate the process of concatenating successive symbols one of which bears an exponential relation to the other.
FIG. 7 is a flowchart illustrating one method for hierarchically storing input information in a tree structure.
FIGS. 8A-N show typical typeset equations.
The detailed descriptions to follow are presented largely in terms of algorithms. These algorithmic descriptions are the means used by those skilled in the data processing arts to most effectively
convey the substance of their work to others skilled in the data processing arts.
An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. These steps are those requiring physical manipulations of physical quantities.
Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It proves
convenient at times, principally for reasons of common usage, to refer to these signals as samples, values, elements, symbols, characters, terms, numbers, or the like. It should be borne in mind,
however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities.
Further, the manipulations performed are often referred to in terms, such as adding or comparing which are commonly associated with mental operations performed by a human operator. No such capability
of a human operator is necessary, or desirable in most cases, in any of the operations described herein which form part of the present invention; the operations are machine operations. Useful
machines for performing the operations of the present invention include general purpose computers of the IBM 7090/94 or various of the IBM System/360 class, the GE-600 class or other similar
machines. In all cases there should be borne in mind the distinction between the method operations in operating a computer and the method of computation itself. The present invention relates to
method steps for operating a computer in processing electrical or other (e.g., mechanical, chemical) physical signals to generate other desired physical signals.
The present invention also relates to apparatus for performing these operations. This apparatus may be specially constructed for the required purposes or it may comprise a general purpose computer as
selectively activated or reconfigured by a computer program stored in the computer. The algorithms presented herein are not inherently related to any particular computer or other apparatus. In
particular, various general purpose machines, including those mentioned above, may be used with programs written in accordance with the teachings herein, or it may prove more convenient to construct
more specialized apparatus to perform the required method steps. The required structure for various of these machines will appear from the description given below.
The following detailed description will be divided into several sections. The first of these will treat a general system arrangement for generating computer typeset formulas. Subsequent sections will
deal with such aspects of the present invention as structuring of input information, the generation of position--indicating signals needed to generate a visible image of formulas, typical input
techniques and symbology, and typical step-by-step procedures used in typesetting using the present invention.
The limitations of readily available typewriter character fonts should be borne in mind in all typed examples given in this description. Thus, superscripts, subscripts and certain other special
symbols will not always appear in this description in their optimum sizes. No such limitations are inherent in the typesetting of such material in accordance with the more general aspects of the
present invention as practiced in an actual computer typesetting system.
FIG. 1 shows a typical computer-based system for generating computer typeset images according to the present invention. Shown there is a computer 100 which comprises three major components. The first
of these is the input/output (I/O) circuit 110 which is used to communicate information in appropriately structured form to and from the other parts of computer 100. Also shown as part of computer
100 is the central processing unit (CPU) 120 and memory 130. These latter two elements are those typically found in most general purpose computers and almost all special purpose computers. In fact,
the several elements contained within computer 100 are intended to be representative of this broad category of data processors. Particular examples of suitable data processors to fill the role of
computer 100 have been given above. Other computers having like capabilities may of course be adapted in a straightforward manner to perform the several functions described below.
Also shown in FIG. 1 is an input device 140, shown in typical embodiment as a keyboard. It should be understood, however, that the input device may actually be a card reader, magnetic or paper tape
reader, or other well-known input device (including, of course, another computer). Tape input store 150 is shown interposed between the input device 140 and the computer 100. It should be understood,
of course, that such a tape input store (which might take the form of a magnetic or paper tape reader and storage facility of a keyboard-to-tape facility) will only be needed where compatibility
between input unit 140 and computer 100 is not immediately available or desirable.
Another store shown in FIG. 1 is the font library store 160. This store, (which in appropriate cases may be incorporated in standard fashion in computer 100 as part of memory 130) is used to provide
computer 100 with detailed information about the exact nature of the symbols and characters which may be selected by coded input signals, e.g., from input unit 140. The font information may be stored
and accessed in any standard manner, including that described in U.S. Pat. No. 3,422,419 issued to M. V. Mathews et al on Jan. 14, 1969 as modified in the manner described below. Output unit 170 is
arranged to receive position signals from computer 100 and generate therefrom a photographic or other permanent record of the desired formula image. In particular, output unit 170 may take the form
of a computer microfilm printer of the type typified by the Stromberg-Carlson model 4020 microfilm printer. For present purposes, output unit 170 may be considered to comprise a display device such
as a cathode ray tube (with well-known appropriate control and deflection circuitry) shown as 175, and a photographic system shown as camera 176.
Also shown in FIG. 1 is a display monitor 180 which is useful in monitoring the images being generated by the rest of the system. Such a display monitor may take the form of any of several well-known
varieties of CRT displays including in particular the Digital Equipment Corporation Model 340 or Graphic-2I Display Systems. Where appropriate, the display facilities of output unit 170 and those of
display monitor 180 can be suitably combined. Light pen 190 is used to indicate to computer 100 the location of information displayed on monitor 180. Thus light pen 190 may be used in standard
fashion to edit (e.g., delete, modify or add to) information stored in memory 130 and/or font store 160. See, for example, U.S. Pat. No. 3,389,404 issued June 18, 1968 to R. A. Koster, or copending
application by W. H. Ninke, Ser. No. 488,639, filed Sept. 20, 1969, or copending application by C. Christensen et al, Ser. No. 682,249, filed Nov. 13, 1967, now U.S. Pat. No. 3,534,338. Each of these
three references is hereby incorporated in the present disclosure.
FIG. 2 shows a typical arrangement of the major programs applicable to typesetting which are stored in memory 130 shown in FIG. 1. In particular, there is shown a monitor and control program 210,
which may take any of several well-known detailed forms depending upon the particular machine used to fill the roll of computer 100. In the case of the GE-635 class machine this program comprises the
GECOS supervisor system described, for example, in General Electric Company reference manuals CPB-1195 and CPB-1518. Program 210 is also used for operations other than typesetting of mathematical and
similar formulas. That is, this is the system monitor program well-known in each case to a computer operator that is used in almost any use of computer 100 for, among other things, compiling input
programs and allocating storage areas.
A formula composition program, shown as 220 in FIG. 2 represents a sequence of instructions, which, when taken together with the various circuit elements shown in FIG. 1, the font information stored
in store 160, and the monitor and control programs 210 shown in FIG. 2, forms one embodiment of the present invention. The remaining programs shown in FIG. 2 are optional in some embodiments of the
present invention but are useful in other embodiments comprising more comprehensive computer typesetting systems. These programs include those designated as "Other Type-setting Programs" and
identified by numeral 230, display program 240, and "Other Programs and Spare Memory" indicated by 250. The latter programs stored in spare memory 250 may include other useful computational or
bookkeeping programs and may profitably be physically resident in main computer memory or a secondary memory such as an auxiliary tape unit or the like. The display control programs resident in the
computers in the Koster, Ninke and Christensen et al references incorporated herein by reference may be stored (where required) in that portion designated by the numeral 240 in FIG. 2.
More detail regarding the operative programs mentioned above will be given below.
Because of their recursive nature, mathematical formulas lend themselves readily to representation by a tree structure, i.e., a hierarchical structure of nodes connected by branches. This recursive
property does not exist, for example, in the relative positioning of symbols and other relations which are involved in the structural formulas for organic compounds.
As an example of how one embodiment of the present invention uses a tree structure to represent mathematical expressions, the formula ##EQU1## is represented by the tree shown in FIG. 3. Note that
the tree structure used depends on the spatial position of the symbols, not on the mathematical meaning of them or of the operators. For example, the characters falling between left and right
parentheses are not treated as a unit and, in fact, a parenthesis is treated in exactly the same way as any other symbol. As illustrated in FIG. 3, the "head" (or "root") of the tree structure is the
symbol at the extreme left of the main line of the formula. All symbols that are on the same line of the formula as the "head" symbol are also on the same "branch" of the tree as the "head" symbol.
New branches in the tree are started by those symbols, such as exponents, initial symbols of numerators and denominators, etc., that start new lines in the formula.
The tree structure representation of the formula illustrated in FIG. 3 is used to determine the sequence in which the symbols of the formula are processed by the local positioning algorithm to be
described below. In order to discuss how the tree structure representation of a formula is used in this way, there is adopted the standard list processing convention of referring to those symbols
attached to a given symbol by arrows leading out from the given symbol as "subordinates" of that given symbol. Conversely, we refer to A as the "superior" of B if B is the subordinate of A. For
example, in FIG. 3, the "1", the "7", and the "h" are subordinates of the integral sign and the "+" sign (shown as 17) is the superior of the integral sign. The local positioning algorithm described
below takes the subordinates of a given symbol and positions them relative to that given symbol.
The circled numbers n in FIG. 3 indicate the order in which the symbols of the tree structure are processed by the local positioning algorithm and in no way form part of the formula itself. In the
terminology of list processing, one would say that, in general (subject to the interpretation described below), the positioning is done in "sublist-first order".
The particular method of entering input data and establishing the hierarchical storage arrangement of it will, of course, vary with the particular computer and computer language used, but a typical
and useful tree-generating and interpreting method is shown in FIG. 7 and is described in the section below entitled "Processing the Input Signals". A useful technique for entering data into computer
100 is given in the section below entitled "Input Techniques".
As mentioned above, the local positioning algorithm is used to position the subordinates of a given symbol relative to that symbol. It is usual in many prior art systems when specifying a type font
to not only specify the shape of the characters, but also to identify with each character a rectangular area called a "matrix". The widths of these rectangular matrices are in general different for
different letters and symbols of the alphabet. When a line of text is typed on a Linotype machine, for example, the matrices corresponding to the letters within a given word are placed side by side
and physical wedges are placed in the spaces between words. The wedges are used to justify the text so that the right margin comes out even. To justify a line of text, the wedges are pushed down
until the line extends to the right margin. Since the letters within a given word are concatenated by placing the corresponding matrices side-by-side, the spacing between letters is determined in
these prior art systems by the widths of the rectangular matrices and the positions of the character images on these matrices.
In accordance with one embodiment of the present invention, the straightforward edge-to-edge concatenation used in a Linotype machine is replaced by a technique involving the assignment of a set of
"concatenation points" to each character. These concatenation points are conveniently arranged to correspond roughly to the eight major compass directions (N, NE, E, SE, S, SW, W, NW). This
arrangement is illustrated in FIG. 4 for the symbols "t", "2", and "small 2" (for use in superscripts and subscripts). The positioning procedure utilizing these concatenation points is best
illustrated by example.
In forming "2t", one desires that the "t" be positioned directly to the right (i.e., east) of the "2", just as if they had been positioned in a Linotype machine by concatenating their rectangular
matrices edge-to-edge as shown on FIG. 5A. To understand how the same result is realized when using the concatenation points to do the positioning, it is convenient to first envision that the east
concatenation point of the "2" lies on the east edge of its (nonexistent) "matrix" and the west concatenation point of the "t" lies on the west edge of its (equally nonexistent) "matrix". This is
illustrated in FIG. 5B. "2t" is then formed in accordance with the principles of this embodiment of the present invention by positioning the "t" such that the west concatenation point (shown enlarged
for emphasis) coincides with the east concatenation point of the "2" (also shown enlarged) as illustrated in FIGS. 5B and 5C. It should be understood of course that the concept of a "matrix" is no
longer essential to the typesetting of characters using the present invention; the location of the concatenation points of a character contains all the necessary information previously contained in
the geometrical information required to specify a matrix. Further, the concatenation points permit a much more general and flexible positioning of adjacent symbols.
One advantage of basing the local positioning algorithm on the use of "concatenation points" is that the same positioning technique that is used for straight linear text can also be applied to
superscripts, subscripts, division signs, integral signs, etc. For example, to form "t^2 " as shown in FIG. 6A, one positions the "small 2" such that its southwest concatenation point (shown
enlarged) coincides with the (enlarged) northeast concatenation point of the "t" as shown in FIGS. 6B and C.
The flexibility afforded by the use of "concatenation points" as described herein provides an important advantage over the earlier techniques described, for example, in the Martin reference, supra.
In this earlier work, the programmed computer enclosed each character and each set of characters, e.g., "A[2] ", "(x+y)^2 ", in an imaginary rectangle. The positioning of the characters in a
mathematical expression is then accomplished by positioning these rectangles with respect to each other, without regard for the detailed nature of the symbols in the rectangles.
As an example of the advantages, which accrue through the use of concatenation points, consider the expression U[A] +V[B] 2+W[C].sbsb.2. Using the concatenation point technique of one embodiment of
the present invention, the subscripts A, B^2, and C[2] would all be placed in the same position relative to their "superior" symbols, U, V, and W, respectively. Specifically, the subscript characters
A, B, and C would each be at the same vertical position relative to the main line of the text.
However, since the superscript "2" extends above the top of "B" in "B^2 ", and the subscript "2" extends below the bottom of the "C" in "C[2] ", positioning the symbols within the expression U[A] +V
[B] 2+W[C].sbsb.2 by the "enclosed rectangle technique" used earlier work would not result in the subscript characters "A", "B", "C" all having the same vertical position relative to the main line of
the text. The results of such an "enclosed rectangle technique" positioning algorithm are readable, but the resulting irregularity does not satisfy the aesthetic requirements of publication quality
typesetting. Nor does it provide the flexibility provided by the apparatus and methods associated with concatenation points and described herein.
Except for some refinements discussed below, the basic local positioning algorithm using concatenation points to typeset mathemetical formulas stored in a hierarchical tree structure may be stated as
(1) Cause an appropriate (specified) concatenation point for subordinates of a given symbol to coincide with appropriate (specified) concatenation points for that given symbol. The means for
specifying the appropriate concatenation points will be treated below.
(2) The order of symbol processing is as follows:
(a) Along a given branch of the tree, positioning starts at the right-hand end and works back to the left. It should be understood that right and left refer to the structure as shown in FIG. 3 (head
at the left). It may be convenient to represent and/or store the structure in a vertical arrangement with the "head" at the top or bottom. In all cases, however, the order of positioning will proceed
in a given branch in a direction toward the head of the structure.
(b) If a given symbol along a given branch has subordinate symbols that start new branches, all of these new branches are positioned internally (with respect to the given symbol) before any
positioning is performed on the given symbol of the given branch. For example, in FIG. 3, the symbols in the branch started by the left parenthesis "(" that is a subordinate of the horizontal
division sign are positioned relative to each other before the local positioning algorithm is applied to any of the symbols on the main (division sign) branch.
The "appropriate" concatenation points are determined by the character or symbols involved, as well as the significance, e.g., superscript or subscript, as stated by the user input. The technique
used to cause designated concatenation points to "coincide" is to merely specify that they be located at the same point when their associated symbols are displayed on the CRT 175 or other output
device. Since the concatenation points occupy a fixed position relative to their associated characters, these characters will necessarily bear the correct spatial relation to each other. The
concatenation points are not themselves normally displayed.
It proves convenient in some cases to associate symbols which have been relatively positioned (by causing respective concatenation points to coincide) together to form a composite symbol having
concatenation points defined by the extremum concatenation points, in each compass direction, of the original symbols.
The exact character size and shape and the location of the concatenation points are conveniently stored in font library store 160 in FIG. 1 and are transferred to memory 130 (or directly to display
device 170) as required for a particular job.
Information stored in the font memory 160 shown in FIG. 1 typically includes a coded representation of a symbol sufficient to select the required character form, e.g., a matrix or other selection
arrangement in a character or symbol generator of any standard design associated with computer 100 or output unit 170 in FIG. 1. This character generator may be of any standard form, including one
wherein the output device is a CRT having an apertured plate between the source of the electron beam and the target phosphor. The selection process responsive to the coded representation then
involves controlling the electron beam to pass through the specified aperture and thereby be shaped to the desired symbol cross-section. Alternately, the required deflection signals are arranged to
be in the correct order and format for the above-mentioned Stromberg-Carlson Model 4020 or similar device.
Other information stored in font memory 160 includes that which specifies the position of the concatenation points for each character. In a system including a device requiring only a code to select a
symbol, this is conveniently specified as the x and y coordinate distances for each concatenation point (in multiples of some fundamental unit of distance) measured from the center (or other
reference point). The unit distance need be specified only once for each symbol set. Thus, the information for a given character set may take the form
______________________________________(Name of type font)(Unit of distance)(Miscellaneous data related to particular font)(Code for first symbol)(x and y distances for east concatenation point)(x and y distances for northeast concatenation point)(x and y distances for southeast concatenation point)(Code for second symbol)(x and y distances for east concatenation point)(Code for third symbol)______________________________________
(x and y distances for southeast concatenation point). The miscellaneous data typically includes the point (center point or other) to be used as a reference from which to measure distances.
In a system of the type shown in FIG. 1 and described above the user typically inputs (enters) the mathematical expressions to be typeset by the system by means of an ordinary teletypewriter or
similar device. According to a useful convention associated with the present invention, some of the standard teletypewriter character codes are used for representing directions, e.g., N, NE, etc.,
and others are used for other control characters. For example, " " is used to represent the character code for northeast, and "t 2" represents t^2. To simplify the discussion, it is assumed that the
directions N, NE, SE, S, SW, and NW are represented by the characters symbolized by ↑, , , ↓, , , and, respectively, although any other convention can be adopted if desired.
Note that there is no symbol for concatenation to the east; this omission is possible because the present invention, in the above described embodiment, employs the convention that if no concatenation
direction is indicated, the next symbol is concatenated to the east of the last symbol. Thus, to specify straight linear text such as (A+B)/y, the user of the system simply types the appropriate
characters, one after another, as he would with an ordinary typewriter. There is ordinarily no symbol indicating concatenation to the west because the user is not ordinarily permitted this option.
This is so because to allow the user to specify that a new symbol is to be concatenated to the west (i.e., left) of a given symbol would greatly complicate the programming without adding anything of
significance to the system. In addition to the six direction characters, a seventh character, denoted R , is used to return processing control from the last sub-branch that was defined. For example,
the formula W^2v +X would be input as W 2v R +X. If the " R " had been left out, the formula would have been typeset as W^2v+X instead of W^2v +X.
It has been found that a previously inexperienced user is able to rapidly adjust to the input language used in this embodiment of the present invention. As one gains even slight familiarity with the
way the system uses a tree structure to represent a mathematical formula, it becomes very easy to write input sequence required to specify a desired mathematical expression--much easier, in fact,
than to type the same mathematical expression using an ordinary typewriter. Using the conventions described above, the expression ##EQU2## would be represented as Z = 7R 1Rh vRdv, where represents
the character corresponding to a space in the mathematical expression. Additional spaces can of course be inserted to improve the appearance of the final typeset product.
The number of distinct character codes available on a teletypewriter or similar device is usually insufficient to allow one to represent by a unique character code all the symbols that occur in
mathematical typesetting. Hence, the input language for one embodiment of the present invention conveniently makes provision for the set of all available letters and symbols to be broken up into
several "cases" (just as there is an upper case and a lower case on a typewriter). Thus, the same character code (except for case) is used to represent different symbols in the different cases, just
as the keys on a typewriter represent different--and not necessarily related"characters in upper and lower case. Different cases are readily specified by preceding each character code by one of
several seldom-used character codes, e.g., the ampersand, &.
The present invention also provides two other features which provide the user with additional control over the precise appearance of the printed mathematical expressions. The first such feature
allows the user to increase or decrease the type size in which symbols are printed when the user is unsatisfied with type size determined by the procedure described below. This is accomplished under
program control in one embodiment by modifying or interpreting (by the addition or subtraction of a specified quantity) the original font size specification for the selected symbols. The second
additional feature allows the user to adjust the position of any individual character in the horizontal and/or vertical directions. The user does this by inputting a control character followed by the
distance (defined in a suitable scale) that the character is to be moved. Alternately, symbols can be moved under the control of light pen 190 in the manner described, e.g., in the Christensen et al
reference, supra.
The input text, representing, e.g., a mathematical formula, is processed by computer 100 in three steps. The first step is to read the input codes and build the tree structure representing the
formula. This process is illustrated in the flow chart of FIG. 7. During this structuring step, the system advantageously automatically adjusts the size of characters used in superscripts and
subscripts according to a predetermined scheme. This is desirable because in most published material, excluding typewritten manuscripts, superscripts, subscripts, exponents and the like are printed
in a smaller type size. To save the user the trouble of having to indicate this size change, the formula composition program operating within the computer automatically adjusts symbol size
specifications to the next lower size whenever a new sub-branch is started. The program maintains a list of exceptions, e.g., numerators and denominators of division signs, where the size remains
While most of the details of FIG. 7 are self explanatory, a few words about the terminology used there may be appropriate. It is understood that the user in entering the input data stream will
ordinarily specify the particular font, symbol size and beginning point for the formula or other text to be compared. A useful convention is to adopt a standard, or default, condition for each of
these parameters which are assumed unless specific provision is made for another condition.
The head of the tree is merely the first element in the main branch of the tree. A scan of the input is then made to see if another input code is present. If there is and it is not a change of branch
code, it is entered in the present branch. It is convenient to consecutively number new branches as they are formed in response to an arrow (,↑, etc.) or equivalent code. The numbering of branches
facilitates the structuring and subsequent application of the local positioning algorithm. As is clear from FIG. 7, then, each input code is read and each code which does not indicate a branch change
is assigned to a list corresponding to the then-current (present) branch.
The second step in processing the input is the actual composition of the signals specifying the relative positioning of the symbols in the mathematical formula. This consists of applying the local
positioning algorithm illustrated in FIG. 3 and described above to the nodes of the tree structure in a sublist first order as illustrated by the circled numbers n in FIG. 3. Finally, the third
processing step is to generate an image of the positioned formula on the CRT of microfilm plotter or similar image producing output apparatus identified as 170 in FIG. 1.
The computer 100, operating under the control of the programs including a coding of the local positioning algorithm described herein, conveniently determines the location of the center point (or
other reference point) for a given symbol on the display surface (CRT or other device) used in output unit 170. Thus, knowing the positions of the selected concatenation points (those to be
superimposed) and the position of the center point for one character, the calculation of the center (or other reference) point for all symbols is immediate. The sequence of signals indicating the
desired position of the center point and the code designation for each desired symbol is usually all that is required by the output device.
The above discussion describes the basic procedure used by the local positioning algorithm. There are, however, several modifications that are useful in dealing with some of the constraints that are
typically encountered in typesetting mathematical equations. A first modification is useful in keeping subscripts and superscripts of a given character from overlapping with the next character to the
right. Consider, for example, the formula whose tree structure is illustrated in FIG. 3. The spacing that is desired between the "h" and the "d" in ##EQU3## is larger than would be desired if the "v"
were not present as a superscript on the "h". The method by which the local positioning algorithm deals with this is to take any subordinate symbol that is concatenated to the east of a given symbol
(as the "d" is to the east of the "h") and delay its positioning until all other subordinates of that given symbol have been positioned. Thus in the example of FIG. 3, the "v" would already have been
positioned relative to the "h" to form "h^v " before the local positioning algorithm determines the spacing between the "h" and the "d". The local positioning algorithm thus increases the spacing
between the "d" and the "h" enough to compensate for the presence of the "v" as a superscript on the "h".
A slight variant of this situation is illustrated by the formula β[2].sbsb.W =X.sub.α +3 in which the expression "β[2] " serves as a superscript of the symbol "W". Just as in the previous example of
"h^v dv", the horizontal spacing between the "β" and the "W" has to be increased because of the presence of the "2". The only difference is that in this case the "2" is associated with the
subordinate symbol, namely the "β", rather than the superior symbol. Since the tree structure representing a formula is processed in "sublist-first order", the "2" will have been positioned relative
to the "β" to form "β[2] " before the local positioning algorithm must determine the spacing between the "β" and the "W". Since the size of the "2" determines the size of the composite character "β
[2] " (as well as the location of the concatenation points for "β[2] ") just enough extra spacing is between the "β" and the "W" to exactly compensate for the presence of the "2". This extra spacing
is automatically and uniformly specified under the control of computer 100 without the use of mechanical or other wedges.
A second modification to the basic local positioning algorithm is useful in treating the case where a superscript concatenated to the northeast of a given symbol would overlap, or nearly overlap,
with a subscript to the southeast, as, for example, in ##EQU4## The program controlled computer checks each superscript concatenated to the northeast to see if it would almost overlap with a
subscript to the southeast. A suitable minimum desirable distance is specified or, by default, assumed for this purpose. When such an overlapping superscript is found, it is moved horizontally past
the right-hand end of the subscript, so that, for example, the last equation would become
A third modification is useful when dealing with the positioning of numerators and denominators of horizontal division signs. The numerator of a horizontal division sign is of course concatenated to
the north of the division sign and the denominator is concatenated to the south. Consider, for example the two expressions "1/α+β" and "α". In the expression "α", the vertical distance between the
"α" and the "^o " should be small. However, if a larger spacing between the "α" and the horizontal division sign in "1/α+β" were not provided, the result would be that the β would overlap the
horizontal division sign.
The basic difference between these two cases is that in positioning the "^o " to form "α", one desires the north concatenation point of the "α" to represent the top of the physical image of the
character "α". But in positioning the expression "α+β" below the horizontal division sign, one desires the north concatenation point of the "α" to represent the top of the line of text containing the
"α", not just the top of the character "α". This problem is solved by defining two new concatenation points, "top-of-text" and "bottom-of-text" concatenation points, in addition to the eight
concatenation points described earlier. Referring to the tree structure illustrated in FIG. 3, the top-of-text concatenation point is used in place of the north concatenation point if the character
in question (such as the "α" in the denominator of "1/α+β") is a subordinate symbol that is being positioned relative to a superior symbol (as the "α" in "α+β" is a subordinate symbol being
positioned relative to its superior symbol, the horizontal division sign). The standard north concatenation point continues to be used when the character in question (such as the "α" in "α") is a
superior symbol relative to which one is now positioning a subordinate symbol. For example, the "α" in "α" is a superior symbol relative to which we are positioning the subordinate symbol "^o ". A
similar rule holds for the bottom-of-text concatenation point.
Even with use of top-of-text and bottom-of-text concatenation points, it still would be possible for a numerator or denominator to extend far enough in the vertical dimension as to intersect, or
almost intersect, the horizontal division sign. The program checks for this and adjusts the vertical position of a numerator or denominator to correct this if it would otherwise occur. A similar
check is made on expressions under a radical (square root) sign. Typical situations where this might occur, and where adjustments are required are illustrated by the expressions ##EQU5## In addition
to checking the spacing between numerators and denominators and their associated horizontal division signs, the program will also center the numerators and denominators in the horizontal dimension.
Lines of text above or below a summation sign, Σ, or a product sign, , are treated in a manner analogous to numerators and denominators. The main difference is that it is possible to have more than
one line of text above or below a summation or product sign. These features are illustrated by the expression ##EQU6##
Other refinements of the basic processing techniques described above are also useful. For example, there is provision for underlining or overscoring text. The user must indicate whether he wants
underlining or overscoring and must insert into the input character stream (described above) an indication of the start and end of the test to be underlined or overscored.
In the various basic features of the present invention and the various extensions thereto, the programmed operation of comparing (as for overlap) is clearly implicit. This operation is expecially
well adapted to performance within a general purpose computer of the type herein envisioned having also stored therein all of the coordinate, font size and related spatial information.
Typical results of computer typesetting using the present invention are shown enlarged in FIGS. 8A-N. While a relatively primitive type font has been employed in these examples, it should be
understood that no such limitation is essential to the present invention.
No particular programming language has been indicated for carrying out the various control procedures described above. This is in part due to the fact that not all languages that might be mentioned
are universally available. Each user of a particular computer will be aware of which language with which he is acquainted is most suitable for his immediate purposes.
One well-known language that has proven useful in FORTRAN. Because the computers, and monitor systems used therein, that may be used in practicing the instant invention are manifold, however, no
detailed program listings have been provided. It is considered that the algorithms and other procedures described above and illustrated in the accompanying drawing are sufficiently disclosed to
permit one of ordinary skill to practice the instant invention or so much of it as is of use to him.
Numerous and varied modifications and extensions of the above-described system within the spirit and scope of the present invention will occur to those skilled in the art. It is clear, for example,
that the symbols to be positioned or "typeset" need not be mathematical symbols but can include, in whole or part, linear test, chemical equations, musical scores, in fact, any visually observable
graphic representation susceptible to storage in a tree structured form as described above. The present techniques and apparatus are readily generalized to three dimensional representations by
specifying and operating on concatenation points for each of the three coordinate directions. When various requirements dictate, such as objects having circular or other symmetry, the directions of
the concatenation points may be chosen in other than the compass point directions (or approximations thereto). Further, the number or location of concatenation points may be chosen for convenience
and flexibility in a particular application. It is clear also that various output devices may be substituted for the CRT shown as 175 in FIG. 1. | {"url":"http://www.google.co.uk/patents/US4195338","timestamp":"2014-04-21T07:05:19Z","content_type":null,"content_length":"114997","record_id":"<urn:uuid:06d1b3bc-e199-4110-8552-019894914d10>","cc-path":"CC-MAIN-2014-15/segments/1398223204388.12/warc/CC-MAIN-20140423032004-00097-ip-10-147-4-33.ec2.internal.warc.gz"} |
Insights Into Algebra 1 . Workshop 1
Topic Overview:
Part 1: Translating Words Into Symbols
Part 2: Linear Equations
Download the Workshop 1 Guide
Part 2: Linear Equations
Linear equations can be used to model situations involving one or more unknowns. A linear equation is an algebraic equation whose variable(s) is/are of degree one. For example, 6x + 3 = 27 and a =
2b are linear equations. Solving linear equations is a key component of the algebra curriculum.
Mathematical Definition
Role in the Curriculum
A linear equation is a polynomial equation of the first degree, such as x + y = 7. Said another way, a linear equation has no variables raised to a power other than one.
The simplest linear equations involve only one unknown, such as x + 2 = 3, and they are solved by finding the value of the unknown that makes the equation true. For example, the equation above is
true when x = 1, because 1 + 2 = 3. More complex linear equations may contain more than one variable, such as x + y = 7 or a - b + c - d + 4 = 14. This workshop will focus on the simplest linear
equations and those whose graph is a line.
Linear equations with just one unknown are solved using equivalence transformations, sometimes informally called "inverse operations." In this process, the operation of multiplication is "undone"
using division, because multiplication and division are multiplicative inverses; similarly, addition is "undone" using subtraction, because addition and subtraction are additive inverses. The
reason this process works is because the equal sign acts as a balance between the left side and the right side of the equation. As long as the same operation is applied to each side of the
equation, the equation remains in balance and the equality is preserved. For example, the equation 2x + 3 = 9 is solved as follows:
Subtraction is the additive inverse of addition. Therefore, to "undo" the addition of 3, subtract 3 on both sides of the equation:
2x + 3 - 3 = 9 - 3, which yields 2x = 6.
Because division is the multiplicative inverse of multiplication, to "undo" the multiplication of x by 2, divide both sides by 2:
• A traditional example involves people's ages. For instance, "Becky is 6 years younger than Sally, and Sally is 13 years old. What is Becky's age?" The equation b + 6 = 13 can represent this
situation, and it is true when b = 7, so Becky is 7 years old.
• A person bought 3 cans of soda as well as several six-packs of soda, and she has a total of 27 cans. The linear equation 6x + 3 = 27 determines the number of six-packs she bought, where x is
the number of six-packs.
• Linear functions can model the "transmission factor" of two gears. The ratio between the number of revolutions made by a 1 cm gear (b) and the number of revolutions made by a 2 cm gear (a) can
be expressed as a = 0.5b and b = 2a.
Mathematical Definition
Linear Equation or Expression: An algebraic equation or expression which is of the first degree in its variable (or variables); i.e., its highest degree term in the variable (or variables) is of
the first degree. The equations x + 2 = 0 and x + y + 3 = 0 are linear. An equation or expression is linear in a certain variable if it is of the first degree in that variable. The equation x + y^2
= 0 is linear in x, but not in y.
(Source: James, Robert C. and Glenn James, Mathematics Dictionary (4th edition). New York: Chapman and Hall, 1976.)
John McLeish provides a useful explanation of linear: "Linear means an equation of the first power of the unknown; such an equation can be represented by a straight line graph, hence 'linear.'"
(McLeish, John. Number: The History of Numbers and How They Shape Our Lives. New York: Fawcett Columbine, 1991.)
Role in the Curriculum
To become comfortable solving and manipulating linear equations, students will need to experience linear relationships in various situations. They will need a significant amount of practice before
developing fluency.
Upon the successful completion of an algebra course, students should be able to use symbolic notation to represent and explain mathematical relationships and solve linear equations. The National
Council of Teacher of Mathematics (NCTM) states:
Although students will probably acquire facility with equations at different times ... students should be able to solve equations like 84 - 2x = 5x + 12 for the unknown number ... and to
recognize that equations such as y = 3x + 10 represent linear functions that are satisfied by many ordered pairs (x, y).
(Principles and Standards for School Mathematics, NCTM, 2000, p. 226)
Students should also be able to produce two or more equivalent expressions that represent the same situation and to use simple formulas.
Solving linear equations is a key part of attaining a global understanding of linear relationships and involves more than the ability to solve for an unknown. The solution of linear equations is
often a necessary step when interpreting a complex situation. Students may describe a linear relationship using a table, graph, or words, and from that description they may generate an expression
or equation to represent the situation. For instance, students may describe the cost of a cell phone plan in various ways:
Some students might describe the pattern verbally: "Keep-in-Touch costs $20.00 [monthly] and then $0.10 more per minute [of use.]" Others might write an equation to represent the cost (y) in
dollars in terms of the number of minutes (x), such as y = 20.00 + 0.10x.
(PSSM, p. 226)
From the function, students should be able to find the cost for any number of minutes. The cost for 25 minutes occurs when x = 25, and finding the associated cost involves solving the equation y =
20.00 + 0.10(25). Similarly, the number of minutes for which the cost would be $35.00 occurs when y = 35.00, and students can find that value by solving the equation 35.00 = 20.00 + 0.10x. | {"url":"http://www.learner.org/workshops/algebra/workshop1/index2.html","timestamp":"2014-04-21T12:17:03Z","content_type":null,"content_length":"58747","record_id":"<urn:uuid:e1d8fc59-8eb0-4b57-b02e-1eb1a74e0744>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00282-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Here's the question you clicked on:
Lol this is FOR REAL my last question of today :) sorry guys! Choose the slope-intercept equation of the line that passes through the point shown and is perpendicular to the line shown. y = -3/2x y =
3/2x - 6 y = -2/3x -5/3 y = 2/3x - 13/3
• one year ago
• one year ago
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@AriPotta im sorry lol
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@Hero promise this is my last today
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im still confused bout this
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so first -5,0 and 0,3 i plug into the y2-y1 thing
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then i got 3/5
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since its perp i change it to -5/3
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then i do the y-y1 formula with the point 2,-3
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(btw I need u to check it
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then im confused help!
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is (2,-3) the point that the perpendicular line is supposed to run through? I think you're almost there... you have the perp slope as -5/3, and you know the point, and it sounds like you know the
formula... the point slope form of a line is y - y1 = m(x -x1) where (x1, y1) is your point, and m is your slope.
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please hurry as i need to go soon
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see i did that but i didnt get any of the options
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so it's y - (-3) = (-5/3)(x-2) y + 3 = -5/3x -10/3 y = -5/3 x -19/3
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but is that an option?
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oh... that's not up there. Hm. Is that the problem? The way you posted this, it didn't show the original line or the point. to run the perp line through.
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hold on ill attach a file!
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The problem is your slope. The actual line looks like it goes through (-5,0), but it doesn't... it's just close. The actual real slope is 2/3. So your perp slope is -3/2 And your equation
becomes: y - (-3) = -3/2 (x - 2) y + 3 = -3/2 x + 3 y = -3/2 x
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thank you!!! SO MUCH!! muah thxx
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you would have gotten it correct if you had been able to read that graph better. Your approach seemed fine, but since you read the slope incorrectly, the answers weren't working out to match your
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got it!
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glad to help :)
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is replying to Can someone tell me what button the professor is hitting...
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Do We Really Need to Learn Math?
Date: 11/19/2002 at 11:31:33
From: Natalie Espinosa
Subject: Math is not needed....
I honestly think that Math is useless subject. How many people use it
unless they REALLY have to? I'm sure that most people if they had a
chance would let a computer do it. Isn't that what they're for - to
make our life easier?
My high school just let us start using calculators, but we still need
to show our work, which I don't know how if we didn't do any.
It may just be me, and I hate Math, but why do we need to know Math if
we can have a calculator do it?
Date: 11/19/2002 at 12:35:45
From: Doctor Ian
Subject: Re: Math is not needed....
Hi Natalie,
You could make the same argument about reading, couldn't you? Why
learn to read, when you can just get other people (and eventually
machines) to do your reading for you? But you're starting from a
couple of interesting premises.
The first premise is that you can just 'let' a calculator solve a
problem for you. I don't know about _your_ calculator, but mine won't
do a thing unless I tell it exactly what to do, step by step. Which
means I have to know what steps to tell it to do. If I tell it to
divide when I'm supposed to be multiplying, it will go ahead and
perform the wrong operation. If I key in 12.3 instead of 1.23, it
will go ahead and use the wrong number. It won't complain, or ask me
if I'm sure about what I'm asking it to do, because it hasn't a clue
about what problem I'm actually trying to solve. One of us ought to
be keeping track, to make sure things are being done correctly, and
that the final answer is at least in the right ballpark, and guess
what? It's not going to be the calculator. That means it has to be me.
The second premise is that there will always be a working calculator
around. They do break, you know, and batteries seem to run out at the
most inconvenient times. I suppose you can argue that you'll always
be able to borrow someone else's calculator, or ask someone else for
help, but this is a little like arguing that you don't need your own
fire extinguisher, because you'll always be able to borrow one when
you need it.
In the end, what makes math 'useful', even for people who don't do
lots of calculations in their daily lives, is that it's very easy for
people who are comfortable with math to lie to people who aren't
comfortable with it.
Think about some very young children that you know. You can tell them
practically anything, and they really have no choice but to believe
you, because they have no way of figuring out whether you're lying or
not. To borrow a memorable phrase from Tennessee Williams, children
have no choice but to 'depend on the kindness of strangers'.
Guess what? If you don't understand math, then you're in exactly the
same boat relative to other people who do understand it. They can
tell you anything, and if you don't have the skills to evaluate what
they're saying, you have no choice but to accept it.
To the extent that you believe that once you get out in the world,
you'll be able to trust other people to look out for you, and act in
your best interest, you're right - you won't need math at all. So I
guess the question is: To what extent do you believe that?
- Doctor Ian, The Math Forum | {"url":"http://mathforum.org/library/drmath/view/61705.html","timestamp":"2014-04-20T14:23:43Z","content_type":null,"content_length":"8215","record_id":"<urn:uuid:933a090f-646c-429e-8f73-98f52211e9f1>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00230-ip-10-147-4-33.ec2.internal.warc.gz"} |
Cadernos de Saúde Pública
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Print version ISSN 0102-311X
Cad. Saúde Pública vol.21 n.5 Rio de Janeiro Sep./Oct. 2005
ARTICLE ARTIGO
Experiments with mathematical models to simulate hepatitis A population dynamics under different levels of endemicity
Modelagem matemática para simular a dinâmica populacional da hepatite A de acordo com diferentes níveis de endemicidade
Mariana Alves de Guimaraens^I; Cláudia Torres Codeço^II
^IInstituto de Ciências Biológicas, Universidade de Pernambuco, Recife, Brasil
^IIPrograma de Computação Científica, Fundação Oswaldo Cruz, Rio de Janeiro, Brasil
Heterogeneous access to sanitation services is a characteristic of communities in Brazil. This heterogeneity leads to different patterns of hepatitis A endemicity: areas with low infection rates have
higher probability of outbreaks, and areas with higher infection rates have high prevalence and low risk of outbreaks. Here we develop a mathematical model to study the effect of variable exposure to
infection on the epidemiological dynamics of hepatitis A. Differential equations were used to simulate population dynamics and were numerically solved using the software Stella^TM. The model uses
parameters from serological surveys in the Greater Metropolitan Rio de Janeiro, in areas with different sanitation conditions. Computer simulation experiments show that the range of infection rates
observed in these communities are characteristic of high and low levels of hepatitis A endemicity. We also found that the functional relationship between sanitation and exposure to infection is an
important component of the model. The analysis of the public health impact of partial sanitation requires a better understanding of this relationship.
Hepatitis A; Mathematical Models; Populations Dynamics
Acesso heterogêneo a serviços sanitários é uma característica de comunidades brasileiras. Essa heterogeneidade promove diferentes níveis de exposição ao vírus da hepatite A, resultando em padrões
variados de endemicidade: áreas com taxas altas de infecção possuem tendência para ocorrência de endemismo, enquanto taxas de infecção baixas mostram tendência para surtos. Neste trabalho,
apresentamos um modelo matemático desenvolvido para estudar o efeito do risco variado de exposição na dinâmica epidemiológica da hepatite A. Equações diferenciais foram usadas para simular a dinâmica
populacional e sua solução numérica obtida usando-se o programa Stella^®. O modelo usa parâmetros de infecção obtidos de estudos realizados na Região Metropolitana do Rio de Janeiro, em áreas com
diferentes condições sanitárias. Simulações mostram que a amplitude observada de valores de taxa de infecção compreende dinâmicas de alta e baixa endemicidades de hepatite A. Observamos que a relação
funcional entre saneamento e exposição à infecção é um componente importante do modelo. A análise do impacto do saneamento parcial requer uma maior compreensão desta relação.
Hepatite A; Modelos Matemáticos; Dinâmica Populacional
Brazil is a very large and heterogeneous country. Szwarcwald et al. ^1 describe the existence of two Brazils, one characterized by adequate access to sanitation and health services and another Brazil
with poor access to such services. These two Brazils are intertwined on all geographic scales. At the national scale, half of the population has adequate access to sewage disposal, while the other
half must dispose of their sewage very rudimentarily. This pattern is repeated on smaller scales. Even in Greater Metropolitan Rio de Janeiro, only 63% of the population has access to sewage disposal
services. Moreover, communities with adequate sanitation services and those with poor access live side by side ^2.
Hepatitis A is a viral disease transmitted from person to person mainly by the fecal-oral route. Worldwide, there are three major patterns of hepatitis A epidemiology ^3. In areas where sanitation is
very poor, nearly all children under 9 years old show evidence of prior infection. In these areas, hepatitis A is considered highly endemic, outbreaks rarely occur, and symptomatic hepatitis is
uncommon. Since almost all residents become naturally immune to hepatitis A during childhood, hepatitis A in adolescents and adults is not observed. Countries of intermediate disease endemicity, on
the other hand, have a relatively large proportion children and adolescents susceptible to the hepatitis A virus, because part of the population has access to adequate sewage disposal and water
supply, which lower the risk of acquiring hepatitis A during childhood. In these areas, there are outbreaks of hepatitis A in adolescent and adults populations, which may represent a significant
public health burden because infection is more virulent in this age class. The third pattern is observed in regions of low disease endemicity, where risk of acquiring the infection is very low.
In Latin America and some other areas of the developing world, the epidemiological pattern of hepatitis A is changing from highly endemic to intermediate ^4,5. Infection rates are decreasing in
children and increasing in teenagers and adults. This shift is not uniform, however, and varies between rural and urban areas and among social classes. These variations reflect underlying differences
in local quality of life. In Brazil, a similar change has been observed. Age at infection has been shifting towards older age groups ^6. Clemens et al. ^7 surveyed the hepatitis A seroprevalence in
four metropolitan areas of Brazil. In Rio de Janeiro, they found that seropositivity at age 10 is some 50% in the lower social class and some 28% in the intermediate plus higher social classes. In
Fortaleza, Ceará, more than 90% of children are seropositive at age 10 in the lower social classes; in the other classes, seroprevalence at age 10 does not reach 25%. These numbers suggest the
existence of areas of high and intermediate endemicity in Brazil. According to serological surveys in Rio de Janeiro, hepatitis A seroprevalence is higher in low-income populations ^8,9. Risk of
infection is associated with crowding and poor hygienic conditions in the domestic and social environment ^10.
Intermediate hepatitis A endemicity poses a public health paradox. The gradual improvement of hygiene reduces but does not eliminate hepatitis A transmission. Since sanitation improvement is not
uniform, viral circulation remains high in some sectors, and part of the population reaches adulthood without being infected. While the infection is mild or asymptomatic in children (and can be
mistaken for a flu infection), in adults it is more virulent. This implies that investment in sanitation may have an initially negative impact on hepatitis A epidemiology. Another important factor
that should be considered when studying hepatitis A dynamics is that seasonal variation in the infection rate is strongly associated with the rainfall pattern ^11.
Several studies on hepatitis A epidemiology show that more research is needed on infection dynamics in order to establish more efficient vaccination programs ^4,11. In this study, we developed a
mathematical model to describe the dynamics of hepatitis A transmission and evaluated it considering different levels of exposure to the disease. The modeling approach consists of developing a
mathematical description of the sequence of events related to transmission and subsequent simulation of the dynamics. Mathematical models are useful tools for testing hypotheses on the system ^12 and
design and control strategies, helping to define when, who, and how to vaccinate, for example ^13. Mathematical models of diseases transmitted by the fecal-oral route, like hepatitis A, cholera, and
typhoid fever, have been developed in literature aimed at evaluating the cost-benefit of alternative control strategies, like sanitation versus vaccination of risk groups ^14,15,16,17,18.
The first set of simulations were performed with equations adapted from Brow & Rothery ^19. This is a simpler model that does not explicitly include the population growth and mortality rates. Since
the model without demographics does not allow persistence, we opted for a more complex model, adapted from Deangelis & Gross ^20 (equation 1). This is the well-known SIR model, originally developed
by Kermack & McKendrick ^21. The equations were numerically solved using the Stella^TM software.
Individuals are classified in three categories, according to their history of contact with the virus. Susceptible individuals (S) are those at risk of infection. They have never experienced an HA
infection and are not vaccinated (seronegative). Infected individuals (I) are those that are currently infected and capable of transmitting infection to others. Recovered individuals (R) are those
that experienced the infection in the past and currently are totally immune. Susceptible individuals acquire infection at rate c bI(t): c is the number of potentially infective contacts that a
susceptible person has per day; b is the probability that a person will actually get an infection after a potentially infective contact. Once infected, the individual leaves class S to class I.
Individuals recover from infection at rate (g = 1/30day^-1) (recovery rate is the inverse of the average infectious period) ^22. Viral fecal excretion is detected from the incubation phase to early
symptomatic phase of the disease, during approximately 10 days ^23.
Birth and death rates were parameterized using data from the Greater Rio de Janeiro Metropolitan Area, as measured in 2000 (Instituto Brasileiro de Geografia e Estatística. Censo Demográfico 2000.
http://www.ibge.gov.br). Demographic process is modeled in a simple way. µN new individuals are born in the population per day and enter into the susceptible class, where µ is the per capita birth
rate and N is the number of individuals in the population. Individuals in any class die at rate m.
Struchiner et al. ^8 estimated the incidence rate of hepatitis A in three localities in Rio de Janeiro, characterized by different access to sanitation facilities. They estimated incidence as a
function of age by fitting a Weibull survival curve to age-specific seroprevalence data. Averaging through all ages, they found a force of infection (hazard rate) equal to 0.0001 year^-1 or 0.27e-6
day^-1. These values are used to parameterize the infection rate in our model (Table 1). We also included the effect of vaccination, removing individuals from the S to the R class.
To evaluate the amount of sanitation required to prevent further spread of hepatitis A, we modified the model considering different assumptions for the functional relationship between sanitation and
contact rate:
where n is the proportion of individuals vaccinated and H is the sanitation level of the community. The function c(H) describes the effect of sanitation on the contact rate. It is reasonable to
assume that the number of infectious contacts decreases as sanitation increases. It is not clear, however, which function should be used to model the relationship between contact rate and sanitation
level. Here, we used three alternative functions (Figure 1), where c[max] is the maximum contact rate and alphas are constants:
The linear function (equation 3) predicts that contact is reduced proportionally to the improvement of sanitation conditions. This is reasonable, if contact with fellow household members is the main
mode of transmission. The exponential function (equation 4) says that a small improvement in hygiene causes great impact on contact reduction. This may be reasonable in a setting where individuals
share the same source of contamination. The third option is a sigmoidal curve (equation 5), applicable to a situation where sanitation has a small effect when low and its effect increases as it is
Without intervention
We begin by describing the temporal dynamics of hepatitis A, according to equation 1. If enough time is given, the system reaches a positive equilibrium:
In this equilibrium, the relationship between contact rate and HA seroprevalence is nonlinear (Figure 2). In a community with 1,000 individuals, 50% seroprevalence is expected when the contact rate
of ca. 0.0002 (i.e., 2 contacts per person per 10 days).
When equation system (equation 1) is solved numerically for different values of infection rate (Table 1), two kinds of results are obtained: either infection persists at a low level in the community
and no outbreaks are observed (after the initial transient) or a chain of outbreaks are expected before the infected population settles to its equilibrium (Figures 3 and 4). These results suggest
that the communities represented by the values in Table 1 experience different levels of endemicity.
With intervention
The ultimate goal of a public health strategy is to change the transmission dynamics of a disease in such a way that if an infected individual arrives in a community, he will not trigger an epidemic.
Mathematically, this means
For hepatitis A, intervention can act in two ways: reducing the number of susceptible individuals (S) by vaccination; or reducing the rate of contact (c) by sanitation. From equation system 1, we
find that
Model 2 introduces three possible expressions for the relationship between the contact rate and H, the proportion of individuals with access to adequate sanitation facilities. Using these functions,
we can define the level of H required to prevent HA outbreaks.
for the linear model
for the exponential model
for the sigmoidal model
Our simulations suggest that the infection rates measured in Rio de Janeiro ^8 are characteristic of high and low endemicity patterns. The impact of partial sanitation on these communities will
depend on the functional relationship between sanitation and its effect on exposure to infection. If this relationship is linear, impact of sanitation is inversely related to the number of
susceptible individuals. That is, in a large population, partial sanitation would be hardly effective (it is either all or nothing). If this relationship is exponential, the impact of sanitation is
inversely related to the log S. If this is the case, partial sanitation is expected to be a public health improvement. If the relationship is sigmoid, improvement is achieved only if sanitation
crosses a threshold H50.
It is not clear which one of these functional relationships is more appropriate. They actually represent different situations that may take place at different places. The important point is that the
impact of sanitation is sensitive to this function and more attention should be devoted to the understanding of the relationship between sanitation and contact.
Mathematical models are useful tools for the development of control strategies. In this work, we present a simple model for hepatitis A. This model is based on the classical SIR model. Further
developments of this model should include spatial heterogeneity in contact rate and age-dependent force of infection. Although many seroepidemiological surveys have been conducted in Brazil as a
whole and Rio de Janeiro, we still know very little about the population dynamics of hepatitis A in Brazilian populations. To be able to build a more detailed model, further information is required
on the patterns of contact in the population (stratified by age, social class, and locality), identification of main sources of disease transmission (direct contact x recreational contact x
sanitation x water availability).
M. A. Guimaraens conducted the programming and testing of simulations with the model using the Stella^TM program and calculated the model's parameters using the literature, with the assistance of C.
T. Codeço. Meanwhile C. T. Codeço performed the theoretical analysis of the model, including the intervention procedure. Both authors conducted the literature research and discussed the drafting of
the introduction, formulation of the model, and final remarks.
This research was supported by the Oswaldo Cruz Foundation, Carlos Chagas Filho Rio de Janeiro State Research Support Foundation, grant number 15254501.
1. Szwarcwald CL, Leal MC, Castilho EA. Infant mortality rate in Brazil: Belgium-India or Bulgaria? Cad Saúde Pública 1997; 13:503-16. [ Links ]
2. Leal MC, Szwarcwald CL. Características da mortalidade neonatal no Estado do Rio de Janeiro na década de 80: uma visão espaço-temporal. Cad Saúde Pública 1997; 31:457-65. [ Links ]
3. Gust ID. Epidemiological patterns of hepatitis A in different parts of the world. Vaccine 1992; 10 Suppl 1:S56-8. [ Links ]
4. Tufenkeji H. Hepatitis A in Middle East and Africa. Vaccine 2000; 18:S65-7. [ Links ]
5. Tanaka J. Hepatitis A shifting epidemiology in Latin America. Vaccine 2000; 18:S57-60. [ Links ]
6. Vitral CL, Yoshida CFT, Lemos ERS, Teixeira CS, Gaspar AMC. Age-specific prevalence of antibodies to hepatitis A in children and adolescents from Rio de Janeiro, Brazil, 1978 and 1995. Mem Inst
Oswaldo Cruz 1998; 93:1-5. [ Links ]
7. Clemens SA, Fonseca JC, Azevedo T, Cavalcanti A, Silveira TR, Castilho MC, et al. Soroprevalência para hepatite A e hepatite B em quatro centros no Brasil. Rev Soc Bras Med Trop 2000; 33:1-10. [
Links ]
8. Struchiner CJ, Almeida LM, Azevedo RS, Massad E. Hepatitis A incidence rate estimates from a pilot survey in Rio de Janeiro, Brazil. Int J Epidemiol 1999; 28:776-81. [ Links ]
9. Saback FL, Sabino RR, Carvalho SMF, Amorin LM, Gaspar AMC, Oliveira MLA, et al. Infection with Hepatitis A and TT viruses and socioeconomic status in Rio de Janeiro, Brazil. Scand J Infect Dis
2001; 33:121-5. [ Links ]
10. Almeida LM, Werneck GL, Cairncross S, Coeli CM, Costa MCE, Coletty PE. The epidemiology of hepatitis A in Rio de Janeiro: environmental and domestic risk factors. Epidemiol Infec 2001; 127:
327-33. [ Links ]
11. Santos DMS, Souto FJD, Santos DRL, Vitral CL, Gaspar AMC. Seroepidemiological markers of enterically transmitted viral hepatitis A and E in individuals in a community located in the North area of
Rio de Janeiro, RJ, Brazil. Mem Inst Oswaldo Cruz 2002; 97:637-40. [ Links ]
12. Guimaraens MA. The influence of environmental factors on the seasonal dynamics of Ulva sp. and Sargassum sp. in the Cabo Frio upwelling region of Brazil [Ph.D. Thesis]. Miami: University of
Miami; 2000. [ Links ]
13. Struchiner CJ, Brunet RC, Halloran ME, Massad E, Azevedo Neto RS. On the use of state-space models for the evaluation of health interventions. Journal of Biological Systems, 1995; 3:851-65. [
Links ]
14. Sundaresan TK, Grab B, Uemura K, Cvjetanovic B. Comparative epidemiological analysis of sanitation and immunization in the control of typhoid and cholera. Am J Public Health 1974; 64:910-2. [
Links ]
15. Cvjetanovic B, Grab B, Uemura K. Dynamics of acute bacterial diseases. Epidemiological models and their application in public health. Part II Epidemiological models of acute bacterial diseases.
Bull World Health Organ 1978; 56 Suppl 1:25-143. [ Links ]
16. Gay NJ. A model of long-term decline in the transmissibility of an infectious disease: implications for the incidence of hepatitis A. Int J Epidemiol 1996; 25:854-61. [ Links ]
17. Ranchov GK. An epidemiometric model of viral hepatitis A and its use. Zh Mikrobiol Epidemiol Immunobiol 1996; 2:36-9. [ Links ]
18. Codeço CT. Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infectious Diseases 2001; 1. http://www.biomedcentral.com/1471-2334/1/1. [ Links ]
19. Brown D, Rothery P. Models in biology: mathematics, statistics and computing. Chichester/ New York: John Wiley & Sons; 1993. [ Links ]
20. Deangelis DL, Gross LJ. Individual-based models and approaches in ecology: populations, communities and ecosystems. New York: Chapman & Hall; 1992. [ Links ]
21. Kermack WO, McKendrick. A contribution to the mathematical theory of epidemics. Proceedings Royal Statistics Society 1927; 115:700-21. [ Links ]
22. Plotkin AS, Orenstein WA. Vaccines. Philadelphia: W. B. Saunders; 1999. [ Links ]
23. Ciocca M. Clinical course and consequences of hepatitis A infection. Vaccine 2000; 18 Suppl 1:S71-4. [ Links ]
Correspondence to
C. T. Codeço
Programa de Computação Científica
Fundação Oswaldo Cruz
Av. Brasil 4365
Rio de Janeiro, RJ 21045-900, Brasil
Submitted on 26/May/2003
Final version resubmitted on 22/Jul/2004
Approved on 21/Oct/2004 | {"url":"http://www.scielosp.org/scielo.php?script=sci_arttext&pid=S0102-311X2005000500026&lng=en&nrm=iso&tlng=en","timestamp":"2014-04-17T15:38:37Z","content_type":null,"content_length":"51854","record_id":"<urn:uuid:ebfe8565-7d90-4ffb-8a16-874c372640eb>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00584-ip-10-147-4-33.ec2.internal.warc.gz"} |
Intuitive Definition
The concept of the limit of a function is essential to the study of calculus. It is used in defining some of the most important concepts in calculus—continuity, the derivative of a function, and the
definite integral of a function.
The limit of a function f( x) describes the behavior of the function close to a particular x value. It does not necessarily give the value of the function at x. You write x “approaches” c, the
function f( x) “approaches” the real number L (see Figure 1).
Figure 1 The limit of f(x) as x approaches c.
In other words, as the independent variable x gets closer and closer to c, the function value f( x) gets closer to L. Note that this does not imply that f( c) = L; in fact, the function may not even
exist at c (Figure 2) or may equal some value different than L at c (Figure 3).
Figure 2 f ( c) does not exist, but
Figure 3 f ( c) and
If the function does not approach a real number L as x approaches c, the limit does not exist; therefore, you write x approaches some value. | {"url":"http://www.cliffsnotes.com/math/calculus/calculus/limits/intuitive-definition","timestamp":"2014-04-18T17:09:07Z","content_type":null,"content_length":"106746","record_id":"<urn:uuid:85be33cf-8c87-46c2-88fd-d91386c93909>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00599-ip-10-147-4-33.ec2.internal.warc.gz"} |
This is the base class of algorithms that learn with supervision and have an internal hypothesis model that allows them to generalize rows that were not available at training time. More...
Public Member Functions
GSupervisedLearner ()
General-purpose constructor.
GSupervisedLearner (GDomNode *pNode, GLearnerLoader &ll)
Deserialization constructor.
virtual ~GSupervisedLearner ()
void basicTest (double minAccuracy1, double minAccuracy2, double deviation=1e-6, bool printAccuracy=false)
This is a helper method used by the unit tests of several model learners.
void calibrate (GMatrix &features, GMatrix &labels)
Calibrate the model to make predicted distributions reflect the training data. This method should be called after train is called, but before the first time predictDistribution
is called. Typically, the same matrices passed as parameters to the train method are also passed as parameters to this method. By default, the mean of continuous labels is
predicted as accurately as possible, but the variance only reflects a heuristic measure of confidence. If calibrate is called, however, then logistic regression will be used to
map from the heuristic variance estimates to the actual variance as measured in the training data, such that the predicted variance becomes more reliable. Likewise with
categorical labels, the mode is predicted as accurately as possible, but the distribution of probability among the categories may not be a very good prediction of the actual
distribution of probability unless this method has been called to calibrate them. If you never plan to call predictDistribution, there is no reason to ever call this method.
virtual bool canGeneralize ()
Returns true because fully supervised learners have an internal model that allows them to generalize previously unseen rows.
virtual void clear ()=0
Discards all training for the purpose of freeing memory. If you call this method, you must train before making any predictions. No settings or options are discarded, so you
should be able to train again without specifying any other parameters and still get a comparable model.
virtual void clearFeatureFilter ()
Clears the filter for features.
virtual void clearLabelFilter ()
Clears the filter for labels.
void confusion (GMatrix &features, GMatrix &labels, std::vector< GMatrix * > &stats)
Generates a confusion matrix containing the total counts of the number of times each value was expected and predicted. (Rows represent target values, and columns represent
predicted values.) stats should be an empty vector. This method will resize stats to the number of dimensions in the label vector. The caller is responsible to delete all of the
matrices that it puts in this vector. For continuous labels, the value will be NULL.
* featureFilter ()
Returns the current feature filter (or NULL if none has been set).
* labelFilter ()
Returns the current label filter (or NULL if none has been set).
void precisionRecall (double *pOutPrecision, size_t nPrecisionSize, GMatrix &features, GMatrix &labels, size_t label, size_t nReps)
label specifies which output to measure. (It should be 0 if there is only one label dimension.) The measurement will be performed "nReps" times and results averaged together
nPrecisionSize specifies the number of points at which the function is sampled pOutPrecision should be an array big enough to hold nPrecisionSize elements for every possible
label value. (If the attribute is continuous, it should just be big enough to hold nPrecisionSize elements.) If bLocal is true, it computes the local precision instead of the
global precision.
void predict (const double *pIn, double *pOut)
Evaluate pIn to compute a prediction for pOut. The model must be trained (by calling train) before the first time that this method is called. pIn and pOut should point to arrays
of doubles of the same size as the number of columns in the training matrices that were passed to the train method.
void predictDistribution (const double *pIn, GPrediction *pOut)
Evaluate pIn and compute a prediction for pOut. pOut is expected to point to an array of GPrediction objects which have already been allocated. There should be labelDims()
elements in this array. The distributions will be more accurate if the model is calibrated before the first time that this method is called.
const GRelation & relFeatures ()
Returns a reference to the feature relation (meta-data about the input attributes). (Note that this relation describes outer data, and may contain types that are not supported
by the inner algorithm.)
const GRelation & relLabels ()
Returns a reference to the label relation (meta-data about the output attributes). (Note that this relation describes outer data, and may contain types that are not supported by
the inner algorithm.)
virtual GDomNode * serialize (GDom *pDoc) const =0
Marshal this object into a DOM that can be converted to a variety of formats. (Implementations of this method should use baseDomNode.)
double sumSquaredError (const GMatrix &features, const GMatrix &labels)
Computes the sum-squared-error for predicting the labels from the features. For categorical labels, Hamming distance is used.
void train (const GMatrix &features, const GMatrix &labels)
Call this method to train the model. It automatically determines which filters are needed to convert the training features and labels into a form that the model's training
algorithm can handle, and then calls trainInner to do the actual training.
virtual double trainAndTest (const GMatrix &trainFeatures, const GMatrix &trainLabels, const GMatrix &testFeatures, const GMatrix &testLabels)
Trains and tests this learner. Returns sum-squared-error.
void wrapFeatures (GIncrementalTransform *pFilter)
Wrap whatever feature filter is currently set with the specified filter. Takes ownership of the filter.
void wrapLabels (GIncrementalTransform *pFilter)
Wrap whatever label filter is currently set with the specified filter. Takes ownership of the filter.
Static Public Member Functions
static void test ()
Runs some unit tests related to supervised learning. Throws an exception if any problems are found.
Protected Member Functions
GDomNode * baseDomNode (GDom *pDoc, const char *szClassName) const
Child classes should use this in their implementation of serialize.
size_t precisionRecallContinuous (GPrediction *pOutput, double *pFunc, GMatrix &trainFeatures, GMatrix &trainLabels, GMatrix &testFeatures, GMatrix &testLabels, size_t label)
This is a helper method used by precisionRecall.
size_t precisionRecallNominal (GPrediction *pOutput, double *pFunc, GMatrix &trainFeatures, GMatrix &trainLabels, GMatrix &testFeatures, GMatrix &testLabels, size_t label, int value)
This is a helper method used by precisionRecall.
virtual void predictDistributionInner (const double *pIn, GPrediction *pOut)=0
This is the implementation of the model's prediction algorithm. (This method is called by predictDistribution).
virtual void predictInner (const double *pIn, double *pOut)=0
This is the implementation of the model's prediction algorithm. (This method is called by predict).
void setupFilters (const GMatrix &features, const GMatrix &labels)
This method determines which data filters (normalize, discretize, and/or nominal-to-cat) are needed and trains them.
double sumSquaredErrorInternal (const GMatrix &features, const GMatrix &labels)
Used to measure SSE with data that has already been converted to the internal format.
virtual void trainInner (const GMatrix &features, const GMatrix &labels)=0
This is the implementation of the model's training algorithm. (This method is called by train).
virtual GMatrix * transduceInner (const GMatrix &features1, const GMatrix &labels1, const GMatrix &features2)
See GTransducer::transduce.
Protected Attributes
GNeuralNet ** m_pCalibrations
* m_pFilterFeatures
* m_pFilterLabels
GRelation * m_pRelFeatures
GRelation * m_pRelLabels
This is the base class of algorithms that learn with supervision and have an internal hypothesis model that allows them to generalize rows that were not available at training time. | {"url":"http://waffles.sourceforge.net/apidoc/html/class_g_classes_1_1_g_supervised_learner.html","timestamp":"2014-04-19T00:24:07Z","content_type":null,"content_length":"94812","record_id":"<urn:uuid:92820dcf-8231-49f9-8325-a3d8aa506acd>","cc-path":"CC-MAIN-2014-15/segments/1398223203235.2/warc/CC-MAIN-20140423032003-00617-ip-10-147-4-33.ec2.internal.warc.gz"} |
How to Make $1,000,000
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Estimating laplace-beltrami spectra for a graph surface in $R^3$
up vote 3 down vote favorite
Consider a surface $\Gamma$ in $R^3$. The surface $\Gamma$ is a graph, i.e. $\Gamma = (x,y, h(x,y))$, for $x \in R^2$ and some smooth function $h$, where $h$ and all its derivatives are periodic on
I'm trying to estimate the eigenfunctions and eigenvalues of the Laplace-Beltrami operator for this surface. Of course, the laplace beltrami operator can be very easily be expressed in local
coordinates on $[0,1]^2$, and so the problem is effectively approximating the spectra of this second order elliptic operator on $L^2[0,1]^2$ with periodic boundary conditions. This is what I am
doing, however I still cannot obtain any useful estimates.
Is anyone aware of any references, or has had any experience with this problem?
Are you interested in the low lying eigenvalues or the asymptotics of the eigenvalues? The second one should follow like Weyl's law .. – Helge Mar 12 '11 at 18:18
Hi, thanks for your answer. It's mainly the low lying eigenvalues. Even a spectral gap result would be a great start. – RadonNikodym Mar 13 '11 at 9:33
Are you not interested also in the spectrum of the non-compact surface $\Gamma$. Periodic BC gives the (discrete) spectrum of the (non flat) torus $\Gamma/Z^2$. – BS. Mar 13 '11 at 13:16
1 @BS: There is more than one operator involved for the non-compact case. It's still "estimating eigenvalues". – Helge Mar 14 '11 at 3:41
I'm interested in the discrete spectrum and the corresponding eigenfunctions. My ultimate aim is to estimate the H1 inner product of a function ($x\cdot k$, where $k$ is a constant vector) against
the eigenfunctions. – RadonNikodym Mar 14 '11 at 12:23
add comment
1 Answer
active oldest votes
Some suggestions:
1. To show there is a spectral gap, one can use the following approach: The variational characterization of the first eigenvalue $$ E_1 = \inf_{\|\psi\| = 1} \langle \psi, H \psi \
rangle $$ can be used to obtain an upper bound on the first eigenvalue. Then Temple's inequality (I think it's in Reed-Simon IV) can be used to obtain a lower bound on the second
eigenvalue. Note in order to show the existence of a spectral gap, one needs to study all the operators $H(k)$ of the Floquet-Bloch decomposition.
2. But I would guess that at least as long as $h$ is "sufficiently small", there is no spectral gap (without having done any of the computations). Denote by $E_1(k)$ and $E_2(k)$ the
up vote 3 first and second eigenvalue of $H_0(k)$. Here $H_0$ denotes the usual Laplacian and the Floquet--Bloch decomposition is done with respect to $[0,1]^2$. I believe that one has that $$
down vote \sup_{k} E_1(k) > \inf_{k} E_2(k). $$ Then using that your operator will be a small perturbation of the Laplacian (in an appropriate sense), one should obtain that there is no
accepted spectral gap.
2b. (added in edit) It is clear that for fixed $k$, one has $E_1(k) < E_2(k)$. This follows from the first eigenfunction being positive.
3. There is what is called "Bohr-Sommerfeld conjecture", which is related to higher eigenvalues.
The first eigenvalue will always be zero, with corresponding eigenfunction being constant. By spectral gap I mean the gap between first and second eigenvalues. Numerically I have
computed the spectrum of my operator for various $h$ and have observed that a spectral gap exists and appears to be inversely proportional to the surface area of my surface (over [0,1]
^2), though I can't prove this. Temple's inequality seems to be a useful tool for this type of problem. Thanks for telling me about it. I admit I know nothing about Floquet-Bloch
decompositions, I'm reading about this now. Thanks. – RadonNikodym Mar 14 '11 at 12:38
The first eigenvalue of $H_0(k)$ is not always $0$ nor is the eigenfunction constant. Look up Floquet-Bloch decomposition. You need to consider multiple operators. – Helge Mar 14 '11
at 19:20
I am reading about the Floquet-Bloch decomposition and I am realising that rather that do all the estimates above, I simply need to compute the Hessian of the first bloch eigenvalue. I
suspect this might be just as hard as what I was doing previously, but I will attempt it. – RadonNikodym Mar 15 '11 at 10:43
add comment
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FairVote - User's Guide
User's Guide
The Monopoly Politics 2002 report contains two Microsoft Excel spreadsheets. The first, mp2002.xls, makes projections in the 2002 House races. The second, mp1996-2000, makes projections for each
House race from 1996 to 2000 and compares the projections to the actual results in those races.
This user's guide describes how to modify the parameters in the model and analyze their impact on the projections and, in the case of 1996-2000, their accuracy.
The spreadsheets use the same algorithm for making projections. For details of the model, check out the file, algorithm.doc, which explains each parameter in greater detail.
If you have questions or problems with the spreadsheet, please contact:
Caleb Kleppner
Center for Voting and Democracy
Part 1: Monopoly Politics 2002 Projections
You can do 4 things with this spreadsheet:
Modify parameters to examine their impact on projections
Enter 2002 results
Views summaries of projections by category and party
View summaries of the accuracy of the projections
1. Modifying parameters
The spreadsheet contains all of the data used to make projections: partisanship of the district, which seats are open seats, date of election of incumbents, and prior 2 election results.
It also contains the following parameters that the user can modify by typing a new number into the specified cell:
Parameter Cell Default value Range
Buffer for open seats A4 11% 0-25%
Increase for underachievers A5 33% 0-100%
Decrease for overachievers A6 67% 0-100%
Reduction for underachievers A7 1% 0-25%
Previous race uncontested A8 35% 0-100%
Decrease for long term overachievers A9 60% 0-100%
Adjustment to better 2nd election A10 33% 0-100%
No proj win H4 3% 0-30%
Win H5 5% 0-30%
Comfortable H6 10% 0-30%
Landslide H7 >10% 0-30%
Dem 2-party share H9 50% 0-100%
If you enter a value outside of the range of a parameter, the projections may not be meaningful.
2. Enter 2002 results
The spreadsheet is set up so that you can enter the winning party (D, R or I) and percent in columns N and O, rows 15 to 449. Once you do that, summaries showing the accuracy of the projections will
automatically appear.
Be sure to enter the winning percentage as a percent (ie, 43.7%, not 43.7, which would appear as 4370%). To enter a party, use a capital letter: D, R or I.
3. View summaries of projections
A variety of summary information about the projections appears in yellow-shaded cells in columns R-S and AA-AF in rows 1 to 10 of the spreadsheet.
Columns R-S: Total number of projections by category
Landslide: The number of projected landslide victories.
Comfortable: The number of projected comfortable victories.
Win: The number of projected wins.
Most vulnerable: The number of “most vulnerable” incumbents.
No proj win: The number of districts in which we do not project a win.
Other: This is a check for errors. It is the number of districts that do not fall in the above categories. If it is not zero, there is a problem with the model or the parameters. Please contact the
Center if this happens.
Columns AA-AF: Projections by party
This table shows the projections by category for seats held by each party. These figures are based on the incumbent party, and since this is a redistricting year, some of the new seats don’t have
incumbent parties. Also, one seat (VT-1) is held by an Independent. That’s why the total number of seats is less than 435.
4. View summaries of the accuracy of projection
Columns M-P: Totals of vulnerable, losing and open seats
Most vulnerable: This lists the number of projections labeled as “Most vulnerable” and, once data on the 2002 results is entered, the number of those incumbents who lost.
Losers (not open): After 2002 results are entered, this will show the number of losing incumbents.
Open seat party changes: The number of open seats whose party changed as a result of the 2002 election.
Open seats: The number of open seats this year (49).
Columns T-U: Accuracy of projections by category
These columns remain zero until 2002 results are entered.
For each of the projection categories, these columns list the number of projections in which the party projection was accurate and the number in which the winning margin was correct.
Columns V-Y: Results of races by prediction category
For each prediction category, these columns show the number of races that ended up being landslide, comfortable, wins or losses (from the perspective of the incumbent party).
The cells highlighted purple indicate races where the winning margin or party was wrong.
For example, with the default settings, there are 100 projected comfortable races. After entering the results (party and winning percent) from the 2002 races in column N and O, you will see in
columns V-Y the results in the 100 projected comfortable races. Some of those races will be won by landslide, others by comfortable margins and others by less than comfortable margins. Any remaining
races in this category would be losses for the incumbent.
Part 2: Monopoly Politics Projections 1996-2000
This spreadsheet works the exactly the same as the 2002 spreadsheet, except that the user can enter the desired year (1996, 1998 or 2000) in cell A4, and all of the election results are already
stored in the spreadsheet, so the summaries of the accuracy of projections appear instantaneously.
We hope you find these spreadsheets useful. Please bring to our attention any data errors or other problems you encounter. | {"url":"http://archive.fairvote.org/global/?page=491","timestamp":"2014-04-17T13:00:39Z","content_type":null,"content_length":"10556","record_id":"<urn:uuid:68361893-79e8-455c-81e9-3194eb7f3913>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00215-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
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Radiation Reaction Force (or Self Force of charge particle)
Is it true that there are cases in which the radiation reaction force on an electron is nonzero even if its acceleration is constant? I am confused because the radiation reaction force is
proportional to the time derivative of the acceleration.
Also when considering the radiation reaction force (or self-force) as a series, the first term, proportional to the acceleration goes to infinity for a point charge. In this case how would you treat
a charged particle in free fall, i.e. what would be its equation of motion? And I am assuming that this particle should radiate as it is in free fall, since radiation is proportional to the square of
the acceleration.
Please HELP! :)
Welcome to PF.
This is a difficult but very interesting issue. There seems to be a disagreement whether acceleration causes a charged particle to radiate.
See for example the discussion
Gravitational acceleration will not cause a charge to radiate. It seems that charges radiate only when interacting with other electric fields. A charge will, of course, accelerate in such a
situation. But can we say that it is the acceleration rather than the interaction with the other field that causes the radiation?
In my view, all we can say is that radiation is observed when a charge experiences a time dependent interaction with another electric field. There is no need to invent the radiation reaction force or
the concept of self-interaction. The laws of physics seem to be the same without it. | {"url":"http://www.physicsforums.com/showthread.php?t=114908","timestamp":"2014-04-20T05:44:52Z","content_type":null,"content_length":"44944","record_id":"<urn:uuid:1295b62a-981f-4e12-966e-1990a8decae5>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00369-ip-10-147-4-33.ec2.internal.warc.gz"} |
Columbia Discrete Math Seminar
Speakers for the Spring Semester 2008
February, 5, 622 Math Joel Spencer (NYU) Propp's Deterministic Realization of Random Walk
February, 12, 317 Mudd Jan Vondrak (Princeton) Combinatorial allocation and submodular maximization over matroids
February, 19, 622 Math Xander Faber (Columbia) Foster coefficients and the Jacobian of a metric graph
February, 26, No seminar
March, 4 No seminar
March, 11, 317 Mudd Andrew King (McGill) Bounding the chromatic number of claw-free graphs
March, 18 No seminar---spring break
SPECIAL SEMINAR March, 24, 4 pm Math 622 Ron Aharoni (The Technion) A topological version of Hall's theorem
March, 25, 622 Math Noga Alon (Tel-Aviv University / IAS) Sparse universal graphs
April, 1, 317 Mudd Dillon Mayhew (Victoria University) Binary matroids with no M(K3,3)-minors
April, 8, No seminar
April, 15, 622 Math Alexandra Ovetsky Fradkin (Princeton) Hadwiger's conjecture for quasi-line graphs
April, 22, 317 Mudd Jim Orlin (MIT) Matroid Parity Made Almost Simple
April, 29, No seminar
Past Talks
If you have any questions, or would like to be added to the seminar mailing list,
please e-mail mchudnov@columbia.edu | {"url":"http://www.columbia.edu/~mc2775/spring08.html","timestamp":"2014-04-18T13:19:04Z","content_type":null,"content_length":"3165","record_id":"<urn:uuid:713d6477-937d-48d8-ae76-e282593ffb6d>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00303-ip-10-147-4-33.ec2.internal.warc.gz"} |
Nicoletta Cancrini: Kinetically constrained spin models: the east model
Kinetically constrained spin models have been introduced in physics literature as models which can have some properties of glass transition. They are lattice particle systems with Glauber like
dynamics reversible with respect to the product Bernoulli measure. Creation/annihilation of one particle on a site can happen iff the configuration around the site satisfies a particular constraint
which completely defines the model. I will discuss one of the models studied with F. Martinelli, C. Roberto, C. Toninelli: the east model (one dimensional). Each site changes its occupation iff its
right neighbor is empty. In particular I will show the results we obtained on the dependence of the relaxation time to equilibrium on the system size and on the particle density.
Anna Maria Cherubini: Asymptotic Behaviour for a collision model
The most popular models of collisions between particles (in granular fluids or elsewhere) are liable to 'inelastic collapse': clusters of particles are subject to an infinite number of collisions in
a finite time. This pathology is common when using a restitution coefficient to model the energy dissipation caused by an impact. We propose a simple model for a bouncing ball that takes explicitely
into account the deformability of the body and the energy dissipation due to internal friction, and show that it doesn't incur anelastic collapse.
Michele Correggi: Rapidly Rotating Bose Gases in Anharmonic Traps
Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the Thomas Fermi
(TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order
contribution to the energy can be computed by minimizing a simple functional of the density alone.
Domenico Finco: Two scale approximation for a class of Many Body Schrödinger equation
We consider a non relativistic quantum system consisting of $K$ heavy and $N$ light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential $\
alpha V$. No interaction is assumed among particles of the same kind.
Choosing an initial state in a product form we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error.
The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group.
Exploiting the asymptotic formula, it can be outlined an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones.
Alessandro Michelangeli:TBA
Daniela Morale: Stochastic many particle systems in biology and medicin
In biology and medicine it is possible to observe a wide spectrum of formation of patterns and clustering, usually due to self-organization phenomena. Some interesting example may be found in the
process of tumour growth and in particular in angiogenesis, where at an individual level, cells interact and perform a branching process during the formation of new vessels, under the stimulus of a
chemical field produced by a tumour. In this way formation of aggregating networks are shown as a consequence of collective behaviour. Aggregation patterns are usually explained in terms of forces,
external and/or internal, acting upon individuals. Over the past couple of decades, a large amount of literature has been devoted to the mathematical modelling of self-organizing populations, based
on the concepts of short-range/long-range social interaction" at the individual level. The main interest has been in catching the main features of the interaction at the lower scale of single
individuals that are responsible, at a larger scale, for a more complex behaviour that leads to the formation of aggregating patterns. Here we discuss the modelling of the dynamics of some
self-organization population via a system of N stochastic differential equations. We consider two working examples: animal grouping and angiogenesis
Laura Morato: Stochastic quantization for a system of N interacting Bose particles
We apply Stochastic Quantization to a system of $N$ interacting identical Bosons in an external potential $\Phi$, by means of a general stationary-action principle. The collective motion is described
in terms of a Markovian diffusion on $\R^{3N}$, with joint density $\hat\rho$ and entangled current velocity field $\hat V$, in principle of non-gradient form, related one to the other by the
continuity equation. Dynamical equations relax to those of canonical quantization, in some analogy with Parisi-Wu stochastic quantization. Thanks to the identity of particles, the one-particle
marginal densities $\rho$, in the physical space $\R^{3}$, are all the same and it is possible to give, under mild conditions, a natural definition of the single-particle current velocity, which is
related to $\rho$ by the continuity equation in $\R^{3}$.
The motion of single particles in the physical space comes to be described in terms of a non-Markovian three-dimensional diffusion with common density $\rho $ and, at least at dynamical equilibrium,
common current velocity $v$. The three-dimensional drift is perturbed by zero-mean terms depending on the whole configuration of the $N$-boson interacting system.
Finally we discuss in detail under which conditions the one-particle dynamical equations, which in their general form allow rotational perturbations, can be particularized, up to a change of
variables, to Gross-Pitaevskii equations.
Benjamin Schlein: Rate of convergence towards Hartree dynamics
The nonlinear Hartree equation can be used to describe the macroscopic time-evolution of bosonic quantum system in the so called mean-field limit. In this talk I am going to present recent bounds on
the error associated with the Hartree approximation, obtained in collaboration with I. Rodnianski.
Petra Scudo: Entanglement in the quantum Ising model
We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse magnetic field. When the field is sufficiently
strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, a
close relative of bond percolation. The generality of this technique allows to apply our analysis to a large class of disordered interactions.
Fabio Zucca: Ecological Equilibrium for Restrained Branching Random Walks
We study a generalized branching random walk where particles breed at a rate which depends on the number of neighbouring particles. Under general assumptions on the breeding rates we prove the
existence of a phase where the population survives without exploding. We construct a non trivial invariant measure for this case (joint work with D.Bertacchi and G.Posta). | {"url":"http://www.matapp.unimib.it/~bertacchi/workshop07/abstracts.html","timestamp":"2014-04-20T15:51:19Z","content_type":null,"content_length":"11168","record_id":"<urn:uuid:bc6b6ca6-6163-4172-adc9-aa08be49dc80>","cc-path":"CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00010-ip-10-147-4-33.ec2.internal.warc.gz"} |
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[Numpy-discussion] C-API for non-contiguous arrays
Oliver Kranz o.kranz@gmx...
Thu Oct 25 09:23:34 CDT 2007
Timothy Hochberg wrote:
> On 10/25/07, *Oliver Kranz* <o.kranz@gmx.de <mailto:o.kranz@gmx.de>> wrote:
> Hi,
> I am working on a Python extension module using of the NumPy C-API. The
> extension module is an interface to an image processing and analysis
> library written in C++. The C++ functions are exported with
> boos::python. Currently I am implementing the support of
> three-dimensional data sets which can consume a huge amount of memory.
> The 3D data is stored in a numpy.ndarray. This array is passed to C++
> functions which do the calculations.
> In general, multi-dimensional arrays can be organized in memory in four
> different ways:
> 1. C order contiguous
> 2. Fortran order contiguous
> 3. C order non-contiguous
> 4. Fortran order non-contiguous
> I believe that this is incorrect. Consider the following:
> >>> import numpy as np
> >>> a = np.arange(27).reshape(3,3,3)
> >>> a.strides
> (36, 12, 4)
> >>> a.transpose(2,1,0).strides
> (4, 12, 36)
> >>> a.transpose(0,2,1).strides
> (36, 4, 12)
> I believe that the last transpose doesn't fit any of these four
> categories and is simply discontiguous.
Yes, you are right. I did not consider this case.
> Am I right that the NumPy C-API can only distinguish between three ways
> the array is organized in memory? These are:
> 1. C order contiguous e.g. with PyArray_ISCONTIGUOUS(arr)
> 2. Fortran order contiguous e.g. with PyArray_ISFORTRAN(arr)
> 3. non-contiguous e.g. with !PyArray_ISCONTIGUOUS(arr) &&
> !PyArray_ISFORTRAN(arr)
> So there is no way to find out if a non-contiguous array has C order or
> Fortran order. The same holds for Python code e.g. by use of the flags.
> a.flags.contiguous
> a.flags.fortran
> This is very important for me because I just want to avoid to copy
> every
> non-contiguous array into a contiguous array. This would be very
> inefficient. But I can't find an other solution than copying the array.
> Also the iterator provided by the C-API only loops over the array in C
> order. Even if the array is in Fortran non-contiguous order.
> Or are there just no Fortran order non-contiguous arrays? I think I can
> construct one.
> a = numpy.ndarray((3,4,5), order="F")
> b = a[:,1:2,:]
> Now, I think b's elements are organized in memory in Fortran
> non-contiguous order. But the flags only tell me that it is
> non-contiguous and not if it is in Fortran order or in C order. And if b
> would be passed to a C++ function it would not be possible to find out
> with the C-API if it is in Fortran order or in C order, too.
> Any ideas? Or do I always have to create contiguous arrays?
> By Fortran and C-Order discontiguous, do you simply mean that the
> strides are in increasing and decreasing order respectively? If so, you
> could check for that without too much trouble.
Since I want to support all the different contiguous and non-contiguous
arrays the best solution for me is always checking the strides if the
array is not in C order contiguous.
More information about the Numpy-discussion mailing list | {"url":"http://mail.scipy.org/pipermail/numpy-discussion/2007-October/029656.html","timestamp":"2014-04-18T16:32:33Z","content_type":null,"content_length":"6810","record_id":"<urn:uuid:16358db7-36dd-4e88-a13f-bd742db20f4c>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00042-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: Primelimit
Ilya Zakharevich on Mon, 1 Feb 1999 12:24:23 -0500
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
On Mon, Feb 01, 1999 at 11:19:34AM +0100, Karim BELABAS wrote:
> I don't understand what you want to achieve by artificially lowering the
> number of primes available to some functions. Could you give more details ?
If I understand Gerhard correct, some functions take primelimit not as
an advice about the number of available primes, but as a directive to
loop over these primes.
Suppose I want to have a table of primes up to 1e9 (very easy with the
current PARI), say, to use forprime() with big primes. This may
significantly slow down the functions which loop over *all* existing | {"url":"http://pari.math.u-bordeaux.fr/archives/pari-dev-9902/msg00001.html","timestamp":"2014-04-16T04:17:15Z","content_type":null,"content_length":"4677","record_id":"<urn:uuid:060d3c30-e251-4586-b5a2-fc74b95f7a36>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00503-ip-10-147-4-33.ec2.internal.warc.gz"} |
What's wrong with Mochizuki's 'proof' of the ABC conjecture?
(Cross-posted at
A few days ago Eric had a
about an
insightful text
that has been making the rounds on the internet, which narrates the story of a mathematical ‘proof’ that is for now sitting somewhere in a limbo between the world of proofs and the world of
non-proofs. The ‘proof’ in question purports to establish the famous ABC conjecture, one of the (thus far) main open questions in number theory. (Luckily, a while back Dennis posted an extremely
helpful and precise
exposition of the ABC conjecture
, so I need not rehearse the details here.) It has been proposed by the Japanese mathematician Shinichi Mochizuki, who is widely regarded as an extremely talented mathematician. This is important, as
crackpot ‘proofs’ are proposed on a daily basis, but in many cases nobody bothers to check them; a modicum of credibility is required to get your peers to spend time checking your purported proof.
(Whether this is fair or not is beside the point; it is a sociological fact about the practice of mathematics.) Now, Mochizuki most certainly does not lack credibility, but his ‘proof’ has been made
public quite a few months ago, and yet so far there is no verdict as to whether it is indeed a proof of the ABC conjecture or not. How could this be?
As it turns out, Mochizuki has been working pretty much on his own for the last 10 years, developing new concepts and techniques by mixing-and-matching elements from different areas of mathematics.
The result is that he created his own private mathematical world, so to speak, which no one else seems able (or willing) to venture into for now. So effectively, as it stands his ‘proof’ is not
communicable, and thus cannot be surveyed by his peers.
Let us assume for a moment that the ‘proof’ is indeed correct in that every inferential step in the lengthy exposition is indeed necessarily truth-preserving, i.e. no counterexample can be found for
any of the steps. In a quasi-metaphysical sense, the ‘proof’ is indeed a proof, which is a success term (a faulty proof is not a proof at all). However, in the sense that in fact matters for
mathematicians, Mochizuki’s ‘proof’ is not (yet) a prof because it has not been able to convince the mathematical community of its correctness; for now, it remains impenetrable. To top it up,
Mochizuki is a reclusive man who so far has made no efforts to reach out for his peers and explain the basic outline of the argument.
What does this all mean, from a philosophical point of view? Now, as some readers may recall, I am currently working on a dialogical conception of deductive proofs (see
). I submit that the dialogical perspective offers a fruitful vantage point to understand what is going on with the ‘Mochizuki affair’, as I will argue in the remainder of the post. (There are also
interesting connections with the debate on computer-assisted proofs and the issue of surveyability, and also with Kenny Easwaran’s notion of the ‘transferability’ of mathematical profs, but for
reasons of space I will leave them aside.)
Let me review some of the details of this dialogical conception of proofs. On this conception, a proof is understood as a semi-adversarial dialogue between two fictitious characters, proponent and
opponent. The dialogue starts when both participants agree to grant certain statements, the premises; proponent then puts forward further statements, which she claims follow necessarily from what
opponent has granted so far. Opponent’s job is to make sure that each inferential step indeed follows of necessity, and if it does not, to offer a counterexample to that particular step. The basic
idea is that the concept of necessary truth-preservation is best understood in terms of the adversarial component of such dialogues: it is strategically in proponent’s interest to put forward only
inferential steps that are
, i.e. which cannot be defeated by a countermove even from an ideal, omniscient opponent. In this way, a valid deductive proof corresponds to a
winning strategy
for proponent.
Now, when I started working on these ideas, my main focus was on the adversarial component of the game, and on how opponent would be compelled to grant proponent’s statements by the force of
necessary truth-preservation. But as I started to present this material to numerous audiences, it became increasingly clear to me that adversariality was not the whole story. For starters, from a
purely strategic, adversarial point of view, the best strategy for proponent would be to go directly from premises to the final conclusion of the proof; opponent would not be able to offer a
counterexample and thus would be defeated. In other words, proponent has much to gain from large, obscure (but truth-preserving) inferential leaps. But this is simply not how mathematical proofs
work; besides the requirement of necessary truth-preservation, proponent is also expected to put forward
individually perspicuous
inferential steps. Opponent would not only not be able to offer counterexamples, but he would also become
of the cogency of the proof; the proof would thus have fulfilled an explanatory function. Opponent would thus be able to see not only
the conclusion follows from the premises, but also
the conclusion follows from the premises. To capture this general idea, in addition to the move of offering a counterexample, opponent also has available to him an inquisitive move: ‘why does this
follow?’ It is a request for proponent to be more perspicuous in her argumentation.
This is why I now qualify the dialogue between proponent and opponent as
-adversarial: besides adversariality, there is also a strong component of
between proponent and opponent. They must of course agree on the premises and on the basic rules of the game, but more importantly, proponent’s goal is not only to force opponent to grant the
conclusion by whatever means, but also to
to opponent why the conclusion follows from the premises. Thus understood, a proof has a crucial
One way to conceptualize this interplay between adversariality and cooperation from a historical point of view is to view the emergence of the deductive method with Aristotle in the two
as a somewhat strange marriage between the adversarial model of dialogical interaction of the Sophists – dialectic – with the didactic, Socratic method of helping interlocutors to find the truth by
themselves by means of questions (as illustrated in Platos’s dialogues). This historical hypothesis requires further scrutiny, and is currently one of the topics of investigation of my
Roots of Deduction
project, in cooperation with the other members of the project.
Going back to Mochizuki, it is now easy to see why he is not being a good player in the game of deduction. He is not fulfilling his task as proponent to make his proof accessible and compelling to
the numerous ‘opponents’ of the mathematical community; in other words, he is failing miserably on the cooperative dimension. As a result, no one is able or willing to play the game of deduction
him, i.e. to be his opponent. Now, a crucial feature of a mathematical proof is that it takes (at least) two to tango: a proponent must find an opponent willing to survey the purported proof so that
it counts as a proof. (Naturally, this is not an infallible process: there are many cases in the history of mathematics of purported ‘proofs’ which had been surveyed and approved by members of the
community, but which were later found to contain mistakes.)
Mochizuki’s tango is for now impossible to dance to/with, and as long as no one is willing to be his opponent, his ‘proof’ is properly speaking not a proof. It is to be hoped that this situation will
change at some point, given the importance of the ABC conjecture for number theory. However, this will only happen if Mochizuki becomes a more cooperative proponent, or else if enough opponents are
found who are willing and able to engage in this dialogue with him.
19 comments:
1. Well, Mochizuki posted several new 2013-04 items, and at least 1 2013-05 item concerning the framework/methods/tools he used at http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html
So I'd say he's not exactly uncooperative on this. He just seems not to be into direct point to point communication right now.
No idea whether his degree of cooperation will be sufficient for his colleagues.
1. Yes, I don't mean to say something about M's psychological state or anything, but rather that whatever effort he has been making to make his results intelligible, it hasn't been enough
(judging from the piece that gave rise to this post.)
2. I'm not sure if I agree that the dialog model captures the problems associated with verifying a proof. These days, proofs are very long and complicated. A classic example is the classification
theorem for finite simple groups.
As Wikipedia point out: "The proof of the theorem consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004."
There is simply too much work for one human to ever verify in a lifetime. I don't believe the adversary model captures the problem of a proof being so large that the verification is more work
that one human can do. I believe this is a fruitful data point for any theory of the sociology of proof acceptance.
3. Anonymous:
Thanks, for a neophyte like me that's real food for thought.
But I would take Catarina's (if I may) point to apply in your case: what justifies confidence in the transitive nature of the supposed proof-effect of all these collective efforts?
FWIW: I am really, really out of my element here. I feel like a child at the big people's table.
1. Yes, that's exactly the point: the fact that very long proofs cannot be surveyed by a single individual does not count against the dialogical account, in fact in a sense it counts *in favor*
of it because it emphasizes the social, collective nature of mathematics. Theorems are proved, and then other theorems rely on the original ones having been proved to use them as 'shortcuts'
(otherwise everything would have to be proved from stretch). But every bit of it has been surveyed by a 'certified opponent' at one point or another and has been recognized as a valid
4. Is it a consequence of the dialogic account that a particular syntactic object might become a proof by way of its writer (or someone) engaging in the dialogic game? so what Mochizuki has provided
so far isn't a proof, but it might become one later?
I don't have anything at stake here, but my intuitions are partly formed by a proof-theoretic definition of proof that we would offer in beginning logic (a sequence of steps licensed by the proof
rules, for example).
1. Yes, that is one way to cash out the general idea. The main point is that a proof is not a proof unless it is recognized as such by the mathematical community. The underlying idea is a
functionalist one. What is the function of a proof? Primarily, to persuade a putative audience that the conclusion follows from the premises. If this function has not been (yet) fulfilled,
then perhaps one could say that the piece of discourse in question is 'potentially' a proof, but that this potentiality has not yet been actualized, or something like that.
5. Maybe he did claim prematuely. This is what Andrew Wiles did. Human beings are imperfect. If we go on like this, we mathematicians will check and balance ourselves with extinction. If you wish
for completely correct all the time, this happens in Heaven only. Mathematics is a field of imagination. But it is also very unforgiving, too much so. If businesmen and politicians were held up
to 1/10 of us, we will all have livable future and we will be happy actually.
1. I agree, mathematics is unforgiving, in fact it's the very core of it: it has a built-in uncharitable opponent! :)
2. Hi Cat, I think I completely disagree with this whole philosophy. Whose idea is it? This is what Thurston said in the Bull AMS years ago. Find and read it. Whole of the mathematics community
hated it so much. I think that this philosophical idea is not correct. I will be uncharitable to this idea. This idea can be very abusive in two accounts: It can lower the standard or raise
the standard of proofs abitrarily by society. The proofs cannot be juried. Second, there is no foundation of mathematics that is completely true beyond all doubt. Unjustifiable mathematical
truth does exists. The nonexistence of proof does not mean it is not true.
6. Also, I want to mention that there are huge amount of literature written by mathematicians who are dead now that are half rigorous but correct. Thurston now fits into this category now. But I
just want to mention that the logical correctness cannot sometimes be accessed for quite a while because humans are limited. I do think that we should have a computer checking system for proofs
by investing tens of billions of dollars. (That is, computers do not seek proof but merely verifies one given by a mathematician in formal language. Seeking proof part comes into many issues in
Logic and so cannot be done. The reverse verification part is doable. After this is done, we mathematicians can act like CS program building to build theorems. Maybe in late 21st century, we will
see this?)
7. Hi Cat!
I've just found this blog today. It' super good, really interesting.
Now - a question - what if there's no opponent? do we cease to have mathematics? do we cease to have proofs?
What about the opposite situation - infinitely many opponents. Does the proponent need to convince/guide all of them? If not, which subset of the opponent set "really matters"?
I believe this sounds more like sociology...
8. Hi, I think that actually Mochizuki is a good player. The combination of the importance of the abc conjecture and his position as recognized mathematician makes that other players follow his
rules. Also i like the social dimension of the dialogical conception of deductive proofs proposed by Catarina but i share the doubts of Manu if this leads you to reduce poofs to a social activity
only. (Sorry for my english if i make grammar mistakes!)
9. Anyone interested in how the story of Mochizuki's claimed proof plays out may enjoy Lieven LeBruyn's "MinuteMochiuzuki" posts, which can be found on Google+. He started by saying:
Starting head-on with the 4 papers on inter-universal Teichmuller theory (IUTeich for the fans) is probably not the smartest move to enter Mochizuki-territory.
If you glanced through any of these papers or one of his numerous talks, you'll know he makes a point of 'extending' or even 'partially dismantling' scheme theory using the new notion of
Frobenioids, which should be some generalisation of Galois categories.
So if you ever feel like wasting some months trying to figure out what his claimed proof of the ABC-conjecture is all about, a more advisable route might be to start with his two papers on 'the
geometry of Frobenioids'.
Lots of people must have tried that entrance before, and some even started a blog to record their progress as did the person (or persons) behind MochizukiDenial. Here's the idea:
"Mochizuki deniers by contrast believe that the claim is not serious. They believe that the body of Mochizuki’s work contains neither a proof outline nor ideas powerful enough to resolve the ABC
conjecture. We might be wrong. How do we propose to determine whether or not we are. In contrast to Mochizuki boosters on the internet, we will do this by determining what it is that Mochizuki’s
papers purport to do. Stay tuned."
Unfortunately, the project was given up after 2 days and three posts...
Today i tried to acquaint myself with the 126 pages of Frobenioids1 and have a splitting headache because i miss an extra 2Gb RAM to remember the 173 (or more) new concepts he introduces.
However, he seems to be making interesting progress in understanding and explaining some of Mochizuki's machinery.
1. Thanks for the pointer, John!
10. Mochizukis paper sounds rather like Grothendiecks 'pursuing stacks' which from what I gather took *some* time before it proved its worth. Heres hoping it makes the same impact even if its looking
fiercely impenetrable now...
11. I wonder if anybody is making a concerted effort to model IUTeich & frobenoids in a modern computer algebra system, as the groundwork for testing elements of the proof in a more automated way.
That's certainly what I do when trying to understand something in mathematics: I implement a model of it, and if the model works exactly the same way as the theorem, I probably understand it
12. It turns out if I take (((10e) (pi - 1) *X) / 2) this produces some differences in sequence near the decimal point, but if I then * (e / pi) the result is an interesting number:
As it turns out, the first two digits are 5 * 5, which I call an irrational factorization of 1 * 10. The second two digits are equal to 2 * 9, the fifth and sixth digits are a straight irrational
factorization, the seventh and eight digits are 3 * 8. Get this, the ninth and tenth digits are 4 * 7.
It would be interesting to get feedback on whether I have found a way to generally exploit the decimal system or predict decimals of pi, since at no point did I divide e out of the system, and I
suspect pi is still present as a factor of some kind.
13. Catarina, initially you write that the proponent has much to gain from skipping steps in inference, but then go on to reject that this is mathematical practice. I tend to agree with your original
statement, actually. For example, although mathematicians sought to elaborate on Perelman's proof of Thurston's geometricization conjecture, still Perelman is considered by the mathematics
community to have proved this conjecture, as evidenced by the offering of prizes to him. This supports the dialogical viewpoint of proof as adversial, in that the proponent wins so long as no
opponent can provide a counterexample.
As for the extent to which a proof is accepted by the community, it depends on the volume and intensity of opposition. If many mathematicians spend a lot of effort and are unable to find a
counterexample to this proof, then the proof in question gains greater acceptance. Framing the debate on Mochizuki's write up, it becomes less of a question whether it is a proof per se, but
rather about the degree that the community accepts it as a proof. The question for the philosophy of mathematical practice then is: what inclines or impedes the mathematics community to oppose a
proposed proof? | {"url":"http://m-phi.blogspot.com/2013/05/whats-wrong-with-mochizukis-proof-of.html","timestamp":"2014-04-21T02:01:01Z","content_type":null,"content_length":"150446","record_id":"<urn:uuid:6baa3e6a-38b1-418a-a4a9-b29fea2fc338>","cc-path":"CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00064-ip-10-147-4-33.ec2.internal.warc.gz"} |
Multiple conversions between moles,mass, volume and number of particles
Type in the content of your page here.
Multiple conversions between mass, volume and number of particles
Find the number of atoms in a given number of molecules.( two steps) Step a) Count the number of atoms in one molecule.
Step b) Multiply the number of molecules
Example 1:
How many atoms are in 3 molecules of (NH4)2SO4 a) the number of atoms in 1 molecule.
N: N×2=2
H: H×4×2=8
S: S×1=1
O: O×4=4
Total atoms in 1 molecule has 2+8+1+4=15
b) there are 3 molecules 15×3=45
Therefore, there are 45 atoms in 3molecules of (NH4)2SO4 Find a part of atoms in a given number of molecules. Step a) Count the number of the atoms that you need to find in 1 molecule. Step b)
Multiply the number of molecules. Example 2:
How many hydrogen atoms are in 3 molecules of (NH4)2SO4 a) H: H×4×2=8
Total atoms in 1 molecule of hydrogen atoms are 8
b) there are 3 molecules 8×3=24
Therefore, there are 24 hydrogen atoms in 3 molecules of (NH4)2SO2of molecules. single step conversion
conversion Conversion factor
Moles ←→ Number of particles 6.02×10^23particles/1 mole
1 mole/6.02×10^23 particles
Moles ←→ Mass (molar mass)g/1 mole
1 mole/(molar mass)g
Moles ←→ Volume (gases at STP) 22.4L / 1 mole
1 mole/ 22.4L
Molecules ←→Atoms (atoms count)atoms/1 molecule
1 molecule/(atoms count)atoms
1) How many molecules are there in 5 moles of molecules?
number of molecules= 5 moles ×(6.02 ×10^23 particles/1 mole) = 3.01×10^24 molecules
2) What is the mass of H2O in 3 moles?
1) Molar mass of H2O= 2H=2×1.0=2.0g, 1O=1×16.0=16.0g 2.0g+16.0g=18.0g
2) number of mass of H2O= 3 moles ×(18.0gH2O/1moleH2O)=54.0gH2O
3) What is the volume occupied by 0.5 mol of SO2 (g) at STP?
number of litres =0.5mol SO2 ×(22.4L SO2/1mol SO2)=12.2L SO2
4) How many atoms are there in 7 molecules of H3PO4?
number of atoms =7 molecules H3PO4×(8 atoms of H3PO4/1 molecule H3PO4)=56 atoms H3PO4 In the calculations, some questions should use conversions more than once; however, mole is in the centre,
because all conversions between mass, particles and volume should be converted to mole at first.
These are some general calculations steps.
Particles ←→ mass:
Convert particles ←→ moles(using 6.02×10^23/1 mole) ←→ mass( using molar mass/1 mole)
Particles ←→ volume:
Convert particles←→ moles(using 6.02×10^23/1 mole) ←→ volume(using 22.4L/1 mole at STP)
Mass to volume:
Convert mass←→ moles(using molar mass/1 mole) ←→ volume(using 22.4L/1 mole at STP) Example 1:
What is the volume occupied by 40.0g of O2 (g) at STP
Plan: convert Mass to Moles then to Volume
mass×(1 mole/ molar mass)×(volume/ 1 mole)
1) molar mass: 2O: 2×16.0g= 32.0g O2 2) 40.0g O2 ×(1 mole O2 / 32.0g O2)×(22.4L O2/ 1 mole O2)=28.0L O2 Example 2: What is the mass of 3.00×10^18 atoms of Fe? Plan: convert # of atoms to Moles then
to Mass mass= number of atoms ×(1 mole/ 6.02×1023 atoms) ×(molar mass/ 1 mole)
1) Molar mass: 1Fe= 1×55.8g= 55.8g Fe
2) Mass=3.00×10^18 atoms Fe×(1 mole Fe/6.02×10^23 Fe)×(55.8g Fe/1 mole Fe)=2.78g Fe
22.4L/1 mole used all refer to gases at STP, but if the density is mentioned at a point in a problem, we should use d=m/v.( three situation) a) if the density is mentioned at a point in a problem, we
should use d=m/v.
b) If the volume of a solid or liquid is unknown, calculate the volume from v=m/d
c) If the mass is unknown, calculate the mass from m=v×d Example 1: What is the volume occupied by 4.00 mole of Al203? (d=3.97g/ml) Hint : density relates to volume to mass, mass is relates to moles.
number of ml= mole ×(molar mass/1 mole)×(1 ml/3.97g)
1) Molar mass:2Al=2×27.0g=54.0g, 3O=3×16.0g=48.0g 54.0g+48.0g=102.0g
2) number of ml= 4.00ml Al203×(102.0g Al203/1 mol Al203)×(1 ml Al203/3.97g Al203)=102.8ml Al203
Example2: How many atoms of Al are in 200 ml of Al2O3? (d=3.97g/ml) Plan: convert volume to mass, then to moles, then to Avogadro’s number, finally to number of atoms
number of atoms= volume×density×(1mole/molar mass)×(6.02×10^23 molecule/1 mole) ×(atoms count/1 molecule)
number of atoms=200ml×(3.97g/1ml)×(1mole/102.0g)×(6.02×10^23molecules/1mole)×(2Al atoms/1 molecule)=9.37×10^23 atoms | {"url":"http://chemistry11mrstandring.wikispaces.com/Multiple+conversions+between+moles%2Cmass%2C+volume+and+number+of+particles?responseToken=0138c8c3dbd6d7f7476612e0131fdd68f","timestamp":"2014-04-19T16:19:02Z","content_type":null,"content_length":"78367","record_id":"<urn:uuid:a6946fbc-9f3a-4515-bcf7-635a1086ef61>","cc-path":"CC-MAIN-2014-15/segments/1397609537271.8/warc/CC-MAIN-20140416005217-00285-ip-10-147-4-33.ec2.internal.warc.gz"} |
Possible Answer
1 gallon covers about 350 square feet, so a quart covers 1/4 of that or about 87 and 1/2 square feet. - read more
How many square feet does a quart of paint cover? \n 1 gallon covers about 350 square feet, so a quart covers 1/4 of that or about\n 87 and 1/2. How many square feet does one quart of paint cover? -
Share your answer: how many sq ft will one quart of paint cover?
Question Analizer
how many sq ft will one quart of paint cover resources | {"url":"http://www.askives.com/how-many-sq-ft-will-one-quart-of-paint-cover.html","timestamp":"2014-04-19T14:45:52Z","content_type":null,"content_length":"35606","record_id":"<urn:uuid:9bd7ade3-fec4-407a-b03a-506b15cef0df>","cc-path":"CC-MAIN-2014-15/segments/1397609537271.8/warc/CC-MAIN-20140416005217-00136-ip-10-147-4-33.ec2.internal.warc.gz"} |
Summary: REVIEW PROBLEMS FOR MIDTERM II
MATH 2574H, SPRING 2012
This is a selection of problems meant to be reasonable practice for the upcoming
exam. These problems (or portions thereof) are possible types of exam questions.
Please note that the usual disclaimer continues to apply, namely, this is not guar-
anteed to be an absolutely complete review. To be perfectly ready you have to have
a grip on all the homework that has been assigned in weeks 4,5,6,7.
Salt tank problem
A tank has a huge capacity, so huge we will not worry about the possibility of
overflow. At time t = 0 the tank contains 64 gallons of water with 10 pounds of the
top secret ingredient of Calca-Cola dissolved in the water. Then solution containing
1 pound of secret ingredient per gallon of water is allowed to flow into the tank
at a rate of 5 gallons per minute. Simultaneously, well-mixed solution is allowed
to drain out of the tank at a rate of 1 gallon per minute. Find a formula for the
amount of secret ingredient in the tank at time t. Show all your work.
Undetermined coefficients
a. Solve the initial value problem
y + 7y + 12y = 550e7t
, y(0) = 2, y (0) = 48 | {"url":"http://www.osti.gov/eprints/topicpages/documents/record/267/5318764.html","timestamp":"2014-04-17T09:55:20Z","content_type":null,"content_length":"8234","record_id":"<urn:uuid:316b7d98-2239-4515-a3eb-0801849592df>","cc-path":"CC-MAIN-2014-15/segments/1397609527423.39/warc/CC-MAIN-20140416005207-00652-ip-10-147-4-33.ec2.internal.warc.gz"} |
Divided differences
August 30th 2010, 02:40 AM #1
Divided differences
my book starts to explain divided difference by saying that :
Suppose that $P_n(x)$ is the nth Lagrange polynomial that agrees with the function $f$at distinct numbers $x_0,x_1,\cdots,x_n$. The divided differences of $f$ with respect to $x_0,x_1,\cdots,x_n$
are used to express $P_n(x)$ in the form
$P_n(x) = a_0+a_1(x-x_0)+a_2(x-x_0)(x-x_1)+\cdots+a_n(x-x_0)(x-x_1)\cdots(x-x_{n-1})$
Since I'm pretty slow, I do not see the logic behind this choice. I'm that I'm lacking some basic theory such that this appears like a mystical choice. Could someone point me in the right
direction please?
I do understand why the interpolating polynomial between two points x_0 and x_1 can be written as,
$P_1(x) = f(x_0) + \frac{f(x_1)-f(x_0)}{x_1-x_0}(x-x_0),$
The literature often states that a convenient form of the 2-order polynomial is,
$P_2(x) =b_0 + b_1(x-x_0)+b_2(x-x_0)(x-x_1).$
How did man figure out that this is a convenient form? Trial and error? Thinking really hard?
Last edited by Mollier; August 30th 2010 at 03:46 AM.
Never mind guys, I found a great explanation at: 5.3 Newton Polynomials | Department of Electrical and Computer Engineering | University of Waterloo.
I have been spoon-fed and am quite happy
August 30th 2010, 11:14 AM #2 | {"url":"http://mathhelpforum.com/calculus/154741-divided-differences.html","timestamp":"2014-04-17T20:46:04Z","content_type":null,"content_length":"34799","record_id":"<urn:uuid:f27ca51a-0211-469b-99b5-17593129b033>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00038-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Here's the question you clicked on:
If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero,then the satellite will: a)continue to move in its orbit with same velocity. b)move
tangentially and escape away. c)become stationary in its orbit. d)move towards the earth.
• one year ago
• one year ago
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@amistre64 @igbasallote @UnkleRhaukus @hartnn @Zarkon @.Sam. @bahrom7893 @cwrw238
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i think it will move tangentially and then escape away
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because nothing is holding it back now.
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but answer is showing is option c
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uhm I would disagree with that answer.
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so answer is wrong
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if anyone else can prove why option C is correct, please do.
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is it a geo-stationary orbit initially
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what it means is it a geo-stationary orbit initially
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in simple def.
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the object orbits as the planet turns
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in what case option a) satisfies
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object orbits becoz of gravity of earth
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so in what case option c satisfies
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geostationary means the object orbital period is same as earth rotation
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thnx.. @sara12345
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in what case option c satisfies
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plz tell me
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i think so
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i mean b is right
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but answer my question fast. in what case option c satisfies
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it never satisfies
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the answer to this question is b)move tangentially and escape away. since the velocity of the satellite is always tangent to the path for case c .. somehow the velocity of the satellite have to
become zero as well as no gravity then it stops
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if the object is stationary initially, it would fall on earth there and then itself
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why? if gravity becomes zero at all the objects
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for gravity to become 0 suddenly, it has to exist first
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when gravity + stationary object are there, the object would fall
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the object wouldnt fall as long as it revolves around the earth
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ok you say that whaen gravity is zero it would fall on earth there and then itself
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no that i didnt say, u r not listening properly
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if the satellite has no speed and there is no force (like gravity) acting upon it it stands still.. so for case c to happen you need to have no gravity + zero speed
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means it would fall on that object
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@sara12345 @Coolsector is right?
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lol i dont need her approval anyway
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but she said when gravity is zero it would fall on that object
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i didnt say that
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i dont think she said it
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i said this : when gravity + stationary object are there, the object would fall
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we see the transition time, when we say the gravity is becoming 0 => gravity existed before
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oh!! sry...
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if gravity existed before, and therez a stationary object sitting there, it cannot sit there, it has to fall
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in what case option d satisfies
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a stationary object case is false
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in case of option d
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d might happen when there is gravity but no speed for example .. then the satellite falls
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oh!! k
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or the speed is not high enough
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so final answer would be
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we said : the answer to your question is b)move tangentially and escape away.
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thnx... @UnkleRhaukus @sara12345 @Coolsector @bahrom7893
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Sorting outer group based on inner group in BI Publisher
I spent almost a day to implement a grouping and sorting requirement and after all that brain storming I found that the requirement can be implemented by an elementary piece of code. I wish to share
this with the rest of the world
Consider the following dataset
<data_node> <text_field>a</text_field> <num_field>5</num_field> </data_node>
<data_node> <text_field>a</text_field> <num_field>3</num_field> </data_node>
<data_node> <text_field>b</text_field> <num_field>6</num_field> </data_node>
<data_node> <text_field>a</text_field> <num_field>9</num_field> </data_node>
<data_node> <text_field>b</text_field> <num_field>4</num_field> </data_node>
<data_node> <text_field>b</text_field> <num_field>7</num_field> </data_node>
<data_node> <text_field>c</text_field> <num_field>2</num_field> </data_node>
<data_node> <text_field>c</text_field> <num_field>8</num_field> </data_node>
<data_node> <text_field>c</text_field> <num_field>10</num_field> </data_node>
<data_node> <text_field>d</text_field> <num_field>1</num_field> </data_node>
<data_node> <text_field>d</text_field> <num_field>11</num_field> </data_node>
<data_node> <text_field>d</text_field> <num_field>2</num_field> </data_node>
The requirement is to group the text_field data together and to order it based on num_field. In the above XML data source, text_field ‘d’ has the smallest number value i.e. 1. So, according to the
requirement, D should be displayed on the top with all its num_fields i.e. (1,2,11). After D, C should be displayed since C has a num_field value of 2. C should again be followed by all its
num_fields i.e. (2,8,10)
So the output should be
After a day of dealing with arrays, variables and tons of rearrangement, the following solution looked most elegant
<?end for-each?>
<?end for-each-group?>
Magic is done by the for-each-group statement at the top. When the field on which grouping is done (text_field in our case) is different from the field on which sorting is done(num_field in our
case), BI Publisher sorts the group-field based on the sort-field
The sort statement inside for-each:current-group() statement is to sort the num_field data inside each text_field group
Till next time | {"url":"http://obiee-oracledb.blogspot.com/2012/06/sorting-outer-group-based-on-inner.html","timestamp":"2014-04-16T15:58:50Z","content_type":null,"content_length":"71632","record_id":"<urn:uuid:95c0224c-7ed0-4191-8c13-5807097c58fb>","cc-path":"CC-MAIN-2014-15/segments/1397609524259.30/warc/CC-MAIN-20140416005204-00119-ip-10-147-4-33.ec2.internal.warc.gz"} |
Cheverly, MD SAT Math Tutor
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The deformation complex for differential graded hopf algebras
- Homology Homotopy Appl
"... Abstract. An A∞-bialgebra is a DGM H equipped with structurally compatible operations { ω j,i: H ⊗i → H ⊗j} such that ( H, ω 1,i) is an A∞-algebra and ( H, ω j,1) is an A∞-coalgebra. Structural
compatibility is controlled by the biderivative operator Bd, defined in terms of two kinds of cup products ..."
Cited by 4 (1 self)
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Abstract. An A∞-bialgebra is a DGM H equipped with structurally compatible operations { ω j,i: H ⊗i → H ⊗j} such that ( H, ω 1,i) is an A∞-algebra and ( H, ω j,1) is an A∞-coalgebra. Structural
compatibility is controlled by the biderivative operator Bd, defined in terms of two kinds of cup products on certain cochain algebras of pemutahedra over the universal PROP U = End(TH). To Jim
Stasheff on the occasion of his 68th birthday. 1.
, 2000
"... To Jim Stasheff on the occasion of his 65th birthday ..."
, 2001
"... Abstract. An A ∞ algebra is given by a codifferential on the tensor coalgebra of a (graded) vector space. An associative algebra is a special case of an A∞ algebra, determined by a quadratic
codifferential. The notions of Hochschild and cyclic cohomology generalize from associative to A ∞ algebras, ..."
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Abstract. An A ∞ algebra is given by a codifferential on the tensor coalgebra of a (graded) vector space. An associative algebra is a special case of an A∞ algebra, determined by a quadratic
codifferential. The notions of Hochschild and cyclic cohomology generalize from associative to A ∞ algebras, and classify the infinitesimal deformations of the algebra, and those deformations
preserving an invariant inner product, respectively. Similarly, an L ∞ algebra is given by a codifferential on the exterior coalgebra of a vector space, with Lie algebras being special cases given by
quadratic codifferentials. There are natural definitions of cohomology and cyclic cohomology, generalizing the usual Lie algebra cohomology and cyclic cohomology, which classify deformations of the
algebra and those which preserve an invariant inner product. This article explores the definitions of these infinity algebras, their cohomology and cyclic cohomology, and the relation to their
infinitesimal deformations. 1.
, 709
"... Abstract. The search for “higher homotopy Hopf algebras ” (known today as A∞-bialgebras) was initiated by this author in a talk at Jim Stasheff’s 1996 schriftfest entitled “In Search of Higher
Homotopy Hopf Algebras. ” The idea in that talk was to think of a DG bialgebra as some (unknown) higher hom ..."
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Abstract. The search for “higher homotopy Hopf algebras ” (known today as A∞-bialgebras) was initiated by this author in a talk at Jim Stasheff’s 1996 schriftfest entitled “In Search of Higher
Homotopy Hopf Algebras. ” The idea in that talk was to think of a DG bialgebra as some (unknown) higher homotopy structure with trivial higher order structure and apply a graded version of
Gerstenhaber and Schack’s bialgebra deformation theory. In retrospect, the bi(co)module structure encoded in the differential detects some (but not all) of the A∞-bialgebra structure relations; we
refer to such deformations as quasi-A∞-bialgebras. This motivated the discovery of A∞-bialgebras given by S. Saneblidze and this author in 2005. 1.
, 1995
"... Let k be a field and n ≥ 1. There exists a differential graded k-module (V,d) and various approximations to a differential d + td1 + t 2 d2 + · · · + t n dn on V [[t]], one of which is a
non-trivial polynomial deformation, another is obstructed, and another is unobstructed at order n. The analogou ..."
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Let k be a field and n ≥ 1. There exists a differential graded k-module (V,d) and various approximations to a differential d + td1 + t 2 d2 + · · · + t n dn on V [[t]], one of which is a non-trivial
polynomial deformation, another is obstructed, and another is unobstructed at order n. The analogous problem in the category of k-algebras in characteristic zero remains a long-standing open
question. 1
, 1998
"... The notion of a Massey F-product was introduced in [4] in order to give a unified description of various deformation problems in terms of an extension of the usual Massey product. The usual
Massey product which arises in algebra deformation theory describes the conditions under which an infinitesima ..."
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The notion of a Massey F-product was introduced in [4] in order to give a unified description of various deformation problems in terms of an extension of the usual Massey product. The usual Massey
product which arises in algebra deformation theory describes the conditions under which an infinitesimal deformation can be | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=14546801","timestamp":"2014-04-19T03:12:25Z","content_type":null,"content_length":"23665","record_id":"<urn:uuid:b06f473a-5cef-4c90-b0ae-9e0a374deeba>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00124-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Please help:) A mass less spring hanging vertically, extends by 5cm when a mass M is attached to its lower and vertical oscillations are started by pulling the mass M downwards by another 5cm and
then releasing it. i.Find the frequency of oscillation and the maximum velocity of the oscillating mass. ii.If a second mass of 300g is added to M the frequency of oscillation is reduced to half the
previous value. Find M.
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is replying to Can someone tell me what button the professor is hitting...
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Language extensions supported by Hugs and GHC
The recursive do-notation (also known as mdo-notation) is implemented as described in: A recursive do for Haskell, Levent Erkök and John Launchbury, Haskell Workshop 2002, pages: 29–37. Pittsburgh,
The do-notation of Haskell does not allow recursive bindings, that is, the variables bound in a do-expression are visible only in the textually following code block. Compare this to a let-expression,
where bound variables are visible in the entire binding group. It turns out that several applications can benefit from recursive bindings in the do-notation, and this extension provides the necessary
syntactic support.
Here is a simple (yet contrived) example:
import Control.Monad.Fix
justOnes = mdo xs <- Just (1:xs)
return xs
As you can guess
will evaluate to
Just [1,1,1,...
The Control.Monad.Fix module introduces the MonadFix class, defined as
class Monad m => MonadFix m where
mfix :: (a -> m a) -> m a
The function
dictates how the required recursion operation should be performed. If recursive bindings are required for a monad, then that monad must be declared an instance of the
class. For details, see the above mentioned reference.
The Control.Monad.Fix module also defines instances of MonadFix for lists, Maybe and IO. Furthermore, several other monad modules provide instances of the MonadFix class, including the
Control.Monad.ST and Control.Monad.ST.Lazy modules for Haskell's internal state monad (strict and lazy, respectively).
There are three important points in using the recursive-do notation:
• The recursive version of the do-notation uses the keyword mdo (rather than do).
• You should "import Control.Monad.Fix".
• Hugs should be started with the flag -98.
The web page:
contains up to date information on recursive monadic bindings.
Historical note: The old implementation of the mdo-notation (and most of the existing documents) used the name MonadRec for the class and the corresponding library.
Parallel list comprehensions are a natural extension to list comprehensions. List comprehensions can be thought of as a nice syntax for writing maps and filters. Parallel comprehensions extend this
to include the zipWith family.
A parallel list comprehension has multiple independent branches of qualifier lists, each separated by a "|" symbol. For example, the following zips together two lists:
[ (x, y) | x <- xs | y <- ys ]
The behavior of parallel list comprehensions follows that of
, in that the resulting list will have the same length as the shortest branch.
We can define parallel list comprehensions by translation to regular comprehensions. Given a parallel comprehension of the form:
[ e | p1 <- e11, p2 <- e12, ...
| q1 <- e21, q2 <- e22, ...
This will be translated to:
[ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
[(q1,q2) | q1 <- e21, q2 <- e22, ...]
is the appropriate zip for the given number of branches. These functions must be in scope; the
, but if you want to handle 4 or more lists in parallel, you will need to import | {"url":"http://cvs.haskell.org/Hugs/pages/users_guide/hugs-ghc.html","timestamp":"2014-04-16T22:25:16Z","content_type":null,"content_length":"7949","record_id":"<urn:uuid:e75a295f-077f-46d7-a78c-532b39cb1cf8>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00572-ip-10-147-4-33.ec2.internal.warc.gz"} |
Complex Numbers and Travelling Waves
February 22nd 2007, 07:34 AM #1
Feb 2007
Complex Numbers and Travelling Waves
At a given instant of time the ripples on the surface of the pond can be described using the expression:
psi-z = Re{e^i*(kx(x) + ky(y))}
where kx and ky are constants (Note: the x is subscript of k)
and k-x = 2pi/lambda-x
Derive an equation involving x and y that defines the crest that passes through the origin of the coordinate system
At a given instant of time the ripples on the surface of the pond can be described using the expression:
psi-z = Re{e^i*(kx(x) + ky(y))}
where kx and ky are constants (Note: the x is subscript of k)
and k-x = 2pi/lambda-x
Derive an equation involving x and y that defines the crest that passes through the origin of the coordinate system
By "defines the crest" you mean the shape of the curve? Simple: Re(e^{if(x,y)}) = cos(f(x,y))
February 22nd 2007, 12:45 PM #2 | {"url":"http://mathhelpforum.com/calculus/11848-complex-numbers-travelling-waves.html","timestamp":"2014-04-18T19:36:27Z","content_type":null,"content_length":"34059","record_id":"<urn:uuid:a05c70d3-040f-4271-a327-f8433ae2f566>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00379-ip-10-147-4-33.ec2.internal.warc.gz"} |
Lamirada, CA Geometry Tutor
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the first resource for mathematics
Stability of solutions to parameterized nonlinear complementarity problems.
(English) Zbl 0955.90138
Summary: We consider the stability properties of solutions to parameterized nonlinear complementarity problems
$\text{Find}\phantom{\rule{4.pt}{0ex}}x\in {ℝ}^{n}\phantom{\rule{4.pt}{0ex}}\text{such}\phantom{\rule{4.pt}{0ex}}\text{that}\phantom{\rule{4.pt}{0ex}}x\ge 0,\phantom{\rule{4pt}{0ex}}F\left(x,u\right)
-v\ge 0,\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{\left(F\left(x,u\right)-v\right)}^{T}·x=0,$
where these are vector inequalities. We characterize the local upper Lipschitz continuity of the (possibly set-valued) solution mapping which assigns solutions $x$ to each parameter pair $\left(v,u\
right)$. We also characterize when this solution mapping is locally a single-valued Lipschitzian mapping (so solutions exist, are unique, and depend Lipschitz continuously on the parameters). These
characterizations are automatically sufficient conditions for the more general (and usual) case where $v=0$. Finally, we study the differentiability properties of the solution mapping in both the
single-valued and set-valued cases, in particular obtaining a new characterization of $B$-differentiability in the single-valued case, along with a formula for the $B$-derivative. Though these
results cover a broad range of stability properties, they are all derived from similar fundamental principles of variational analysis.
90C33 Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C31 Sensitivity, stability, parametric optimization | {"url":"http://zbmath.org/?q=an:0955.90138","timestamp":"2014-04-19T12:37:05Z","content_type":null,"content_length":"22701","record_id":"<urn:uuid:e75c6aa2-e908-4491-8421-cb4f31a4ff3d>","cc-path":"CC-MAIN-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00532-ip-10-147-4-33.ec2.internal.warc.gz"} |
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The Coordinate Plane
4.1: The Coordinate Plane
Created by: CK-12
Learning Objectives
• Identify coordinates of points.
• Plot points in a coordinate plane.
• Graph a function given a table.
• Graph a function given a rule.
We now make our transition from a number line that stretches in only one dimension (left to right) to something that exists in two dimensions. The coordinate plane can be thought of as two number
lines that meet at right angles. The horizontal line is called the $x-$ and the vertical line is the $y-$. Together the lines are called the axes, and the point at which they cross is called the
origin. The axes split the coordinate plane into four quadrants. The first quadrant (I) contains all the positive numbers from both axes. It is the top right quadrant. The other quadrants are
numbered sequentially (II, III, IV) moving counter-clockwise from the first.
Identify Coordinates of Points
When given a point on a coordinate plane, it is a relatively easy task to determine its coordinates. The coordinates of a point are two numbers - written together they are called an ordered pair. The
numbers describe how far along the $x-$$y-$$x-$ (also called the ordinate) first and the $y-$ (or the ordinate) second.
$& (1, 7) && \text{An ordered pair with an} \ x-\text{value of one and a} \ y-\text{value of seven}\\& (0, 5) && - \text{an ordered pair with an} \ x-\text{value of zero and a} \ y-\text{value of
five}\\& (-2.5, 4) && \text{An ordered pair with an} \ x-\text{value of}\ -2.5\ \text{and a}\ y-\text{value of four}\\& (-107.2, -.005) && \text{An ordered pair with an} \ x-\text{value of} -107.2\ \
text{and a} \ y-\text{value of}\ -0.005.$
The first thing to do is realize that identifying coordinates is just like reading points on a number line, except that now the points do not actually lie on the number line! Look at the following
Example 1
Find the coordinates of the point labeled $P$
Imagine you are standing at the origin (the points where the $x-$$y-$$P$right (we say this is in the positive $x$ direction).
The $x-$$P$
Now if you were standing at the three marker on the $x-$$P$positive $y$ direction).
The $y-$$P$
The coordinates of point $P$
Example 2
Find the coordinates of the points labeled $Q$and $R$in the diagram to the right.
In order to get to $Q$$-x$down. This time we are moving in the negative $y$ direction. The $x$$Q$$y$$Q$
The coordinates of $R$$x$$x$$y-$
$Q(3, -2)$
$R(5, -2)$
Example 3
Triangle $ABC$is shown in the diagram to the right. Find the coordinates of the vertices $A, B$and $C$
Point $A$
$x-$$= -2$
$y-$$= +5$
Point $B$
$x-$$= +3$
$y-$$= -3$
Point $C$
$x-$$= -4$
$y-$$= -1$
$A (-2, 5)\! \\B (3, -3)\! \\C (-4, -1)$
Plot Points in a Coordinate Plane
Plotting points is a simple matter once you understand how to read coordinates and read the scale on a graph. As a note on scale, in the next two examples pay close attention to the labels on the
Example 4
Plot the following points on the coordinate plane.
$A (2, 7) && B (-5, 6) && C(-6, 0) && D (-3, -3) && E (0, 2) && F (7, -5)$
Point $A (2, 7)$
Point $B (-5, 6)$
Point $C (-6, 0)$on the $x$.
Point $D (-3, -3)$
Point $E (0, 2)$on the $y$.
Point $F (7, -5)$
Example 5
Plot the following points on the coordinate plane.
$A (2.5, 0.5) && B (\pi, 1.2) && C (2, 1.75) && D (0.1, 1.2) && E (0, 0)$
Choice of axes is always important. In Example Four, it was important to have all four quadrants visible. In this case, all the coordinates are positive. There is no need to show the negative values
of $x$$y$$x$$y$$\{ 0 \leq x \leq 3.5 \}$$\{ 0 \leq y \leq 2 \}$
Here are some important points to note about this graph.
• The tick marks on the axes do not correspond to unit increments (i.e. the numbers do not go up by one).
• The scale on the $x-$$y-$
• The scale is chosen to maximize the clarity of the plotted points.
Graph a Function Given a Table
Once we know how to plot points on a coordinate plane, we can think about how we would go about plotting a relationship between $x$$y$relation, and there isn’t necessarily a relationship between the
$x$$y$$x$domain and the set of $y$range. If there is a relationship between the $x$$y$$x$$y$function. Remember that a function is a particular way to relate one quantity to another. If you read a
book and can read twenty pages an hour, there is a relationship between how many hours you read and how many pages you read. You may even know that you could write the formula as either:
$m & = 20 \cdot h && n = \text{number of pages};\ h = \text{time measured in hours.\ OR} \ldots\\h & = \frac{n} {20}$
So you could use the function that related $n$$h$$3 \frac{1}{2}$
Generally, the graph of a function appears as a line or curve that goes through all points that satisfy the relationship that the function describes. If the domain of the function is all real
numbers, then we call this a continuous function. However, if the domain of the function is a particular set of values (such as whole numbers), then it is called a discrete function. The graph will
be a series of dots that fall along a line or curve.
In graphing equations, we assume the domain is all real numbers, unless otherwise stated. Often times though, when we look at data in a table, the domain will be whole numbers (number of presents,
number of days, etc.) and the function will be discrete. Sometimes the graph is still shown as a continuous line to make it easier to interpret. Be aware of the difference between discrete and
continuous functions as you work through the examples.
Example 6
Sarah is thinking of the number of presents she receives as a function of the number of friends who come to her birthday party. She knows she will get a present from her parents, one from her
grandparents and one each from her uncle and aunt. She wants to invite up to ten of her friends, who will each bring one present. She makes a table of how many presents she will get if one, two,
three, four or five friends come to the party. Plot the points on a coordinate plane and graph the function that links the number of presents with the number of friends. Use your graph to determine
how many presents she would get if eight friends show up.
Number of Friends Number of Presents
The first thing we need to do is decide how our graph should appear. We need to decide what the independent variable is, and what the dependant variable is. Clearly in this case, the number of
friends can vary independently (the domain). The number of presents must depend on the number of friends who show up (the range).
We will therefore plot friends on the $x-$$y-$
No. of friends $(x)$ no. of presents $(y)$ coordinates $(x, y)$
0 4 (0, 4)
1 5 (1, 5)
2 6 (2, 6)
3 7 (3, 7)
4 8 (4, 8)
5 9 (5, 9)
Next we need to set up our axes. It is clear that the number of friends and number of presents both must be positive, so we do not need to worry about anything other than Quadrant I. We need to
choose a suitable scale for the $x$$y$little extra room on your graph. We also need the $y$
The scale of the graph on the right shows room for up to 12 friends and 15 presents. This will be fine, but there are many other scales that would be equally as good!
Now we proceed to plot the points. The first five points are the coordinates from our table. You can see they all lay on a straight line, so the function that describes the relationship between $x$
$y$linear. To graph the function, we simply draw a line that goes through all five points. This line represents the function.
This is a discrete problem since Sarah can only invite a whole numbers of friends. For instance, it would be impossible for 2.4 friends to show up. Keep in mind that the only permissible points for
the function are those points on the line which have integer $x$$y$
The graph easily lets us find other values for the function. For example, the question asks how many presents Sarah would get if eight friends come to her party. Don't forget that $x$$y$$x=8$$y$
If 8 friends show up, Sarah will receive a total of 12 presents.
Graph a Function Given a Rule
If we are given a rule instead of a table, we can proceed to graph the function in one of two ways. We will use the following example to show each way.
Example 7
Ali is trying to work out a trick that his friend showed him. His friend started by asking him to think of a number. Then double it. Then add five to what he got. Ali has written down a rule to
describe the first part of the trick. He is using the letter $x$$y$
Help him visualize what is going on by graphing the function that this rule describes.
Method One - Construct a Table of Values
If we wish to plot a few points to see what is going on with this function, then the best way is to construct a table and populate it with a few $x, y$$x$
$x$ $y$
0 $2\cdot 0 + 5 = 0 + 5 = 5$
1 $2\cdot 1+ 5 = 2 + 5 = 7$
2 $2\cdot 2 + 5 = 4 + 5 = 9$
3 $2\cdot 3 + 5 = 6 + 5 = 11$
Next, we plot the points and join them with our line.
This method is nice and simple. Plus, with linear relationships there is no need to plot more than two or three points. In this case, the function is continuous because the domain (the number Ali is
asked to think of) is all real numbers, even though he may only be thinking of positive whole numbers.
Method Two - Intercept and Slope
One other way to graph this function (and one that we will learn in more detail in the next lesson) is the slope-intercept method. To do this, follow the following steps:
1. Find the $y$$x=0$
$y(0) = 2\cdot 0 + 5 = 5$So our $y-$ (0, 5)
2. Look at the coefficient multiplying the $x$
Every time we increase $x$$y$
3. Plot the line with the given slope that goes through the intercept. We start at the point (0, 5) and move over one in the $x$$y$
We will properly examine this last method in the next lesson!
Lesson Summary
• The coordinate plane is a two-dimensional space defined by a horizontal number line (the $x-$axis) and a vertical number line (the $y-$axis). The origin is the point where these two lines meet.
Four areas, or quadrants, are formed as shown in the diagram at right.
• Each point on the coordinate plane has a set of coordinates, two numbers written as an ordered pair which describe how far along the $x-$$y-$$x-$coordinate is always written first, then the $y-$
coordinate. Here is an exaxmple $(x, y)$
• Functions are a way that we can relate one quantity to another. Functions can be plotted on the coordinate plane.
Review Questions
1. Identify the coordinates of each point, $A - F$
2. Plot the following points on a graph and identify which quadrant each point lies in:
1. (4, 2)
2. (-3, 5.5)
3. (4, -4)
4. (-2, -3)
3. The following three points are three vertices of square $ABCD$$D$$A (-4, -4)\! \\B (3, -4)\! \\C (3, 3)$
4. Becky has a large bag of M&Ms that she knows she should share with Jaeyun. Jaeyun has a packet of Starburst. Becky tells Jaeyun that for every Starburst he gives her, she will give him three M&Ms
in return. If $x$$y$
1. Write an algebraic rule for $y$$x$
2. Make a table of values for $y$$x$
3. Plot the function linking $x$and $y$$\{ 0 \leq x \leq 10 \}, \{0 \leq y \leq 10 \}$
Review Answers
1. $A (5, 6) \quad B (-5, 5) \quad C (-2, 3) \quad D (-2, -2) \quad E(3, -4) \quad F(2, -6)$
1. Quadrant I
2. Quadrant II
3. Quadrant IV
4. Quadrant III
4. (a) $y = 3x$
$x$ $y$
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Mathematica discrete functions
April 29th 2012, 08:33 PM
Mathematica discrete functions
What I want to be able to do with Mathematica is define a discrete function with a discrete domain and range that I create and designate. For example:
$A = \{a, b, c, d\}$
$B = \{1, 2, 9, \pi\}$
$f: A \rightarrow B$
$f(x) = \begin{cases} 1 &\text{ if }x = a\\2 &\text{ if }x = c\\ \pi &\text{ if }x = b\\ 9 &\text{ if }x = d \end{cases}$
So that when I type f[a] in Mathematica, it spits out 1, f[b] spits out $\pi$, etc.
I have plowed through the DC trying to find out how to do something like this, and although I discovered a lot of neat things you can do involving functions with Mathematica, I could not find how
to do something as simple as this.
Thanks for any help!
April 29th 2012, 09:59 PM
Re: Mathematica discrete functions
You are talking about piecewise defined functions - so use
April 30th 2012, 07:18 AM
Re: Mathematica discrete functions
In[1]:= f[x_]:=Which[x===a,1,x===b,Pi,x===c,2,x===d,9];f[d]
Out[2]= 9
In[3]:= A={a,b,c,d};B={1,Pi,2,9};f[x_]:=x/.Thread[Rule[A,B]];f[d]
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Why use games as activities in your Maths class?
There are online and computer games that can help your kids learn more about math. These games will not only make math more fun for your kids, they can also help your kids become more familiar with
basic computer operations. There are also math computer games that are designed for the whole family so you can play with your children as they learn more about mathematics.
Many of these math games are available through the internet. Some other games are sold as games for Wii. It is really your choice which games to choose for the learning needs of your kids.
Below are some examples of games which will build Mathematics skills. Enjoy!
Mathematics games for Wii
• Be sure & check this- Mathsduck.co.uk-: Mathematics games for ages 9-15 can be used with #WiiMote http://j.mp/gtLZEm
• WiiMaths: A wiki with examples of Wii games which will build Maths skills http://wiimaths.wikispaces.com/
• Sums: Free sample games for Nintendo Wii, which will build Maths skills (full games must be purchased) http://www.wsums.com/
• Some examples of games which can build Mathematics skills, and can be played on Wii http://www.ehow.com/facts_5201674_math-games-wii.html
• Check these out! Free games, teachers can keep records of student outcomes, and it is all online! http://www.arcademicskillbuilders.com/
• Clever Kids: A book which contain information of Maths games for Wii http://www.amazon.co.uk/Midas-Interactive-Clever-Kids-Maths/dp/B001PO5I5W (You have to purchase the book)
• My favorite site for math is Arcademic Skill Buildershttp://bit.ly/3KeXyK Kids love racing each other with math facts
Mathematics Games Online
* Note: Scroll down for a huge list of games you can use in Maths class...have fun!
Duplicon Shape game: Work at your shapes! Mini Pool Game: Work at your angles!
1. HUGE list: Fantastic interactive Maths/Numeracy games and activities http://jmathpage.com
2. Free games, teachers can keep records of student outcomes, and it is all online! http://www.arcademicskillbuilders.com/
3. Make my Number: cool number game from Michael Ymer http://www.edgalaxy.com/numeracy/2011/2/16/make-my-number-choosing-and-using-operations-equations.html
4. Place value dominoes http://www.gather.com/viewArticle.action?articleId=281474978377084
5. Math Games - Free & Fun Interactive Games for Kids http://bit.ly/d2XxwY
6. Maths online practice in grades and topics, gives immediate feedback and tracks scores http://www.ixl.com
7. Educational Videos and Games for Kids about Science, Math, Social Studies and English: http://www.neok12.com/
8. Woodlands site: Click on the Maths zone icon for interactive games http://www.woodlands-junior.kent.sch.uk/
9. Copacabana site: Stacks of interactive games for every year level and every subject http://www.copacabana-p.schools.nsw.edu.au/Get_Smart_Pages/Get_Smart.htm
10. Multiplication and Division memory games http://www.gather.com/viewArticle.action?articleId=281474978391533
11. Great interactive brain games, updated on regular basis http://coolmathgames.seoconnect.net/fullscreen/
12. That Quiz: Practice your Maths skills, get feedback That Quiz - Math Test Activities http://www.thatquiz.org/
13. Cool Maths sites http://cte.jhu.edu/techacademy/web/2000/heal/mathsites.htm
14. TopicBox: Wow! great Maths activities and interactives here http://www.topicbox.org.uk/Maths/
15. FUSE Maths games and activities https://fuse.education.vic.gov.au/pages/Results.aspx?d=discipline%2fmathematics&sb=KBNGStarRating+DESC%2c+KBNGModified+DESC%2c+Rank+DESC
16. Wishball! Fantastic game to learn about placevalue Whole Numbers: http://www.southmoor.vic.edu.au/HandyLinks/KLAs/Maths/Wishball/index.html , http://intranet.kngplism.catholic.edu.au/
learnObjects/Wishball%20challenge%20hundredths/index.html http://students.stcolumba.com.au/vlib/V%20learning%20objects/webpages/maths_num/number/wishball.htm
17. Wishball: Hundredths https://fuse.education.vic.gov.au/pages/View.aspx?id=a63ccd67-fe13-442d-8597-742a99acb54f
18. Wishball: Thousandths https://fuse.education.vic.gov.au/content/04d6048e-455f-4716-bfb8-a3e256bd0796/p/index.html
19. National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vLibrary.html
20. Interactive lessons, numeracy and literacy, free flashcards, printables http://www.learningtoday.com/corporate/teacher-resources.asp
21. Coolmath4kids: http://www.coolmath4kids.com
22. Action Fraction Game: http://funschool.kaboose.com/formula-fusion/number-fun/games/game_action_fraction.html
23. Number Nut http://numbernut.com/index.html
24. Cool Maths games and info http://www.coolmath.com/
25. Funschool http://funschool.kaboose.com/index.html
26. Kaboose http://resources.kaboose.com/games/
27. Fun games, worksheets, flashcards, Maths careers etc. http://www.xpmath.com/index.php
28. Primary Games http://www.primarygames.com/math.htm
29. Interactive games and resources under the strands of Maths http://mathematics.hellam.net/
30. Arcade style games with Maths applications (multiply, divide, add subtract while racing or shooting aliens!) http://www.arcademicskillbuilders.com/games/
31. Interactive games and drills under the strands http://www.woodlands-junior.kent.sch.uk/maths/
32. Online Maths resource blog: http://onlinemaths.globalteacher.org.au/
33. Maths games and interactives random list http://members.optusnet.com.au/~borishandal/MathsInternetGuide/SearchGeneral.htm
34. Multiplication games and worksheets http://www.woodlands-junior.kent.sch.uk/maths/timestable/index.html
35. Times tables games http://www.woodlands-junior.kent.sch.uk/maths/timestable/interactive.htm and interactive games http://www.woodlands-junior.kent.sch.uk/maths/timestable/interactive.htm
36. Mathionaire http://www.woodlands-junior.kent.sch.uk/maths/mathionaire/index.htm
37. Maths Olympics http://www.mathplayground.com/olympic_math1.html
38. Count Down http://www.woodlands-junior.kent.sch.uk/maths/countdown/index.htm
39. Broken Calculator investigation http://www.woodlands-junior.kent.sch.uk/maths/broken-calculator/index.htm
40. Hi Lo Cards http://www.woodlands-junior.kent.sch.uk/maths/higher-lower/index.htm
41. Leapfrogs http://www.woodlands-junior.kent.sch.uk/maths/leapfrog/index.htm
42. Measuring jugs http://www.woodlands-junior.kent.sch.uk/maths/jugs/index.htm
43. Tower of Hanoi http://www.woodlands-junior.kent.sch.uk/Games/lengame/tower.html
44. Lemonade Stand http://www.woodlands-junior.kent.sch.uk/Games/educational/maths/index.html
45. Dominoes to print and make http://www.senteacher.org/Worksheet/22/Dominoes.xhtml
46. Create Follow me loops http://www.senteacher.org/Worksheet/46/Loopcards.xhtml
47. Interactive games http://www.vtaide.com/png/puzzles.htm
48. Free games to download http://www.senteacher.org/Files/
49. Printables, colouring pages, mazes, posters etc. http://nicholasacademy.com/math.html
50. Whiteboard games or just for fun: http://www.subtangent.com/maths/games.php
51. Maths hangman http://www.quia.com/hm/26073.html
52. Jumbled Maths words http://www.quia.com/jw/12748.html?AP_rand=1131490249
53. Pentominoes, Magic Squares, Tangrams, Data:http://www.mathsphere.co.uk/fun/
54. http://www.superkids.com/aweb/tools/logic/: Battleships, Chinese Checkers, Tic Tac Toe, Towers of Hanoi, Peg, Paddocs/Connect-the-squares, Four-in-a-row, etc.
55. Algebra Games: http://www.squidoo.com/algebragames
56. Decimal Squares Interactive Games:http://www.decimalsquares.com/dsGames/
57. Dreambox: Maths calendar for July http://2pl.us/1kJ
58. Lots of different interactive games and linkshttp://students.stcolumba.com.au/vlib/V%20learning%20objects/webpages/maths.htm
59. Heaps of options here, games under each headinghttp://www.onlinemathlearning.com/measurement-games.html
60. Good selection of interactive Maths games for different year levels and in different strands of Maths http://www.copacabana-p.schools.nsw.edu.au/Get_Smart.htm
61. Great sites to use with Smartboardhttp://www.juliethompson.com/SMART.html
62. Measurement and other games, you can test yourself etc.http://www.subtangent.com/maths/games.php
63. Interactive Sudokuhttp://www.diigo.com/annotated/29a8ba7c65f3e0fb1b15a60011ffe4cd and http://www.jigsawdoku.com/
64. Maths Fraction game using “Baking Cookies” http://ow.ly/jrSC
65. Dartboard, missing number (also worksheets and songs)http://www.bbc.co.uk/schools/numbertime/games/index.shtml
66. CBeebies Numberjacks:http://www.bbc.co.uk/cbeebies/numberjacks/Lots of number games to play from dominoes to sudoku, plus songs to listen to puzzles.
67. CBeebies Grown-ups: http://www.bbc.co.uk/cbeebies/grownups/A range of resources designed for use by parents to help children fulfil their potential in all areas of their development. Also
including special educational needs activities, technical information and a regular newsletter.
68. Algebra games…many to choose fromhttp://www.mathsisfun.com/algebra/index.html
69. All Content in Geometry for Perimeter, area, and volume http://mathforum.org/mathtools/cell/g,10.12,ALL,ALL/
70. Children’s Money World:http://www.childrensmoneyworld.com/Teachers of reception and key stage 1 can download lesson plans and resources here on the subject of money. Registration is free.
There are also fun games for your class inluding Mother Pound’s Memory Game!
71. Range of interactive maths games The Primary Games Series provides a wide range of highly engaging and enjoyable maths games which allow children to learn while having fun. Whether used
individually or as a whole class resource with an Interactive Whiteboard (such as SMART or PROMETHEAN boards), they are guaranteed to stimulate and motivate whilst meeting lesson
72. English Money games http://www.teachingmoney.co.uk/
73. Tables e.g. Bingo game http://www.teachingtables.co.uk/
74. Primary Resources: http://www.primaryresources.co.uk/Worksheets, lesson plans and ideas are gathered together here covering the full primary school curriculum.
75. Some games explained http://orion.math.iastate.edu/danwell/MathNight/oldhomepage.html
76. Teaching Time: http://www.teachingtime.co.uk/Ideal for use as part of the national numeracy strategy, this site has a collection of worksheets and games on the subject of telling the time.
Children will learn to read both the digital and analogue clocks.
77. http://labyrinth.thinkport.org/www/index.php Lure of the Labyrinth is a digital game for middle-school pre-algebra students. It includes a wealth of intriguing math-based puzzles wrapped into
an exciting narrative game in which students work to find their lost pet – and save the world from monsters! Linked to both national and state mathematics standards, the game gives students a
chance to actually think like mathematicians. In the world of Lure of the Labyrinth, students progress through three sections, or “wings.” Each is related to a different math strand that is
part of a the typical pre-algebra curriculum: Proportions (including fractions and ratios), Variables and Equations, Number and Operations (including geometry, order of operations and modular
82. Math games in year levels
Games 3 Games 2 Games 4
Games 1 http://www.mathsisfun.com/puzzles/index.html Puzzle Games
Jigsaws: http://www.mathsisfun.com/puzzles/jigsaw-puzzles-index.html
Khan Academy Presents: Using what we know to solve for angles in the Angle Game. (09:00) Khan Academy Presents: More examples of the Angle Game. (09:48) Video Brain Teaser - Part 52: Videos that
provide viewers with brain teasers/mental puzzles. These may consist of problems dealing with the arrangement of matchsticks, coins, and other items. May include pencil drawing games, optical
illusions, hidden ima (00:45) Video Brain Teaser - Part 51: Videos that provide viewers with brain teasers/mental puzzles. These may consist of problems dealing with the arrangement of matchsticks,
coins, and other items. May include pencil drawing games, optical illusions, hidden ima (00:44) Video Brain Teaser - Part 50: Videos that provide viewers with brain teasers/mental puzzles. These may
consist of problems dealing with the arrangement of matchsticks, coins, and other items. May include pencil drawing games, optical illusions, hidden ima (00:44) | {"url":"http://mathsyear7.wikispaces.com/Games?responseToken=0e6bf9f11e10e14d0ef02496ab950e64a","timestamp":"2014-04-16T16:10:54Z","content_type":null,"content_length":"97305","record_id":"<urn:uuid:31602b30-1cc3-4e5f-aaa7-46e2c70934cc>","cc-path":"CC-MAIN-2014-15/segments/1397609524259.30/warc/CC-MAIN-20140416005204-00185-ip-10-147-4-33.ec2.internal.warc.gz"} |
Test (LaTex Practice)
May 15th 2010, 07:39 PM
Test (LaTex Practice)
x squared - i = 0
What symbol(s) is(are) needed to make Delimiters (. . .) bigger to completely encompass fraction?
May 16th 2010, 03:10 AM
Either you can just choose bigger ones, like \big( and \big), or \Big( and \Big), or \Big[ and \Big].
Or you can use pairs of \left( and \right) or \left[ and \right] that will be resized automatically to the height of the expression that is contained in them, like this | {"url":"http://mathhelpforum.com/latex-help/144933-test-latex-practice-print.html","timestamp":"2014-04-25T02:06:24Z","content_type":null,"content_length":"6443","record_id":"<urn:uuid:015500a7-77be-45a1-bcd2-752c3b7dc3d6>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00567-ip-10-147-4-33.ec2.internal.warc.gz"} |
Lecture #19: Martingales
1. Some definitions
Recall that a martingale is a sequence of r.v.s ${Z_0, Z_1, Z_2, \ldots}$ (denoted by ${(Z_i)}$) if each ${Z_i}$ satisfies ${E[|Z_i|] < \infty}$, and
$\displaystyle E[Z_i \mid Z_0,...,Z_{i-1}] = Z_{i-1}.$
Somewhat more generally, given a sequence ${(X_i)}$ of random variables, a martingale with respect to ${(X_i)}$ is another sequence of r.v.s ${Z_0, Z_1, Z_2, \ldots}$ (denoted by ${(Z_i)}$) if each $
{Z_i}$ satisfies
• ${E[|Z_i|] < \infty}$,
• there exists functions ${g_i}$ such that ${Z_i = g_i(X_1, X_2, \ldots, X_i)}$, and
• ${E[Z_i \mid X_1, \ldots ,X_{i-1}] = Z_{i-1}}$.
One can define things even more generally, but for the purposes of this course, let’s just proceed with this. If you’d like more details, check out, say, books by Grimmett and Stirzaker, or Durett,
or many others.)
1.1. The Azuma-Hoeffding Inequality
Theorem 1 (Azuma-Hoeffding) If ${(Z_i)}$ is a martingale such that for each ${i}$, ${|Z_i - Z_{i-1}| < c_i}$. Then
$\displaystyle \Pr[|Z_n - Z_0| \geq \lambda] \leq 2\exp\left\{-\frac{\lambda^2}{2 \sum_i c_i^2} \right\}.$
(Apparently Bernstein had essentially figured this one out as well, in addition to the Chernoff-Hoeffding bounds, back in 1937.) The proof of this bound can be found in most texts, we’ll skip it
here. BTW, if you just want the upper or lower tail, replace ${2e^{blah}}$ by ${e^{blah}}$ on the right hand side.
2. The Doob Martingale
Most often, the case we will be concerned with is where our entire space is defined by a sequence of random variables ${X_1, X_2, \ldots, X_n}$, where each ${X_i}$ takes values in the set ${\Omega}$.
Moreover, we will be interested in some bounded function ${f: \Omega^n \rightarrow {\mathbb R}}$, and will want to understand how ${f(X_1, X_2, \ldots, X_n)}$ behaves, when ${(X_i)}$ is drawn from
the underlying distribution. (Very often these ${X_i}$‘s will be drawn from a “product distribution”—i.e., they will be independent of each other, but they need not be.) Specifically, we ask:
How concentrated is ${f}$ around its mean ${E[f] := E_{X_1, X_2, \ldots, X_n}[f(X_1, X_2, \ldots, X_n)]}$?
To this end, define for every ${i \in \{0,1, \ldots, n\}}$, the random variable
$\displaystyle Z_i := E[ f(X) \mid X_1, X_2, \ldots,X_i ].$
(At this point, it is useful to remember the definition of a random variable as a function from the sample space to the reals: so this r.v. ${Z_i}$ is also such a function, obtained by taking
averages of ${f}$ over parts of the sample space.)
How does the random variable ${Z_0}$ behave? It’s just the constant ${E[f]}$: the expected value of the function ${f}$ given random settings for ${X_1}$ through ${X_n}$. What about ${Z_1}$? It is a
function that depends only on its first variable, namely ${Z_1(x_1) = E_{X_2, \ldots, X_n}[f(x_1, X_2, \ldots, X_n)]}$—instead of averaging ${f}$ over the entire sample space, we partition ${\Omega}$
according to value of the first variable, and average over each part in the partition. And ${Z_2}$ is a function of ${x_1, x_2}$, averages over the other variables. And so on to ${Z_n}$, which is the
same as the function ${f}$. So, as we go from ${0}$ to ${n}$, the random variables ${Z_i}$ go from the constant function ${E[f]}$ to the function ${f}$.
Of course, we’re defining this for a reason: ${(Z_i)}$ is a martingale with respect to ${(X_i)}$.
Lemma 2 For a bounded function ${f}$, the sequence ${(Z_i)_{i = 0}^n}$ is a martingale with respect to ${(X_i)}$. (It’s called the Doob martingale for ${f}$.)
Proof: The first two properties of ${(Z_i)}$ being a martingale with respect to ${(X_i)}$ follow from ${f}$ being bounded, and the definition of ${Z_i}$ itself. For the last property,
$\displaystyle \begin{array}{rl} E[Z_i \mid X_1, \ldots X_{i-1}] &= E[\, E[f \mid X_1, X_2, \ldots, X_i] \mid X_1, \ldots X_{i-1} ] \\ &= E[ f \mid X_1, \ldots X_{i-1} ] = Z_{i-1}. \end{array}$
The first equaility is the definition of ${Z_i}$, the second from the fact that ${E[ U \mid V ] = E[ E[ U \mid V, W ] \mid V ]}$ for random variables ${U, V, W}$, and the last from the definition of
${Z_{i-1}}$. $\Box$
Assuming that ${f}$ was bounded was not necessary, one can work with weaker assumptions—see the texts for more details.
Before we continue on this thread, let us show some Doob martingales which arise in CS/Math-y applications.
1. Throw ${m}$ balls into ${n}$ bins, and let ${f}$ be some function of the load: the number of empty bins, the max load, the second-highly loaded bin, or some similar function. Let ${\Omega = [n]}$
, and ${X_i}$ be the index of the bin into which ball ${i}$ lands. For ${Z_i = E[ f \mid X_1, \ldots, X_i ]}$, ${(Z_i)}$ is a martingale with respect to ${(X_i)}$.
2. Consider the random graph ${G_{n,p}}$: ${n}$ vertices, each of the ${\binom{n}{2}}$ edges chosen independently with probability ${p}$. Let ${\chi}$ be the chromatic number of the graph, the
minimum number of colors to properly color the graph. There are two natural Doob martingales associated with this, depending on how we choose the variables ${X_i}$.
In the first one, let ${X_i}$ be the ${i^{th}}$ edge, and which gives us a martingle sequence of length ${\binom{n}{2}}$. This is called the edge-exposure martingale. For the second one, let $
{X_i}$ be the collection of edges going from the vertex ${i}$ to vertices ${1, 2, \ldots, i-1}$: the new martingale has length ${n}$ and is called the vertex exposure martingale.
3. Consider a run of quicksort on a particular input: let ${Q}$ be the number of comparisons. Let ${X_1}$ be the first pivot, ${X_2}$ the second, etc. Then ${Z_i = E[ Q \mid X_1, \ldots, X_i ]}$ is
a Doob martingale with respect to ${(X_i)}$.
BTW, are these ${X_i}$‘s independent of each other? Naively, they might depend on the size of the current set, which makes it dependent on the past. One way you can make these independent is by
letting these ${X_i}$‘s be, say, random independent permutations on all ${n}$ elements, and when you want to choose the ${i^{th}}$ pivot, pick the first element from the current set according to
the permutation ${X_i}$. (Or, you could let ${X_i}$ be a random independent real in ${[0,1]}$ and use that to pick a random element from the current set, etc.)
4. Suppose we have ${r}$ red and ${b}$ blue balls in a bin. We draw ${n}$ balls without replacement from this bin: what is the number of red balls drawn? Let ${X_i}$ be the indicator for whether the
${i^{th}}$ ball is red, and let ${f = X_1 + X_2 + \ldots + X_n}$ is the number of red balls. Then ${Z_i = E[ f \mid X_1, \ldots, X_i ]}$ is a martingale with respect to ${(X_i)}$.
However, in this example, the ${X_i}$‘s are not independent. Nonetheless, the sequence is a Doob martingale. (As in the quicksort example, one can define it with respect to a different set of
variables which are independent of each other.)
So yeah, if we want to study the concentration of ${f}$ around ${E[f]}$, we can now apply Azuma-Hoeffding to the Doob martingale, which gives us the concentration of ${Z_n}$ (i.e., ${f}$) around $
{Z_0}$ (i.e., ${E[f]}$). Good, good.
Next step: to apply Azuma-Hoeffding to the Doob martingale ${(Z_i)}$, we need to bound ${|Z_i - Z_{i-1}|}$ for all ${i}$. Which just says that if we can go from ${f}$ to ${Ef}$ in a “small” number of
steps (${n}$), and each time we’re not smoothing out “too agressively” (${|Z_i - Z_{i-1}| \leq c_i}$), then ${f}$ is concentrated about its mean.
2.1. Indepedence and Lipschitz-ness
One case when it’s easy to bound the ${|Z_i - Z_{i-1}|}$‘s is when the ${X_i}$‘s are independent of each other, and also ${f}$ is not too sensitive in any coordinate—namely, changing any coordinate
does not change the value of ${f}$ by much. Let’s see this in detail.
Definition 3 Given values ${(c_i)_{i =1}^n}$, the function ${f}$ is \underline{${(c_i)}$-Lipschitz} if for all ${j}$ and ${x_j \in \Omega}$, for all ${i \in [n]}$ and for all ${x_i' \in \Omega}$,
it holds that
$\displaystyle |f(x_1, \ldots, x_{i-1}, x_i, x_{i+1}, \ldots, x_n ) - f(x_1, \ldots, x_{i-1}, x_i', x_{i+1}, \ldots, x_n ) | \leq c_i.$
If ${c_i = c}$ for all ${i}$, then we just say ${f}$ is ${c}$-Lipschitz.
Lemma 4 If ${f}$ is ${(c_i)}$-Lipschitz and ${X_1, X_2, \ldots, X_n}$ are independent, then the Doob martingale of ${f}$ with respect to ${(X_i)}$ satisfies
$\displaystyle |Z_i - Z_{i-1}| \leq c_i.$
Proof: Let us use ${X_{(i:j)}}$ to denote the sequence ${X_i, \ldots, X_j}$, etc. Recall that
$\displaystyle \begin{array}{rl} Z_i &= E[ f \mid X_{(1:i)} ] = \sum_{a_{i+1}, \ldots, a_n} f(X_{(1:i)}, a_{(i+1:n)}) \Pr[ X_{(i+1:n)} = a_{(i+1:n)} \mid X_{(1:i)} ] \\ &= \sum_{a_{i+1}, \ldots, a_n}
f(X_{(1:i)}, a_{(i+1:n)}) \Pr[ X_{(i+1:n)} = a_{(i+1:n)} ] \end{array}$
where the last equality is from independence. Similarly for ${Z_{i-1}}$. Hence
$\displaystyle \begin{array}{rl} | Z_i - Z_{i-1} | &= \sum_{a_{i+1}, \ldots, a_n} \bigg| f(X_{(1:i)}, a_{(i+1:n)}) - \sum_{a_i'} \Pr[X_i = a_i'] f(X_{(1:i-1)}, a_i', a_{(i+1:n)}) \bigg| \cdot \Pr[ X_
{(i+1:n)} = a_{(i+1:n)} ] \\ &\le \sum_{a_{i+1}, \ldots, a_n} c_i \cdot \Pr[ X_{(i+1:n)} = a_{(i+1:n)} ] = c_i. \end{array}$
where the inequality is from the fact that changing the ${i^{th}}$ coordinate from ${a_i}$ to ${a_i'}$ cannot change the function value by more than ${c_i}$, and that ${\sum_{a_i'} \Pr[X_i = a_i'] =
1}$. $\Box$
Now applying Azuma-Hoeffding, we immediately get:
Corollary 5 (McDiarmid’s Inequality) If ${f_i}$ is ${c_i}$-Lipschitz for each ${i}$, and ${X_1, X_2, \ldots, X_n}$ are independent, then
$\displaystyle \begin{array}{rl} \Pr[ f - E[f] \geq \lambda ] &\leq \exp\left( - \frac{ \lambda^2 }{2 \sum_i c_i^2 } \right), \\ \Pr[ f - E[f] < \lambda ] &\leq \exp\left( - \frac{ \lambda^2 }{2
\sum_i c_i^2 } \right). \end{array}$
(Disclosure: I am cheating. McDiarmid’s inequality has better constants, the constant ${2}$ in the denominator moves to the numerator.) And armed with this inequality, we can give concentration
results for some applications we mentioned above.
1. For the ${m}$ balls and ${n}$ bins example, say ${f}$ is the number of empty bins: hence ${Ef = n(1-1/n)^m \approx n\,e^{-m/n}}$. Also, changing the location of the ${i^{th}}$ ball changes ${f}$
by at most ${1}$. So ${f}$ is ${1}$-Lipschitz, and hence
$\displaystyle \Pr [ | f - Ef | \geq \lambda ] \leq 2 \exp\left( - \frac{\lambda^2}{2m} \right).$
Hence, whp, ${f \approx n\,e^{-m/n} \pm O(\sqrt{m \log n})}$.
2. For the case where ${\chi}$ is the chromatic number of a random graph ${G_{n,p}}$, and we define the edge-exposure martingale ${Z_i = E[ \chi \mid E_1, E_2, \ldots, E_i ]}$, clearly ${\chi}$ is $
{1}$-Lipschitz. Hence
$\displaystyle \Pr [ | \chi - E\chi | \geq \lambda ] \leq 2 \exp\left( - \frac{\lambda^2}{2\binom{n}{2}} \right)$
This is not very interesting, since the right hand side is ${< 1}$ only when ${\lambda \approx n}$—but the chromatic number itself lies in ${[1,n]}$, so we get almost no concentration at all.
Instead, we could use a vertex-exposure martingale, where at the ${i^{th}}$ step we expose the vertex ${i}$ and its edges going to vertices ${1, 2, \ldots, i-1}$. Even with respect to these
variables, the function ${\chi}$ is ${1}$-Lipschitz, and hence
$\displaystyle \Pr [ | \chi - E\chi | \geq \lambda ] \leq 2 \exp\left( - \frac{\lambda^2}{2n} \right)$
And hence the chromatic number of the random graph ${G_{n,p}}$ is concentrated to within ${\approx \sqrt{n}}$ around its mean.
3. Concentration for Random Geometric TSP
McDiarmid’s inequality is convenient to use, but Lipschitz-ness often does not get us as far as we’d like (even with independence). Sometimes you need to bound ${|Z_i - Z_{i-1}|}$ directly to get the
full power of Azuma-Hoeffding. Here’s one example:
Let ${X_1, X_2, \ldots, X_n}$ be ${n}$ points picked independently and uniformly at random from the unit square ${[0,1]^2}$. Let ${\tau: ([0,1]^2)^n \rightarrow {\mathbb R}}$ be the length of the
shortest traveling salesman tour on ${n}$ points. How closely is ${\tau}$ concentrated around its mean ${E[\tau(X_1, X_2, \ldots, X_n)]}$?
In the HW, you will show that ${E\tau = \Theta(n^{1/2})}$; in fact, one can pin down ${E\tau}$ up to the leading constant. (See the work of Rhee and others.)
3.1. Using McDiarmid: a weak first bound
Note that ${\tau}$ is ${2\sqrt{2}}$-Lipschitz. By Corollary 5 we get that
$\displaystyle \Pr[ |\tau - E\tau| \geq \lambda ] \leq 2 \exp( -\frac{\lambda^2}{16n}).$
If we want the deviation probability to be ${1/poly(n)}$, we would have to set ${\lambda = \Omega(\sqrt{n \log n})}$. Not so great, since this is pretty large compared to the expectation itself—we’d
like a tighter bound.
3.2. So let’s be more careful: an improved bound
And in fact, we’ll get a better bound using the very same Doob martingale ${(Z_i)}$ associated with ${\tau}$:
$\displaystyle Z_i = E[ \tau(X_1, X_2, \ldots, X_n) \mid X_1, X_2, \ldots, X_i ].$
But instead of just using the ${O(1)}$-Lipschitzness of ${\tau}$, let us bound ${|Z_i - Z_{i-1}|}$ better.
Lemma 6
$\displaystyle |Z_i - Z_{i-1}| \leq \min\left\{ 2 \sqrt{2}, \frac{O(1)}{\sqrt{n-i}} \right\}.$
Before we prove this lemma, let us complete the concentration bound for TSP using this. Setting ${c_i = O(1/\sqrt{n-i})}$ gives us ${\sum_i c_i^2 = O(\log n)}$, and hence Azuma-Hoeffding gives:
$\displaystyle \Pr[ |\tau - E\tau| \geq \lambda ] \leq 2 \exp\left( -\frac{\lambda^2}{2\sum_{i} c_i^2}\right) \leq 2 \exp\left( - \frac{\lambda^2}{O(\log n)} \right).$
$\displaystyle \Pr[ | \tau - E\tau | \leq O(\log n) ] \geq 1 - 1/poly(n).$
Much better!
3.3. Some useful lemmas
To prove Lemma 6, we’ll need a simple geometric lemma:
Lemma 7 Let ${x \in [0,1]^2}$. Pick ${k}$ random points ${A}$ from ${[0,1]^2}$, the expected distance of point ${x}$ to its closest point in ${A}$ is ${O(1/\sqrt{k})}$.
Proof: Define the random variable ${W = d(x,A)}$. Hence, ${W \geq r}$ exactly when ${B(x,r) \cap A = \emptyset}$. For ${r \in [0,\sqrt{2}]}$, the area of ${B(x, r) \cap [0,1]^2}$ is at least ${c_0 r^
2}$ for some constant ${c_0}$.
Define ${r_0 = \sqrt{c_0/k}}$. For some ${r = \lambda r_0 \in [0,\sqrt{2}]}$, the chance that ${k}$ points all miss this ball, and hence ${\Pr[ W \geq r = \lambda r_0 ]}$ is at most
$\displaystyle (1 - c_0 r^2)^k = (1 - \lambda^2/k)^k \leq e^{-\lambda^2}.$
Of course, for ${r > \sqrt{2}}$, ${\Pr[W \geq r ] = 0}$. And hence
$\displaystyle E[W] = \int_{r \geq 0} \Pr[ W \geq r ] dr = \sum_{\lambda \in {\mathbb Z}_{\geq 0}} \int_{r \in [\lambda r_0, (\lambda+1)r_0]} \Pr[ W \geq r ] dr \leq \sum_{\lambda \in {\mathbb Z}_{\
geq 0}} (\lambda+1)r_0 \cdot e^{-\lambda^2} \leq O(r_0).$
Secondly, here is another lemma about how the TSP behaves:
Lemma 8 For any set of ${n-1}$ points, ${A = \{x_1, x_2, \ldots, x_{i-1}, x_{i+1}, \ldots, x_n\}}$, we get
$\displaystyle |\tau(A + x_i) - \tau(A + x_i')| \leq 2(d(x_i, A) + d(x_i', A)).$
Proof: Follows from the fact that ${\tau(A + x) \in [TSP(A), TSP(A) + 2d(x, A)]}$, for any ${x}$. $\Box$
3.4. Proving Lemma \ref
OK, now to the proof of Lemma 6. Recall that we want to bound ${|Z_i - Z_{i-1}|}$; since ${\tau}$ is ${2\sqrt{2}}$-Lipschitz, we get ${|Z_i - Z_{i-1}| \leq 2\sqrt{2}}$ immediately. For the second
bound of ${O(1/\sqrt{k - i})}$, note that
$\displaystyle \begin{array}{rl} Z_{i-1} &= E[ \tau(X_1, X_2, \ldots, X_{i-1}, X_i, \ldots, X_n) \mid X_1, X_2, \ldots, X_{i-1} ] \\ &= E[ \tau(X_1, X_2, \ldots, X_{i-1}, \widehat{X}_i, \ldots, X_n)
\mid X_1, X_2, \ldots, X_{i-1} ] \\ &= E[ \tau(X_1, X_2, \ldots, X_{i-1}, \widehat{X}_i, \ldots, X_n) \mid X_1, X_2, \ldots, X_{i} ] \end{array}$
where ${\widehat{X}_i}$ is a independent copy of the random variable ${X_i}$. Hence
$\displaystyle |Z_i - Z_{i-1}| = E[ \tau(X_1, \ldots, X_{i-1}, X_i, \ldots, X_n) - \tau(X_1, \ldots, X_{i-1}, \widehat{X}_i, \ldots, X_n) \mid X_1, X_2, \ldots, X_{i} ].$
Then, if we define the set ${S = X_1, X_2, \ldots, X_{i-1}}$ and ${T = X_{i+1}, \ldots, X_n}$, then we get
$\displaystyle \begin{array}{rl} |Z_i - Z_{i-1}| &= E[ TSP(S \cup T \cup \{X_i\}) - TSP(S \cup T \cup \{\widehat{X}_i\}) \mid X_1, X_2, \ldots, X_{i} ] \\ &\leq E[ 2( d(X_i, S\cup T) + d(\widehat{X}
_i, S\cup T)) \mid X_1, X_2, \ldots, X_{i} ] \\ &\leq E_{\widehat{X}_i, T}[ 2( d(X_i, T) + d(\widehat{X}_i, T)) \mid X_{i} ]. \end{array}$
where the first inequality uses Lemma 8 and the second uses the fact that the minimum distance to a set only increses when the set gets smaller. But now we can invoke Lemma 7 to bound each of the
terms by ${O(1)/\sqrt{|T|} = O(1)/\sqrt{n-i}}$. This completes the proof of Lemma 6.
3.5. Some more about Geometric TSP
For constant dimension ${d>2}$, one can consider the same problems in ${[0,1]^d}$: the expected TSP length is now ${\Theta(n^{1 - 1/d})}$, and using similar arguments, you can show that devations of
${\Omega(t n^{1/2 - 1/d})}$ have probability ${\leq e^{-t^2}}$.
The result we just proved was by Rhee and Talagrand, but it was not the last result about TSP concentration. Rhee and Talagrand subsequently improved this bound to the TSP has subgaussian tails!
$\displaystyle \Pr[ |\tau - E\tau| \geq \lambda ] \leq ce^{-\lambda^2/O(1)} .$
We’ll show a proof of this using Talagrand’s inequality, in a later lecture.
If you’re interested in this line of research, here is a survey article by Michael Steele on concentration properties of optimization problems in Euclidean space, and another one by Alan Frieze and
Joe Yukich on many aspects of probabilistic TSP.
4. Citations
As mentioned in a previous post, McDiarmid and Hayward use martingales to give extremely strong concentration results for QuickSort . The book by Dubhashi and Panconesi (preliminary version here)
sketches this result, and also contains many other examples and extensions of the use of martingales.
Other resources for concentration using martingales: this survey by Colin McDiarmid, or this article by Fan Chung and Linyuan Lu.
Apart from giving us powerful concentration results, martingales and “stopping times” combine to give very surprising and powerful results: see this survey by Yuval Peres at SODA 2010, or these
course notes by Yuval and Eyal Lubetzky. | {"url":"http://cmurandomized.wordpress.com/2011/03/21/lecture-19-martingales/","timestamp":"2014-04-17T06:41:34Z","content_type":null,"content_length":"105488","record_id":"<urn:uuid:15d600d6-cb37-4972-b193-1639d508ff0d>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00271-ip-10-147-4-33.ec2.internal.warc.gz"} |
electricity (physics) :: Dielectrics, polarization, and electric dipole moment
Article Free Pass
The amount of charge stored in a capacitor is the product of the voltage and the capacity. What limits the amount of charge that can be stored on a capacitor? The voltage can be increased, but
electric breakdown will occur if the electric field inside the capacitor becomes too large. The capacity can be increased by expanding the electrode areas and by reducing the gap between the
electrodes. In general, capacitors that can withstand high voltages have a relatively small capacity. If only low voltages are needed, however, compact capacitors with rather large capacities can be
manufactured. One method for increasing capacity is to insert between the conductors an insulating material that reduces the voltage because of its effect on the electric field. Such materials are
called dielectrics (substances with no free charges). When the molecules of a dielectric are placed in the electric field, their negatively charged electrons separate slightly from their positively
charged cores. With this separation, referred to as polarization, the molecules acquire an electric dipole moment. A cluster of charges with an electric dipole moment is often called an electric
Is there an electric force between a charged object and uncharged matter, such as a piece of wood? Surprisingly, the answer is yes, and the force is attractive. The reason is that under the influence
of the electric field of a charged object, the negatively charged electrons and positively charged nuclei within the atoms and molecules are subjected to forces in opposite directions. As a result,
the negative and positive charges separate slightly. Such atoms and molecules are said to be polarized and to have an electric dipole moment. The molecules in the wood acquire an electric dipole
moment in the direction of the external electric field. The polarized molecules are attracted toward the charged object because the field increases in the direction of the charged object.
The electric dipole moment p of two charges +q and −q separated by a distance l is a vector of magnitude p = ql with a direction from the negative to the positive charge. An electric dipole in an
external electric field is subjected to a torque τ = pE sin θ, where θ is the angle between p and E. The torque tends to align the dipole moment p in the direction of E. The potential energy of the
dipole is given by U[e] = −pE cos θ, or in vector notation U[e] = −p · E. In a nonuniform electric field, the potential energy of an electric dipole also varies with position, and the dipole can be
subjected to a force. The force on the dipole is in the direction of increasing field when p is aligned with E, since the potential energy U[e] decreases in that direction.
The polarization of a medium P gives the electric dipole moment per unit volume of the material; it is expressed in units of coulombs per metre squared. When a dielectric is placed in an electric
field, it acquires a polarization that depends on the field. The electric susceptibility χ[e] relates the polarization to the electric field as P = χ[e]E. In general, χ[e] varies slightly depending
on the strength of the electric field, but for some materials, called linear dielectrics, it is a constant. The dielectric constant κ of a substance is related to its susceptibility as κ = 1 + χ[e]/ε
[0]; it is a dimensionless quantity. Table 1 lists the dielectric constants of a few substances.
Dielectric constants of some materials
(at room temperature)
material dielectric constant
vacuum 1.0
air 1.0006
oil 2.2
polyethylene 2.26
beeswax 2.8
fused quartz 3.78
water 80
calcium titanate 168
barium titanate 1,250
The presence of a dielectric affects many electric quantities. A dielectric reduces by a factor K the value of the electric field and consequently also the value of the electric potential from a
charge within the medium. As seen in Table 1, a dielectric can have a large effect. The insertion of a dielectric between the electrodes of a capacitor with a given charge reduces the potential
difference between the electrodes and thus increases the capacitance of the capacitor by the factor K. For a parallel-plate capacitor filled with a dielectric, the capacity becomes C = Κε[0]A/d. A
third and important effect of a dielectric is to reduce the speed of electromagnetic waves in a medium by the factor √K .
Capacitors come in a wide variety of shapes and sizes. Not all have parallel plates; some are cylinders, for example. If two plates, each one square centimetre in area, are separated by a dielectric
with Κ = 2 of one millimetre thickness, the capacity is 1.76 × 10^−12 F, about two picofarads. Charged to 20 volts, this capacitor would store about 40 picocoulombs of charge; the electric energy
stored would be 400 picojoules. Even small-sized capacitors can store enormous amounts of charge. Modern techniques and dielectric materials permit the manufacture of capacitors that occupy less than
one cubic centimetre and yet store 10^10 times more charge and electric energy than in the above example.
Applications of capacitors
Capacitors have many important applications. They are used, for example, in digital circuits so that information stored in large computer memories is not lost during a momentary electric power
failure; the electric energy stored in such capacitors maintains the information during the temporary loss of power. Capacitors play an even more important role as filters to divert spurious electric
signals and thereby prevent damage to sensitive components and circuits caused by electric surges. How capacitors provide such protection is discussed below in the section Transient response.
Basic phenomena and principles
Many electric phenomena occur under what is termed steady-state conditions. This means that such electric quantities as current, voltage, and charge distributions are not affected by the passage of
time. For instance, because the current through a filament inside a car headlight does not change with time, the brightness of the headlight remains constant. An example of a nonsteady-state
situation is the flow of charge between two conductors that are connected by a thin conducting wire and that initially have an equal but opposite charge. As current flows from the positively charged
conductor to the negatively charged one, the charges on both conductors decrease with time, as does the potential difference between the conductors. The current therefore also decreases with time and
eventually ceases when the conductors are discharged.
In an electric circuit under steady-state conditions, the flow of charge does not change with time and the charge distribution stays the same. Since charge flows from one location to another, there
must be some mechanism to keep the charge distribution constant. In turn, the values of the electric potentials remain unaltered with time. Any device capable of keeping the potentials of electrodes
unchanged as charge flows from one electrode to another is called a source of electromotive force, or simply an emf.
Figure 12 shows a wire made of a conducting material such as copper. By some external means, an electric field is established inside the wire in a direction along its length. The electrons that are
free to move will gain some speed. Since they have a negative charge, they move in the direction opposite that of the electric field. The current i is defined to have a positive value in the
direction of flow of positive charges. If the moving charges that constitute the current i in a wire are electrons, the current is a positive number when it is in a direction opposite to the motion
of the negatively charged electrons. (If the direction of motion of the electrons were also chosen to be the direction of a current, the current would have a negative value.) The current is the
amount of charge crossing a plane transverse to the wire per unit time—i.e., in a period of one second. If there are n free particles of charge q per unit volume with average velocity v and the
cross-sectional area of the wire is A, the current i, in elementary calculus notation, is
where dQ is the amount of charge that crosses the plane in a time interval dt. The unit of current is the ampere (A); one ampere equals one coulomb per second. A useful quantity related to the flow
of charge is current density, the flow of current per unit area. Symbolized by J, it has a magnitude of i/A and is measured in amperes per square metre.
Wires of different materials have different current densities for a given value of the electric field E; for many materials, the current density is directly proportional to the electric field. This
behaviour is represented by Ohm’s law:
The proportionality constant σ[J] is the conductivity of the material. In a metallic conductor, the charge carriers are electrons and, under the influence of an external electric field, they acquire
some average drift velocity in the direction opposite the field. In conductors of this variety, the drift velocity is limited by collisions, which heat the conductor.
If the wire in Figure 12 has a length l and area A and if an electric potential difference of V is maintained between the ends of the wire, a current i will flow in the wire. The electric field E in
the wire has a magnitude V/l. The equation for the current, using Ohm’s law, is
The quantity l/σ[J]A, which depends on both the shape and material of the wire, is called the resistance R of the wire. Resistance is measured in ohms (Ω). The equation for resistance,
is often written as
where ρ is the resistivity of the material and is simply 1/σ[J]. The geometric aspects of resistance in equation (20) are easy to appreciate: the longer the wire, the greater the resistance to the
flow of charge. A greater cross-sectional area results in a smaller resistance to the flow.
The resistive strain gauge is an important application of equation (20). Strain, δl/l, is the fractional change in the length of a body under stress, where δl is the change of length and l is the
length. The strain gauge consists of a thin wire or narrow strip of a metallic conductor such as constantan, an alloy of nickel and copper. A strain changes the resistance because the length, area,
and resistivity of the conductor change. In constantan, the fractional change in resistance δR/R is directly proportional to the strain with a proportionality constant of approximately 2.
A common form of Ohm’s law is
where V is the potential difference in volts between the two ends of an element with an electric resistance of R ohms and where i is the current through that element.
Table 2 lists the resistivities of certain materials at room temperature. These values depend to some extent on temperature; therefore, in applications where the temperature is very different from
room temperature, the proper values of resistivities must be used to calculate the resistance. As an example, equation (20) shows that a copper wire 59 metres long and with a cross-sectional area of
one square millimetre has an electric resistance of one ohm at room temperature.
Electric resistivities
(at room temperature)
material resistivity
silver 1.6 × 10^−8
copper 1.7 × 10^−8
aluminum 2.7 × 10^−8
carbon (graphite) 1.4 × 10^−5
germanium* 4.7 × 10^−1
silicon* 2 × 10^3
carbon (diamond) 5 × 10^12
polyethylene 1 × 10^17
fused quartz >1 × 10^19
*Values very sensitive to purity.
Do you know anything more about this topic that you’d like to share? | {"url":"http://www.britannica.com/EBchecked/topic/182915/electricity/71560/Dielectrics-polarization-and-electric-dipole-moment","timestamp":"2014-04-18T20:36:55Z","content_type":null,"content_length":"133201","record_id":"<urn:uuid:405412ca-05e7-476e-b552-85eb9a57fd20>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00420-ip-10-147-4-33.ec2.internal.warc.gz"} |
Pure implementations of the SHA suite of hash functions. The implementation is basically an unoptimized translation of FIPS 180-2 into Haskell. If you're looking for performance, you probably won't
find it here.
sha1 :: ByteString -> DigestSource
Compute the SHA-1 hash of the given ByteString. The output is guaranteed to be exactly 160 bits, or 20 bytes, long. This is a good default for programs that need a good, but not necessarily
hyper-secure, hash function.
sha224 :: ByteString -> DigestSource
Compute the SHA-224 hash of the given ByteString. Note that SHA-224 and SHA-384 differ only slightly from SHA-256 and SHA-512, and use truncated versions of the resulting hashes. So using 224/384 may
not, in fact, save you very much ...
sha256 :: ByteString -> DigestSource
Compute the SHA-256 hash of the given ByteString. The output is guaranteed to be exactly 256 bits, or 32 bytes, long. If your security requirements are pretty serious, this is a good choice. For
truly significant security concerns, however, you might try one of the bigger options.
sha384 :: ByteString -> DigestSource
Compute the SHA-384 hash of the given ByteString. Yup, you guessed it, the output will be exactly 384 bits, or 48 bytes, long.
sha512 :: ByteString -> DigestSource
For those for whom only the biggest hashes will do, this computes the SHA-512 hash of the given ByteString. The output will be 64 bytes, or 512 bits, long. | {"url":"http://hackage.haskell.org/package/SHA-1.0.2/docs/Data-Digest-Pure-SHA.html","timestamp":"2014-04-24T12:07:57Z","content_type":null,"content_length":"8746","record_id":"<urn:uuid:ad40d1b1-79db-4db7-9b00-98d74c342b24>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00216-ip-10-147-4-33.ec2.internal.warc.gz"} |
RATE - A Mathematica guessing machine
The file rate.m (given the - in this case - unwanted simplification features of the recent versions of Mathematica, I recommend to use rate2.m) allows you to guess a closed form expression (if
existent) for a sequence of numbers, given the first few terms of the sequence. (See the appendix of my paper "Advanced determinant calculus" for explanations of how the program works.)
There are 5 objects provided by the program: Rate, Ratekurz, Rateeins, Rateint, Ratepol.
Rate tries to find a closed form for a sequence within the hierarchy of expressions of the form <rational function>, <product of rational function>, <product of product of rational function>, etc. It
may give several answers.
Ratekurz tries to find a closed form for a sequence within the hierarchy of expressions of the form <rational function>, <product of rational function>, <product of product of rational function>.
(I.e., it searches only within the first 3 levels of the search that is done by Rate.)
Rateeins does the same thing as Ratekurz, with the difference that it immediately exits if one answer is found.
Rateint just tries rational interpolation.
Ratepol just tries (polynomial) interpolation.
You may want to try the examples
Rate[1, 2, 3]
Rate[1, 4, 9, 16]
Rate[1, 3, 6, 10]
Rate[1, 2, 6, 24]
Rate[1, 2, 7, 42, 429, 7436, 218348, 10850216] (alternating sign matrices)
Rateeins, Ratekurz, Rateint, and Ratepol work in the same way.
For users of rate2.m: The function PProduct that features in guessed results stands for "product". Having obtained a result, in case you are interested to see what the simplification procedures of
Mathematica do, you enter
General Hint/Warning: It is (most of the time) wise to first enter just a moderate number of terms. The formula that you are looking forward may not be so complicated, and therefore this moderate
number of terms may already suffice to guess the formula. The more terms you enter, Rate* will try to find higher and higher order formulae, and that may require more time.
If you are looking for something similar within the "q-world", then the file rate.q is exactly the right thing for you. It contains the analogous objects Rateq, Ratekurzq, Rateeinsq, Rateintq und
Here you may want to try
Rateq[1, 1+q, 1+q+q^2, 1+q+q^2+q^3, q]
which explains the syntax. It is the same for Ratekurzq, Rateeinsq, Rateintq, and Ratepolq.
A small excerpt from the German-English Dictionary:
Rate! is German for Guess!
kurz is German for short
eins is German for one
Back to Christian Krattenthaler's home page. | {"url":"http://www.mat.univie.ac.at/~kratt/rate/rate.html","timestamp":"2014-04-19T22:06:57Z","content_type":null,"content_length":"3680","record_id":"<urn:uuid:8bac23be-8c47-4628-b87b-c7064c30363e>","cc-path":"CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00351-ip-10-147-4-33.ec2.internal.warc.gz"} |
Combinations for Casting a Play
Date: 11/15/95 at 21:47:58
From: Anonymous
Subject: Permutations & Combinations
I gave this problem to a class of mine, but I now realize it is tad
more difficult than I first thought. They however, are dying for an
answer. Can you help? I would like to show them the solution using
the fundamental counting principle.
The following shows the lists of people trying out for parts in
the school play. If someone does not get a part they may try out for
another if they have signed up. How many possible casts are there?
Part Ron Alice the butler Grandpa Jones Aunt Minnie
Billy Susan Sam Ralph Debbie
Sam Sally Ralph Peter Alison
Ralph Alison Peter Joe Tamara
Joe Veronica Bob Ruth
Debbie Lisa
Date: 11/19/95 at 14:44:28
From: Doctor Ken
Subject: Re: Permutations & Combinations
Yes, you're right, this problem is kind of hairy. Let me examine the
There are three parts for the boys and two parts for the girls. What we
can do is figure out how many ways there are to cast the boys' roles, and
how many ways there are to cast the girls, and then multiply these two
numbers together to find the total number of casts for the play. So let's
look at the girls' roles first, since I bet they're easiest.
Alice Minnie
Susan Lisa
Sally Tamara
Veronica Ruth
Alison Alison
Debbie Debbie
What we'll do is first treat the problem as if there were five people
trying out for Alice and five _different_ people trying out for Minnie;
then we'll get rid of all the combinations that had one person in two
different parts.
So let's do it: the number of pairs of roles without elimination is
5*5=25, and then there are two we'll have to eliminate: (Alison, Alison)
and (Debbie, Debbie). So the total number of different combinations for
the girls' roles will be 25 - 2 = 23.
The same thinking will apply to the boys' roles, but it will be a little
more complicated. Give it a try though, and see what happens. If
you're still having trouble, write us back and let us know. Good luck!
-Doctor Ken, The Geometry Forum | {"url":"http://mathforum.org/library/drmath/view/56127.html","timestamp":"2014-04-19T22:52:23Z","content_type":null,"content_length":"7302","record_id":"<urn:uuid:9ebce766-5b62-4b36-ab49-84f62df1ad2d>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00394-ip-10-147-4-33.ec2.internal.warc.gz"} |
Field constructions
up vote 2 down vote favorite
If $F$ is a field of characteristic $p$ prime, how can one create a field $K$ such that $K$ is created from $F$ (either by modding out or by taking a product which includes $F$ or by some other
method which involves $F$) such that $K$ has a different characteristic $j \ne p$? Also, does this question depend on $p$? I would also like to consider creations which are field extensions of $F$.
Also, how many of each kind of extension are possible?
5 How about Witt vectors? – Tom Goodwillie Mar 14 '12 at 0:43
Since you allow products of fields, consider $A= \prod_{p} {\mathbf Z}/p{\mathbf Z}$. This ring has characteristic 0: for no positive integer $n$ does $n=0$ in A. Let I be the ideal of elements of
2 A which have finitely many nonzero coordinates. By Zorn's lemma, I is contained in a maximal ideal M of A. What's the characteristic of the field A/M? If it were a prime $p$ then $p=0$ in A/M, so
$p$ is in M. But as a (diagonal) sequence in A, $p$ has all but one nonzero coordinate. Use this and the fact that I is in M to show 1 is in M, which is a contradiction. So char(A/M) = 0. –
KConrad Mar 14 '12 at 1:19
7 You really should read about Witt vectors, as Tom suggests. Although the construction in my previous comment leads to a (nonconstructive) field of char. 0 out of infinitely many fields of
different positive characteristics, Witt vectors are a mathematically more significant way to create fields (well, domains) of characteristic 0 out of finite fields in a good (= functorial)
manner. – KConrad Mar 14 '12 at 1:21
2 I think this question is quite vague. – Martin Brandenburg Mar 14 '12 at 10:11
add comment
3 Answers
active oldest votes
It should be noted that the characteristic of a field is either prime or zero. If it is zero, then it contains the rational numbers. These are two statements you can probably prove even
if algebra isn't your cup of tea.
You can study valuation rings of mixed characteristic. A classic example is $\mathbb{Z}_p$ the p-adic integers. This is a ring of characteristic 0 and its fraction field $\mathbb{Q}_p$
is a field of characteristic 0. However, $\mathbb{Z}_p$ has a (unique) maximal ideal generated by $(p)\mathbb{Z}_p$ such that $$\mathbb{F}_p \cong \mathbb{Z}_p/(p)\mathbb{Z}_p$$ which is
a finite field of characteristic $p$.
There is the famous Ax-Kochen theorem, which is the following
$$\Pi_\mathcal{F} \mathbb{Q}\_p \cong \Pi_\mathcal{F} \mathbb{F}_p((t))$$
where $\mathcal{F}$ is a non-principal ultra-filter on $\mathbb{N}$. This result depends on the continuum hypothesis. (J. Ax and S. Kochen, Diophantine problems over local fields I,
American Journal of Mathematics,87 (1965), 605–630.)
However, there is also an isomorphism
up vote 4 $$\Pi_\mathcal{F} \mathbb{Z}\_p \cong \Pi_\mathcal{F} \mathbb{F}_p[[t]]$$
down vote
accepted where $\mathcal{F}$ is a non-principal ultrafilter on $\mathbb{N}$, which does not depend on the Continuum Hypothesis, in "Use of Ultrapoducts in Commutative Algebra" by Hans Schoutens,
found here http://www.springer.com/mathematics/algebra/book/978-3-642-13367-1
Witt Vectors allow you to move from pure characteristic (either zero or positive) to mixed characteristic.
Another way of studying different characteristics is through Algebraic Geometry, by thinking of fields of different characteristics as fibers living over primes in $\mathbb{Z}$.
Edit: It occurred to me that an example here might be useful in order to illustrate this point. Given a curve $C$ over a field of characteristic p>0, we know (Winter's theorem) that
there exists a discrete valuation ring (for example, $\mathbb{Z}_p$ of mixed characteristic), call it B, and a family of curves over B. Over the generic fiber, we have a GAGA principle,
which means that things we can define over $\mathbb{C}$ (e.g., fundamental group), we can define over a field of $char(k)=0$. Now using Winter's theorem we can 'transfer' our definitions
from analytic geometry to algebraic geometry over a field of positive characteristic, which gives us new tools when studying number theory.
Finally, there is even an "physical" way to interpret moving between fields. I highly recommend this article of A. Connes on the topic: "Characteristic one, entropy and the absolute
point," Connes & Consani http://arxiv.org/abs/0911.3537
1 I've fixed it, I hope I haven't destroyed any of the mathematical content. – David Roberts Mar 14 '12 at 2:00
Thanks. No, you haven't. – Andrew Stout Mar 14 '12 at 2:17
add comment
"By some other method" is quite vague. If, by modding out, you are thinking of taking a subring and then modding that ring by a maximal ideal (i.e., you obtain $\mathbb{Z}/p\mathbb{Z}$
from the rationals in this way), then it cannot be done.
Call the field $F$, the subring $R$, and the maximal ideal $I$, and assume $F$ has finite characteristic $p$. By definition of subring, the unit of the $R$ is also the unit of $F$. If the
up vote 3 field has characteristic $p$, then $p \cdot 1 = 0$ is also true in the subring, and hence, in the quotient field $R/I$. Thus, the quotient field must also have characteristic $p$ if the
down vote original field does.
By definition, an extension field $K$ of $F$ would then contain $F$ as a subring, so again, they would have to have the same characteristic.
I see from your answer that you cannot change the characteristic of a field by an inner field, by modding out. – Erin K Carmody Mar 14 '12 at 0:47
How many fields can one construct in this way? – Erin K Carmody Mar 14 '12 at 1:10
add comment
Even if you are interested in fields $K$ that are extensions of $F$, you left the door open for something else.
If $K$ is an extension of $F$, then $K$ has the same characteristic $p$ as $F$, because $p$ is the number of terms in the shortest non-trivial identity $1+\cdots+1=0$.
up vote 1 down vote
But you can also start from $F=\mathbb Z/p\mathbb Z$ and build $\mathbb Q_p$, the field of $p$-adic numbers. This one is has characteristic zero. See Dwork's book.
add comment
Not the answer you're looking for? Browse other questions tagged fields or ask your own question. | {"url":"http://mathoverflow.net/questions/91138/field-constructions/91143","timestamp":"2014-04-21T09:50:42Z","content_type":null,"content_length":"69214","record_id":"<urn:uuid:bc5577ba-71de-4567-88c5-009e8f569737>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00448-ip-10-147-4-33.ec2.internal.warc.gz"} |
Self Similarity
August 16th 2010, 11:11 PM #1
Sep 2009
Self Similarity
Hey, I was just wondeirng if anyone has ever come across a formal definition of self similarity. I'm playing around with simple, self-similar objects, and I need to know if I can just say ' this
object is self similar' (provided that its similarity is obvious enough), or if I need to prove self similarity. I've tried to find definitions of this concept on the interent, yet I've not found
any formal definition. Usually, people state that an object A is self similar iff the structure completly or approximiitly preserved in a small part of it.
You can check out the wikipedia page on Hausdorff dimension.
September 11th 2010, 08:51 AM #2 | {"url":"http://mathhelpforum.com/advanced-math-topics/153879-self-similarity.html","timestamp":"2014-04-19T13:16:45Z","content_type":null,"content_length":"31687","record_id":"<urn:uuid:7570b553-94ae-45a6-8abd-9d1e6450c6ce>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00179-ip-10-147-4-33.ec2.internal.warc.gz"} |
exponential base. logarithm.
November 30th 2008, 06:34 PM #1
Nov 2008
exponential base. logarithm.
so working on a few exponential functions. i know that you can make the exponents equal to one another if the bases are the same but what if there is a single variable and the terms are
what i have so far:
$3^{2x}-2*3^{x+5}+3^{10} = 0$
$(3^{2x})(3^{x+5})+3^{10} = 2$
is it correct to move over the 2 to work with the same bases easier?
or is this completely off and i should use logarithm and natural log? if so, please give hints as to how to work it out.
Last edited by ninjuhtime; November 30th 2008 at 08:16 PM.
Hello, ninjuhtime!
What i have so far:
$3^{2x}-2\cdot3^{x+5}+3^{10} \:= \:0$
$(3^{2x})(3^{x+5})+3^{10} = 2$ . . . . Definitely illegal!
It's hard to see it, but the expression is a perfect square . . .
We have: . $\left(3^x - 3^5\right)^2 \:=\:0 \quad\Rightarrow\quad 3^x - 3^5 \:=\:0 \quad\Rightarrow\quad 3^x \:=\:3^5 \quad\Rightarrow\quad\boxed{ x \:=\:5}$
thankyou! i guess i oversaw what it was since long problems are usually intimidating.
November 30th 2008, 07:14 PM #2
Super Member
May 2006
Lexington, MA (USA)
November 30th 2008, 08:15 PM #3
Nov 2008 | {"url":"http://mathhelpforum.com/algebra/62524-exponential-base-logarithm.html","timestamp":"2014-04-24T00:22:28Z","content_type":null,"content_length":"36328","record_id":"<urn:uuid:81f9e0d4-a654-427a-a4dd-ad117c26533b>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00138-ip-10-147-4-33.ec2.internal.warc.gz"} |
String theory
Critical string models
Extended objects
Topological strings
The theory of 11-dimensional supergravity contains a higher gauge field – the supergravity C-field – that naturally couples to higher electrically charged 2-branes (membranes). By a process called
double dimensional reduction, these are related to superstrings (Bergshoeff-Sezgin-Townsend 87).
When in (Witten95) it was argued that the 10-dimensional target space theories of the five types of superstring theories are all limiting cases of one single 11-dimensional target space theory that
extends 11-dimensional supergravity (M-theory), it was natural to guess that this supergravity membrane accordingly yields a 3-dimensional sigma-model that reduces in limiting cases to the string
But there were two aspects that make this idea a little subtle, even at this vague level: first, there is no good theory of the quantization of the membrane sigma-model, as opposed to the well
understood quantum string. Secondly, Secondly, that hypothetical “theory extending 11-dimensional supergravity” (“M-theory”) has remained elusive enough that it is not clear in which sense the
membrane would relate to it in a way analogous to how the string relates to its target space theories (which is fairly well understood).
Later, with the BFSS matrix model some people gained more confidence in the idea, by identifying the corresponding degrees of freedom in a special case (Nicolai-Helling 98).
In a more modern perspective, the M2-brane worldvolume theory appears under AdS4-CFT3 duality as a holographic dual of a 4-dimensional Chern-Simons theory. Indeed, its Green-Schwarz action functional
is entirely controled by the super-Lie algebra 4-cocycle of super Minkowski spacetime given by the brane scan. This exhibits the M2-brane worldvolume theory as a 3-dimensional higher WZW model?.
M2-branes at orbifold fixed points – BLG and ABJM
In some situations stacks of M2-branes are accurately described by ABJM theory of the BLG model.
AdS4-CFT3 duality
Under AdS-CFT duality the M2-brane is given by AdS4-CFT3 duality. (Maldacena 97, section 3.2, Klebanov-Torri 10).
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
brane in supergravity charged under gauge field has worldvolume theory
black brane supergravity higher gauge field SCFT
D-brane type II RR-field super Yang-Mills theory
$(D = 2n)$ type IIA $\,$ $\,$
D0-brane $\,$ $\,$ BFSS matrix model
D2-brane $\,$ $\,$ $\,$
D4-brane $\,$ $\,$ D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane $\,$ $\,$
D8-brane $\,$ $\,$
$(D = 2n+1)$ type IIB $\,$ $\,$
D1-brane $\,$ $\,$ 2d CFT with BH entropy
D3-brane $\,$ $\,$ N=4 D=4 super Yang-Mills theory
D5-brane $\,$ $\,$ $\,$
D7-brane $\,$ $\,$ $\,$
D9-brane $\,$ $\,$ $\,$
(p,q)-string $\,$ $\,$ $\,$
(D25-brane) (bosonic string theory)
NS-brane type I, II, heterotic circle n-connection $\,$
string $\,$ B2-field 2d SCFT
NS5-brane $\,$ B6-field little string theory
M-brane 11D SuGra/M-theory circle n-connection $\,$
M2-brane $\,$ C3-field ABJM theory, BLG model
M5-brane $\,$ C6-field 6d (2,0)-superconformal QFT
M9-brane/O9-plane heterotic string theory
topological M2-brane topological M-theory C3-field on G2-manifold
topological M5-brane $\,$ C6-field on G2-manifold
solitons on M5-brane 6d (2,0)-superconformal QFT
self-dual string self-dual B-field
3-brane in 6d
Early speculations trying to model the electron by a relativistic membrane are due to Paul Dirac:
• Paul Dirac, An Extensible Model of the Electron, Proc. Roy. Soc. A268, (1962) 57-67.
• Paul Dirac, Motion of an Extended Particle in the Gravita- tional Field, in Relativistic Theories of Gravitation, Proceedings of a Conference held in Warsaw and Jablonna, July 1962, ed. L.
Infeld, P. W. N. Publishers, 1964, Warsaw, 163-171; discussion 171-175
• Paul Dirac, Particles of Finite Size in the Gravitational Field, Proc. Roy. Soc. A270, (1962) 354-356.
The Green-Schwarz sigma-model-type formulation of the supermembrane (as in the brane scan) appears in
and its quantization was first explored in
• B. de Wit, Jens Hoppe, Hermann Nicolai, On the Quantum Mechanics of Supermembranes, Nucl. Phys. B305 (1988) 545.
• B. de Wit, W. Lüscher, Hermann Nicolai, The supermembrane is unstable, Nucl. Phys. B320 (1989) 135.
The interpretation of the membrane as as an object related to string theory, hence as the M2-brane was proposed in
around the time when M-theory was envisioned in
The interpretation of the M2-brane worldvolume theory as realted to the matrix model of D0-branes is discussed in some detail in
• Hermann Nicolai, Robert Helling, Supermembranes and M(atrix) Theory, Lectures given by H. Nicolai at the Trieste Spring School on Non-Perturbative Aspects of String Theory and Supersymmetric
Gauge Theories, 23 - 31 March 1998 (arXiv:hep-th/9809103)
• Arundhati Dasgupta, Hermann Nicolai, Jan Plefka, An Introduction to the Quantum Supermembrane, Grav.Cosmol.8:1,2002; Rev.Mex.Fis.49S1:1-10, 2003 (arXiv:hep-th/0201182)
Meanwhile AdS-CFT duality was recognized in
where a dual description of the worldvolume theory of M2-brane appears in seciton 3.2. More on this is in
Other recent developments are discussed in
Formulations of multiple M2-branes on top of each other are given by the BLG model and the ABJM model. See there for more pointers. The relation of these to the above is discussed in section 3 of
Discussion of general phenomena of M-branes in higher geometry and generalized cohomology is in
Discussion from the point of view of Green-Schwarz action functional-∞-Wess-Zumino-Witten theory is in
The role of and the relation to duality in string theory of the membrane is discussed in the following articles.
Relation to T-duality:
• J.G. Russo, T-duality in M-theory and supermembranes (arXiv:hep-th/9701188)
• M.P. Garcia del Moral, J.M. Pena, A. Restuccia, T-duality Invariance of the Supermembrane (arXiv:1211.2434)
Relation to U-duality: | {"url":"http://www.ncatlab.org/nlab/show/M2-brane","timestamp":"2014-04-21T02:02:10Z","content_type":null,"content_length":"63790","record_id":"<urn:uuid:920dfffe-82d8-4819-aaa5-df81692738f2>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00638-ip-10-147-4-33.ec2.internal.warc.gz"} |
Volume of Solids of Revolution
July 27th 2005, 05:01 AM #1
Jul 2005
Volume of Solids of Revolution
This question has been taxing me for some time. I am a first year Mathematics student in London and for some reason am struggling with the substitution needed to answer this question.
Find the volume of the solid of revolution obtained when the region undr the graph of f(x)= (1/x)sec(1/x), from x=3/pi to x=4/pi, is rotated about the x-axis. Give your answers to 2 decimal
Can anyone give me a breakdown of the answer please?
Find the volume of the solid of revolution obtained when the region undr the graph of f(x)= (1/x)sec(1/x), from x=3/pi to x=4/pi, is rotated about the x-axis. Give your answers to 2 decimal
Lets see... When you have an integrable function $f(x), x \ \in [a,b]$, then the volume of the solid obtained by rotation about the x-axis is given by
$V=\pi \int_a^b f^2(x)dx.$ (1)
In this case, you will need to find the value of $\pi\int_{\frac{3}{\pi}}^{\frac{4}{\pi}} \frac{1}{x^2 \cos^2(\frac{1}{x})} \ dx.$
There are math packages than can save you the bother, but I guess they ask of you, to calculate by numerical integration. If this is the case, search your textbook for the appropriate method, or
ask again if I talk crap.
Note: (1) holds true. (BO-RING...
Consider a partition $(x_i), 1\leq i\leq n$ of [a,b], and intermediate points $x_{i-1}\leq\xi_i\leq x_i$. In revolving the function, we obtain n-1 elementary volumes of cylinders, with height
$x_i-x_{i-1}$, radious $f(\xi_i)$ and -therefore- volume $\pi f^2(\xi_i)(x_i-x_{i-1})$. Adding up, we get the Riemmanian sum
$\sum_{i=1}^{n}\pi f^2(\xi_i)(x_i-x_{i-1}) \rightarrow \int_a^b\pi f^2(x)dx$ as $n\rightarrow\infty$, due to integrability.
Last edited by Rebesques; July 27th 2005 at 10:38 AM.
Thank you very much for your timely response. I can see the need to substitute (1/x) in the integrand to get pi(-tan(1/x)dx as my answer.
You are right!
$<br /> \int_{\frac{3}{\pi}}^{\frac{4}{\pi}} \frac{1}{x^2 \cos^2(\frac{1}{x})} \ dx = -\int_{\frac{3}{\pi}}^{\frac{4}{\pi}} d\left\{\tan (\frac{1}{x})\right\} \ dx,<br />$
and childsplay henceforth...
July 27th 2005, 07:30 AM #2
July 27th 2005, 10:34 AM #3
Jul 2005
July 27th 2005, 11:39 AM #4 | {"url":"http://mathhelpforum.com/calculus/661-volume-solids-revolution.html","timestamp":"2014-04-21T00:58:17Z","content_type":null,"content_length":"41229","record_id":"<urn:uuid:214407e2-9f27-4013-a178-4989ccec7f1e>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00442-ip-10-147-4-33.ec2.internal.warc.gz"} |
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)
Perturbation theory for evaluation algorithms of arithmetic expressions
Author: F. Stummel
Journal: Math. Comp. 37 (1981), 435-473
MSC: Primary 65G99
MathSciNet review: 628707
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The paper presents the theoretical foundation of a forward error analysis of numerical algorithms under data perturbations, rounding error in arithmetic floating-point operations, and
approximations in 'built-in' functions. The error analysis is based on the linearization method that has been proposed by many authors in various forms. Fundamental tools of the forward error
analysis are systems of linear absolute and relative a priori and a posteriori error equations and associated condition numbers constituting optimal bounds of possible accumulated or total errors.
Derivations, representations, and properties of these condition numbers are studied in detail. The condition numbers enable simple general, quantitative definitions of numerical stability, backward
analysis, well- and ill-conditioning of a problem and an algorithm. The well-known illustration of algorithms and their linear error equations by graphs is extended to a method of deriving condition
numbers and associated bounds. For many algorithms the associated condition numbers can be determined analytically a priori and be computed numerically a posteriori. The theoretical results of the
paper have been applied to a series of concrete algorithms, including Gaussian elimination, and have proved to be very effective means of both a priori and a posteriori error analysis.
• [1] I. Babuška, Numerical Stability in Numerical Analysis, Proc. IFIP-Congress 1968, Amsterdam, North-Holland, Amsterdam, 1969, pp. 11-23.
• [2] Ivo Babuška, Numerical stability in problems of linear algebra, SIAM J. Numer. Anal. 9 (1972), 53–77. MR 0386252 (52 #7110)
• [3] Ivo Babuška, Milan Práger, and Emil Vitásek, Numerical processes in differential equations, In cooperation with R. Radok. Translated from the Czech by Milada Boruvková, Státní Nakladatelství
Technické Literatury, Prague, 1966. MR 0223101 (36 #6150)
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• [5] F. L. Bauer, Computational graphs and rounding error, SIAM J. Numer. Anal. 11 (1974), 87–96. MR 0356482 (50 #8952)
• [6] F. L. Bauer et al., Moderne Rechenanlagen, Chap. 3, Teubner, Stuttgart, 1964.
• [7] W. S. Brown, A realistic model of floating-point computation, Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1977), Academic Press, New York,
1977, pp. 343–360. Publ. Math. Res. Center, No. 39. MR 0483616 (58 #3605)
• [8] Peter Henrici, Elements of numerical analysis, John Wiley & Sons Inc., New York, 1964. MR 0166900 (29 #4173)
• [9] John Larson and Ahmed Sameh, Efficient calculation of the effects of roundoff errors, ACM Trans. Math. Software 4 (1978), no. 3, 228–236. MR 506787 (80a:65092a), http://dx.doi.org/10.1145/
• [10] Seppo Linnainmaa, Taylor expansion of the accumulated rounding error, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), no. 2, 146–160. MR 0421065 (54 #9070)
• [11] D. D. McCracken & W. S. Dorn, Numerical Methods and Fortran Programming, Wiley, New York, 1964.
• [12] Webb Miller, Software for roundoff analysis, ACM Trans. Math. Software 1 (1975), 108–128. MR 0405830 (53 #9622)
• [13] Webb Miller, Computer search for numerical instability, J. Assoc. Comput. Mach. 22 (1975), no. 4, 512–521. MR 0478584 (57 #18061)
• [14] Webb Miller and David Spooner, Software for roundoff analysis. II, ACM Trans. Math. Software 4 (1978), no. 4, 369–387. MR 513705 (81i:65035), http://dx.doi.org/10.1145/356502.356496
• [15] John R. Rice, A theory of condition, SIAM J. Numer. Anal. 3 (1966), 287–310. MR 0211576 (35 #2454)
• [16] F. Stummel, Fehleranalyse numerischer Algorithmen, Lecture Notes, Univ. of Frankfurt, 1978.
• [17] F. Stummel, Rounding errors in numerical solutions of two linear equations in two unknowns, Math. Methods Appl. Sci. 4 (1982), no. 4, 549–571. MR 681254 (84d:65030), http://dx.doi.org/
• [18] F. Stummel, Rounding error analysis of elementary numerical algorithms, analysis) (Proc. Conf., Tech. Univ. Berlin, Berlin, 1979) Comput. Suppl., vol. 2, Springer, Vienna, 1980, pp. 169–195.
MR 586230 (81m:65065)
• [19] F. Stummel, "Rounding error anlaysis of difference and extrapolation schemes." (To appear.)
• [20] Friedrich Stummel, Rounding error in Gaussian elimination of tridiagonal linear systems. Survey of results, Interval mathematics, 1980 (Freiburg, 1980) Academic Press, New York, 1980, pp.
223–245. MR 651366 (83c:65055)
• [21] F. Stummel, "Rounding error in Gaussian elimination of tridiagonal linear systems. I," SIAM J. Numer. Anal. (Submitted.)
• [22] F. Stummel, "Rounding error in Gaussian elimination of tridiagonal linear systems. II," Linear Algebra Appl. (Submitted.)
• [23] F. Stummel, "Forward error analysis of Gaussian elimination." (To appear.)
• [24] Martti Tienari, On some topological properties of numerical algorithms, Nordisk Tidskr. Informationsbehandling (BIT) 12 (1972), 409–433. MR 0334582 (48 #12901)
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Additional Information
DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0628707-8
PII: S 0025-5718(1981)0628707-8
Keywords: Rounding error analysis, evaluation algorithms, a priori and a posteriori error estimates, condition numbers, linear error equations, graphs
Article copyright: © Copyright 1981 American Mathematical Society | {"url":"http://www.ams.org/journals/mcom/1981-37-156/S0025-5718-1981-0628707-8/","timestamp":"2014-04-20T13:49:44Z","content_type":null,"content_length":"37927","record_id":"<urn:uuid:216d44b1-3ac2-457c-87cb-78a861ea2b13>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00149-ip-10-147-4-33.ec2.internal.warc.gz"} |
Trigonometric Formulas Pdf
Trigonometric Formulas Pdf PDF
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1 Trigonometric addition formulas Trigonometric functions can be interpreted on a unit circle. Unit circle trigonometry,like this,hasonebigadvantageover | {"url":"http://ebookily.org/pdf/trigonometric-formulas-pdf","timestamp":"2014-04-23T10:42:28Z","content_type":null,"content_length":"40971","record_id":"<urn:uuid:e3c9a061-859d-4b09-85c9-6e6895ba8c10>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00112-ip-10-147-4-33.ec2.internal.warc.gz"} |
Multiplying Fractions with Whole Numbers
Multiplying Fractions with Whole Numbers
This fraction worksheet is great for great for working with multiplying fractions with Whole Numbers. The problems may be selected for three different degrees of difficulty. The easiest will
keep the denominators 2, 3, 4, 5, & 10, the numerators between 1 and 9, and the Whole Number between 2 and 10. The hardest will keep the denominators 2 thru 20, numerators between 1 and 19, and
the Whole Numbers between 2 and 30. The answer worksheet will show the progression on how to solve the problems. First rewrite the problem, next multiply the numerators and then the
denominators. Then check to see if we need to simplify or reduce the fraction. This fraction worksheet will generate 10 or 15 fraction addition problems per worksheet.
Numerators 1 thru 9.
Denominators 2, 3, 4, 5, & 10.
Whole Numbers 2 thru 10.
Numerators 1 thru 9.
Denominators 2 thru 10.
Whole Numbers 2 thru 20.
Numerators 1 thru 19.
Denominators 2 thru 20.
Whole Numbers 2 thru 30.
Problem Format to Use
Label problems 2/3 x 15
Label problems 2/3 of 15
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Corresponding Angles
When two lines are crossed by another line (called the Transversal):
The angles in matching corners are called Corresponding Angles.
In this example, these are corresponding angles:
• a and e
• b and f
• c and g
• d and h
Parallel Lines
If the two lines being crossed are Parallel Lines, then the Corresponding Angles are equal.
(Click on "Corresponding Angles" to have them highlighted for you.) | {"url":"http://www.mathsisfun.com/geometry/corresponding-angles.html","timestamp":"2014-04-18T13:53:48Z","content_type":null,"content_length":"6754","record_id":"<urn:uuid:f6c74939-f995-40cd-bf5e-15797e3ac438>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00540-ip-10-147-4-33.ec2.internal.warc.gz"} |
Truths and Facts. Does Science prove anything? | A conversation on TED.com
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Truths and Facts. Does Science prove anything?
There is a great deal of interest of us in examining claims of ‘truths’ and ‘facts’. In such examination there is a noticeable stress on scientifically proven facts which can be taken as
fundamentally true. This is possibly because mathematics is the language of Science and we make mistake thinking mathematical proofs to be reflecting the essence of scientifically proven facts.
Does science necessarily prove anything? The way mathematics proves a proposition?
It is surprising that such a basic debate cannot be laid to rest and a conclusion arrived at even after 1934 book by Karl Popper: The Logic of Scientific Discovery.
Alan Moghissi, Matthew Amin and Connor McNulty of Institute for Regulatory Science, Alexandria, Va wrote to the editor of Science (the magazine) disagreeing with Peter Gleick and 250 members of the
(US) National Academy of Sciences writing to the editor of Science : All citizens should understand some basic scientific facts. There is always some uncertainty associated with scientific
conclusions; science never absolutely proves anything.
Is there an absolutely proven scientific fact?
Showing single comment thread. View the full conversation.
May 10 2013: You have made the common mistake of looking at science in reverse. The scientist doesn't prove he disproves. Experiments are designed to disprove a hypothesis. The more experiments
that are done which don't disprove the hypothesis the more reliable it becomes, but technically there is no truth only "what we think now" which must change if an experiment disproves it.
May 12 2013: Newton and Einstein were both wrong in several ways and I can show proof, just as I did with gravitational lensing, which Pabitra could not refute and neither can you or
anyone in science. I can do the same with speed of light theory and gravity.
If you or science can refute what I offer, then and only then will I play follow the leader.
Showing single comment thread. View the full conversation. | {"url":"http://www.ted.com/conversations/18256/truths_and_facts_does_science.html?c=667970","timestamp":"2014-04-21T07:32:23Z","content_type":null,"content_length":"47059","record_id":"<urn:uuid:d624b664-1a45-446a-a5f3-d6365e43441b>","cc-path":"CC-MAIN-2014-15/segments/1397609539665.16/warc/CC-MAIN-20140416005219-00541-ip-10-147-4-33.ec2.internal.warc.gz"} |
Struve function H: Series representations
Series representations
Generalized power series
Expansions at generic point z==z[0]
For the function itself
Expansions on branch cuts
For the function itself
Expansions at z==0
For the function itself
General case
Special cases
Asymptotic series expansions
Expansions inside Stokes sectors
Expansions containing z->infinity
In exponential form ||| In exponential form
In trigonometric form ||| In trigonometric form
Containing Bessel functions
Expansions containing z->-infinity
In exponential form ||| In exponential form
In trigonometric form ||| In trigonometric form
The general formulas
Expansions for any z in exponential form
Using exponential function with branch cut-containing arguments
Using exponential function with branch cut-free arguments
Expansions for any z in trigonometric form
Using trigonometric functions with branch cut-containing arguments
Using trigonometric functions with branch cut-free arguments
Residue representations
Other series representations | {"url":"http://functions.wolfram.com/Bessel-TypeFunctions/StruveH/06/ShowAll.html","timestamp":"2014-04-17T18:44:31Z","content_type":null,"content_length":"77321","record_id":"<urn:uuid:a95d443d-5057-413c-8849-8c21ecd56c15>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00639-ip-10-147-4-33.ec2.internal.warc.gz"} |
the encyclopedic entry of grating
A grating is any regularly spaced collection of essentially identical, parallel, elongated elements. Gratings usually consist of a single set of elongated elements, but can consist of two sets, in
which case the second set is usually perpendicular to the first (as illustrated). When the two sets are perpendicular, this is also known as a grid.
Gratings as filters
A grating covering a drain (as illustrated) can be a collection of iron bars (the identical, elongated elements) held together (to ensure the bars are parallel and regularly spaced) by a lighter iron
frame. Gratings over drains and air vents are used as filters, to block movement of large particles (such as leaves) and to allow movement of small particles (such as water or air).
Diffraction gratings
Grating can also be a diffraction grating: a reflecting or transparent optical component on which there are many fine, parallel, equally spaced grooves.
Gratings as pictures
A grating can also be a picture having the characteristics of a grating. For example, a picture might be of a collection of parallel black bars separated by equal-sized white bars. These sorts of
gratings are described by a graph (illustrated). On the y-axis of the graph is the luminance obtained by moving a light meter over the grating perpendicular to the orientation of the grating. On the
x-axis of the graph is the distance the light meter moved. The example is a square-wave grating (see second panel of the illustration); the graph consists of flat, low lines (corresponding to the
black bars), with abrupt corners leading to flat high lines (corresponding to the white bars). One period (or cycle) of such a grating consists of one black bar and one adjacent white bar. Gratings
where the black bars have a different width from the white bars are rectangular and are described by the duty cycle. The duty cycle is the ratio of width of the black bar to period (or pitch, i.e.
the sum of the widths of one black and one white bar).
Gratings are usually specified by four parameters. Spatial frequency is the number of cycles occupying a particular distance (e.g., 10 lines [or cycles] per millimeter). Contrast is a measure of the
difference in luminance between the light parts of the grating and the dark parts. It is usually expressed as Michelson contrast: the maximum luminance minus the minimum luminance divided by the
maximum luminance plus the minimum luminance. Phase is the position of the graph relative to some standard position. It is usually measured in degrees (from 0 to 360 for one complete cycle) or in
radians (2π for one complete cycle). Orientation is the angle the grating makes with some standard orientation (such as the y-axis in a picture). It is also usually measured in degree or in radians.
Grating elements can have luminances other than that of sharp-edged bars. If the graph of a grating is sinusoidal (see top panel in the illustration), the grating looks like a set of blurry light and
dark bars and it is called a sine-wave grating.
Sine-wave gratings are used extensively in optics to determine the transfer functions of lenses. A lens will form an image of a sine-wave grating that is still sinusoidal, but with some reduction in
its contrast depending on the spatial frequency and possibly some change in phase. The branch of mathematics dealing with this part of optics is Fourier analysis.
Gratings are also used extensively in research into visual perception. Campbell and Robson promoted using sine-wave gratings by arguing that the human visual performs a Fourier analysis on retinal
See also
External links | {"url":"http://www.reference.com/browse/grating","timestamp":"2014-04-18T03:45:59Z","content_type":null,"content_length":"85476","record_id":"<urn:uuid:5236d989-af1d-4954-be91-a29aa3579b0e>","cc-path":"CC-MAIN-2014-15/segments/1397609532480.36/warc/CC-MAIN-20140416005212-00440-ip-10-147-4-33.ec2.internal.warc.gz"} |
Corresponding Angles
When two lines are crossed by another line (called the Transversal):
The angles in matching corners are called Corresponding Angles.
In this example, these are corresponding angles:
• a and e
• b and f
• c and g
• d and h
Parallel Lines
If the two lines being crossed are Parallel Lines, then the Corresponding Angles are equal.
(Click on "Corresponding Angles" to have them highlighted for you.) | {"url":"http://www.mathsisfun.com/geometry/corresponding-angles.html","timestamp":"2014-04-18T13:53:48Z","content_type":null,"content_length":"6754","record_id":"<urn:uuid:f6c74939-f995-40cd-bf5e-15797e3ac438>","cc-path":"CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00540-ip-10-147-4-33.ec2.internal.warc.gz"} |
Shiri Artstein - home page
Shiri Artstein-Avidan ùéøé àøèùèééï-àáéãï
I am an associate professor at the School of Mathematical Science at Tel Aviv University.
I received my Ph.D. from Tel Aviv University in 2004.
My thesis was titled Entropy Methods, you can view it here.
My Ph.D. advisor was Vitali Milman.
Here is my cv in Pdf format.
My publication list (and most online available papers) can be viewed here: papers.
In Pdf format my publication list is here: publist (with slightly different numbering than above, because of some TAU regulations).
A few on-line lectures of mine are available here: Entropy increases at every step, Viterbo'sconjecture implies Mahler's, On Weighted covering numbers
Current graduate students:
M.Sc.: Keshet Gutman,
Ph.D.: D. Florentin (jointly with V. Milman), B. Slomka.
Past graduate students:
M.Sc.: T. Weisblatt (jointly with V. Milman), O. Raz, Yoav Nir (jointly with Y. Ostrover).
This fall (2013) I am teaching Chedva I for math. Also a seminar for MSc.
Some past courses: Chedva II and CHEDVA III for mathematics students, the course HILBERT SPACES, also for math students. An undergrad course called convex bodies in high dimensions.
Contact Info:
shiri at post dot tau dot ac dot il
Office: Schreiber 306
Phone: 972 (0) 3 640 7614 | {"url":"http://www.tau.ac.il/~shiri/","timestamp":"2014-04-17T01:00:52Z","content_type":null,"content_length":"28891","record_id":"<urn:uuid:bae27847-2e76-48b0-9831-0673f1de2bdb>","cc-path":"CC-MAIN-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00172-ip-10-147-4-33.ec2.internal.warc.gz"} |
Brockton, MA Precalculus Tutor
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Confidence-based progress-driven self-generated goals for skill acquisition in developmental robots
1. Introduction
During our lifetimes, we continually learn, and our learning is often intrinsically motivated (Piaget, 1955; Berlyne, 1966). We do not just learn declarative knowledge, such as that exhibited by
contestants appearing on the popular quiz show Jeopardy, but also procedural knowledge, such as how to write a Ph.D. thesis. In general, a skill is a program able to solve a limited set of problems (
Schmidhuber, 1997; Srivastava et al., 2013), but the notion of a skill is often coupled with procedural knowledge, which is typically demonstrated through action. In continually learning artificial
agents, skill acquisition (Newell et al., 1959; Ring, 1994; Barto et al., 2004; Konidaris, 2011; Lang, 2011; Sutton et al., 2011) is a process involving the discovery of new skills, learning to
reproduce the skills reliably and efficiently, and building upon the acquired skills to support the acquisition of more skills. This process should never stop. An eventual goal of ours, and others,
is the development of lifelong learning robot agents (Ring, 1994; Thrun and Mitchell, 1995; Ring, 1997; Sutton et al., 2011).
Traditional Markovian Reinforcement Learning (RL) (Sutton and Barto, 1998; Szepesvári, 2010) provides a formal framework that facilitates autonomous skill acquisition. In the Markov Decision Process
(MDP) framework, a skill is represented as a policy that, when executed, is guaranteed to efficiently reach a particular state, which would be a “goal” state for that skill. RL involves optimizing a
policy, to allow the agent to achieve the maximum expected reward.
There exist iterative planning methods, such as value iteration (Bellman, 1957) and policy iteration (Howard, 1960), to find an optimal policy for an MDP if a model of the environment is known to the
agent; see (Mausam and Kolobov, 2012) for recent reviews. The model is the set of transition probabilities P(s[t + 1]|s[t], a[t]) of reaching successor state s[t + 1], together with the associated
expected immediate rewards R(s[t], a[t]) when the agent takes action a[t] in state s[t]. By selecting different goal states and creating appropriate “phantom” rewards, which are not provided by the
environment, the agent could calculate a policy for a self-generated goal immediately through planning (Luciw et al., 2011; Hester and Stone, 2012; Ngo et al., 2012). An autonomous skill learner for
model-based Markovian RL needs only learn a single transition model (or another type of predictive world model) and to be able to generate a different reward function for each skill.
An important issue in learning a world model is systematic exploration. How can an agent explore the environment to quickly and effectively learn? Early methods were based on common-sense heuristics
such as “visit previously unvisited states,” or “visit states that have not been visited in a while” (Sutton, 1990). More recent methods are those based on Artificial Curiosity (Schmidhuber, 1991;
Storck et al., 1995; Wiering and Schmidhuber, 1998; Meuleau and Bourgine, 1999; Barto et al., 2004; Şimşek and Barto, 2006; Schmidhuber, 2010; Ngo et al., 2011), which can be exploited in
developmental robotics (Weng et al., 2001; Lungarella et al., 2003; Oudeyer et al., 2007; Asada et al., 2009; Hester and Stone, 2012; Ngo et al., 2012).
Artificial curiosity uses an intrinsic reward, which is the learning progress, or expected improvement, of the adaptive world model [i.e., predictor/compressor of the agent's growing history of
perceptions and actions (Schmidhuber, 2006)]. The expected learning progress becomes an intrinsic reward for the reinforcement learner. To maximize expected intrinsic reward accumulation, the
reinforcement learner is motivated to create new experiences such that the adaptive learner makes quick progress.
We investigate an autonomous learning system that utilizes such a progress-based curiosity drive to explore its environment. This is a “pure exploration” setting, as there are no external rewards.
The general framework is formulated as a selective sampling problem in which an agent samples any action in its current situation as soon as it sees that the effects of this action are statistically
unknown. We present one possible implementation of the framework, using online linear classifiers (Azoury and Warmuth, 2001; Vovk, 2001; Cesa-Bianchi and Lugosi, 2006) as predictive action models,
which essentially predict some aspects of the next state, given the current state-action features.
If no available actions have a statistically unknown outcome, the agent generates a plan of actions to reach a new setting where it expects to find such an action. The planning is implemented using
approximate policy iteration, and depends on the procedural knowledge accumulated so far in the adaptive world model. The agent acquires a collection of skills through these self-generated
exploration goals and the associated plans.
The framework is applied to a simulated and actual Katana robot arm manipulating blocks. Results show that our method is able to generate sample-efficient curious exploratory behavior, which exhibits
developmental stages, continual learning, and skill acquisition, in an intrinsically motivated playful agent. Specifically, a desirable characteristic of a lifelong learning agent is exhibited: it
should gradually move away from learned skills to focus on yet unknown but learnable skills. One particularly notable skill learned, as a by-product of its curiosity-satisfying drive, is the stable
placement of a block. Another skill learned is that of stacking several blocks.
2. Materials and Methods
In this section, we describe the setting of the learning environment, followed by introducing the selective sampling formulation (which is not environment specific). We then describe the planner and
the online learning of the world model, and finally present the derivation of the query condition.
2.1. Katana in Its Blocks-World Environment
Our robot, a Katana arm (Neuronics, 2004), and its environment, called blocks-world, are shown in Figure 1. There are four different colored blocks scattered in the robot's play area. In Section 3.1
we describe a simulated version of blocks-world with eight blocks. We use the simulated version for a thorough evaluation of our method. In both versions, the agent “plays” with the blocks, through
the curiosity-driven exploration framework, and learns how the world works.
FIGURE 1
In the real-world environment, detection and localization of the blocks is done with straightforward computer vision techniques. The overhead camera was calibrated using the toolbox developed by
Bouguet (2009), so that the system can convert 2D image coordinates to the robot's arm-centered Cartesian coordinates. Since all the blocks have different colors, a color-based detection and pixel
grouping is used for segmentation, leading to a perceptual system that reliably detects the positions and orientations (in the image coordinate system) of the visible, non-occluded blocks. The
positions and orientations of occluded blocks are stored in a memory module. Since any occluded block was once a fully visible block, and the occluded block positions do not change, the memory module
updating is also straightforward, requiring basic logic. The purpose of the memory module is to infer the heights of the blocks on top of occluded ones, since the overhead camera does not provide the
height information.
When a block is selected for grasping, or a location selected for placement, the system converts the image coordinates to the arm-centered Cartesian coordinates. For reaching and grasping, we use the
Katana's inverse kinematics module, which solves for joint angles given the desired pose (position and orientation) of the gripper, and its motion planning module.
In each environment setting, defined as a configuration of blocks, the agent first moves the gripper out of view of the camera, and takes a snapshot of the workspace below. The fundamental choice it
needs to make is to decide what the most interesting block placement location would be. A placement location is specified by a vector including pixel-coordinates and orientation parameters in the
workspace image, as well as the height, in terms of the number of blocks. After the desired placement location is decided, the agent needs to decide which block to pick up for placement. The block
that is grasped could be selected via a variety of heuristics. We choose to have the robot grasp the accessible (e.g., non-occluded) block furthest away from the desired placement location, which
avoids interference with the blocks at the selected placement location. Grasping will succeed as long as the perception is accurate enough and the block is within the workspace. In the real
experiments, grasping is rarely not successful. In these cases, we reset the situation (including internal values related to learning) and have the robot do it again. After grasping, the robot
performs another reach, while holding a block, and places it at the desired location.
Next we will illustrate how the robot represents its world, and how this representation leads to something resembling, and which, functionally, serves as an MDP.
2.2. Fovea and Graph Representation
The top-down camera image (640 × 480 pixels) is searched using a subwindow of 40 × 40 pixels, which we call a fovea. Each fovea center location represents a possible block placement location.
At any fovea location, the state s is the maximum height of a stack of blocks visible in the fovea window. The action a is a function of the feature vector that encapsulates the placement location
relative to the blocks in any stacks below. How this feature vector is computed will be described below. Any feature vector is converted into one of six possible actions. After an action is executed,
i.e., a block is picked and placed at the fovea central location, the outcome state s' is identified in the same way as s, with the fovea location unchanged. The resulting graph resembles a discrete
MDP and serves as a basis for tractable exploration in the blocks-world environment.
In a given setting (block configuration), each fovea location maps onto a single (s, a, s') transition in a graph. But only s and a are visible before the placement experiment. The missing piece of
knowledge, which the agent needs to place a block to acquire, is the outcome state s'. The fovea can be thought of as a window into a “world” where the robot can do an experiment. Yet, what the robot
learns in one “world” applies to all other “worlds.” The question is: which transition is most worth sampling?
Instead of being provided a single state and having to choose an action, as in a classical RL formulation, our system is able to choose one of multiple available state-action pairs from each setting.
Availability is determined from the known block positions. The agent's estimated global state-action value function Q(s, a) is used to identify an available state-action pair (s*[t], a*[t]) with the
highest value, constrained by availability. The agent knows the heights of all blocks in the workspace, which informs it of the possible states currently available. It also knows the fovea location
that centers on each block. The desired state s*[t] is selected from the available heights in the current setting, by selecting the one with maximum state value. Next, the desired action a*[t] is
selected as the one with maximum Q-value of all action pairings with s*[t]. To find a fovea location for the desired (s*[t], a*[t]), the agent searches by moving the fovea to different placement
locations around the stacks of height s*[t], until the contextual information (feature vector x[t]) associated with the action is matched.
The fovea search occurs in this “top-down” way, since it is computationally burdensome to extract the contextual information of state-action pairs at all fovea positions in each setting. This biased
and informed search mechanism is much more efficient. As a future extension, fovea movement would be learned as well [(Whitehead and Ballard, 1990; Schmidhuber and Huber, 1991); see also recent work
by Butko and Movellan (2010)].
Figure 2 (left) shows six examples to illustrate the features used. The thick black lines represent the boundaries of actual blocks. Example fovea locations are represented by the blue dashed
squares. The central point of the fovea is shown as a small blue circle. The pink dotted lines show the convex hulls constructed from the block pixels inside the fovea. If the central placement point
is inside the convex hull, the feature value is set to one, and zero otherwise. Note the case shown in (c), where the central placement point is not on top of any block at the fovea, but still within
the convex hull, and so the feature is set to one. For stacks of several blocks as in (d), the intersection of all the block pixels are constructed, and used to construct the convex hull.
FIGURE 2
Figure 2. Left: (a–f) Examples illustrating the features that were used. Right: An example showing how the state and action are encoded (bottom) for a given blocks-world setting (top). See text for
As shown in (e) and (f), the features are calculated around the central location, which results in a five-element feature group. In our real robot implementation we use this setup. With a placement
location as in (e) four bits are “on,” while in (f), only one bit is “on.” The number of bits that are on, plus one, provides the action index. For example, a fovea location with only one bit on, as
described above, would correspond to action a = A[2] and is encoded by feature vector x = (0, 1, 0, 0, 0, 0). Figure 2 (right) shows an illustration of states and actions at different fovea locations
for a particular block configuration. In the lower subfigure, we see the state-action representation underneath a few sampled fovea locations. This representation allows for generalization: the same
state-action (S[1], A[2]) can be accessed at both the red block (to the lower right) and the black block.
We note in passing that this Katana and blocks-world environment is simplified to become functionally discrete, but the method we use for learning, approximate policy iteration, is not tabular(as the
name suggests), nor is the way we use linear basis functions to convert each observation to a feature vector. Our general framework, which will be described next, does not require a tabular
environment. Furthermore, the subsystem relevant to a “placement experiment,” i.e., the blocks in the stack right below the fovea, is an MDP according to the formulated graph we use. The approach of
considering only relevant features in learning and planning makes the learning, and particularly the planning process, more efficient, as well as tractable^1.
2.3. Selective Sampling Formulation
Consider an online learning scenario where a learner i, nature presents a setting [i]. A setting may refer to a single state, or a set of subsystem states (as in our Katana blocks-world environment).
Within each setting, the learner will observe a sequence of instances x[t] ∈ ℝ^d. Here, and for the remainder of this article, we use subscript i to denote the setting, and the subscript t to denote
the instances observed within. Every time the setting is updated, i ← i + 1, and the observation counter t persists (e.g., if there were five instances in setting [1], the first observation in the
next setting [2] will be x[6]).
For every instance, the learner must decide whether or not to “query” nature for the true label y[t] of the current instance x[t], where y[t] ∈ {±1} (for binary classification^2). By query we mean
the learner takes an action (interact with nature) and observes its outcome. Hence, we can think of x[t] as the contextual information associated with each action a[t]. An observed feature vector,
once queried, becomes a training instance to improve the learner. The training will be described in Section 2.5.
Let Q[t] ∈ {0, 1} denote the query indicator at time t. If a query is issued, i.e., Q[t] = 1, the setting is updated (i ← i + 1), and the learner observes the label of the queried instance. It then
updates its hypothesis, taking into account the queried example (x[i], y[i]) as well as the previous hypothesis, which was learned over previous queries. Otherwise, i.e., Q[t] = 0, the learner skips
the current instance x[t] (meaning its label is not revealed) and continues to observe new instances from the current setting (i ← i).
Clearly, this constitutes a sequential decision process, which generates training examples for the learner. Since each interaction can require the learner to spend time and effort, i.e., labels are
expensive to get, it is reasonable to set the objective of the decision process to be such that the learner learns as much and as fast as it can.
As a concrete example of this framework, consider our blocks-world environment. Here, a setting is a configuration of all the blocks on the table, while an instance x[t] is a feature vector encoding
a possible placement location. The fovea sequentially provides possible placement locations, and, for each one, a new instance x[t] is observed. For each new instance in turn, the agent predicts the
outcome of placement. Here, the binary outcome label indicates the success or failure of stacking. The label y[t] = 1 indicates a stable placement, while the label y[t] = −1 indicates an unstable
After the action is taken, “nature” reveals a new setting [i + 1] and the agent obtains, through observation, the outcome and therefore the label, which will be used to improve its world model. In
implementation, the agent obtains the outcome label by comparing two images of the configurations before and after the placement. This is possibly noisy, but usually correct.
2.4. Planning in Exploration
Our system has a set of adaptive classifiers to predict the block placement outcomes, which, together, constitute the world model knowledge about the world, and a curiosity-drive causes the agent to
desire to accumulate such knowledge (learning progress) as quickly as possible.
The agent is greedy in its pursuit of knowledge. For every instance x[t] observed during setting i, a query condition Q[t] ∈ {0, 1} is generated. The query condition is used to decide if this
instance is worth querying for its label (outcome), based on the current model [t] = [i]. As soon as it encounters a true query condition, it executes the query, observes the outcome, and updates the
model to [i + 1]. Figure 3 illustrates this exploration behavior in our blocks-world environment.
FIGURE 3
Figure 3. A single robot-environment interaction, illustrating a setting change. Each pick and place “experiment” causes a change in setting. The outcome of the previous experiment was that the robot
placed the blue block on top of the yellow block, and observed the label +1, corresponding to “stable.” Now (middle), the robot examines three fovea locations (t, t' and t”), each of which involves a
query. The query is false for t' and t”, but true for t, and the robot immediately (greedily) grasps the furthest block, which happens to be the red one, and places it at the queried location. The
action causes a change in setting to i + 1 and the outcome −1 is observed (“unstable”).
But in the case where no instances in the setting are deemed to be valuable to query, the agent has to plan. In that case, the curiosity drive wants to quickly reach a new setting from which an
instance worth querying can be observed. To decide which instances are worth querying, the agent simulates future experience of performing different actions from the current setting, and sees, for
the simulated new settings, if the query condition becomes true at any point. If so, an intrinsic reward is placed at that transition. A true query condition in simulated experience becomes a binary
curiosity reward indicating if an instance is worth exploring. By planning on the induced MDP with “phantom” reward function, the agent generates an efficient exploration policy whenever it needs to.
These policies for reaching self-generated goals are the skills learned by the agent. Note that this curiosity reward is instantaneous, taking into account the current state of the learners, and not
a previous learner. See Algorithm 1 for a sketch of this process.
The planner can be implemented using any relevant MDP planning algorithms (Mausam and Kolobov, 2012), for instance, local methods (i.e., for the current state only) like UCT (Kocsis and Szepesvári,
2006), or global methods (for every state) like LSPI (Lagoudakis and Parr, 2003). In our implementation we use approximate policy iteration (LSPI, specifically the algorithm LSTDQ-Model), a global
method, to allow the agent to choose between different states/heights (if several stacks are available) in each setting.
In the MDP constructed for our Katana blocks-world environment, the transition probabilities are derived from the adaptive classifiers. At planning time, we update the transition matrix P(s'|s, a)
for all state-action-state triplets as follows: P(s'|s, a) = 0 if s' > s + 1; P(s'|s, a) = (1 + $\stackrel{{^}}{{\Delta }}$)/2 if s' = s + 1; and P(s'|s, a) = (1 − $\stackrel{{^}}{{\Delta }}$)/2/s if
s' ≤ s, with the prediction margin $\stackrel{{^}}{{\Delta }}$ computed as the inner product between the contextual feature x representing action a, and the linear weight vector w of the predictor,
i.e., $\stackrel{{^}}{{\Delta }}$ = w · x (more details will be provided in the next section). In other words, the transition probability to current height plus one is equal to the probability of a
stable placement. It is zero for any height which is two or higher above the current one, and is a uniform fraction of the probability of instability for the lower heights. Note that this is just an
approximation, but it is good enough for effective planning to reach higher heights.
The next two sections describe our adaptive learners and the derivation of query condition, based on these learning models.
2.5. Online Learners
We focus on adaptive binary linear classifiers. There are multiple such classifiers in our system—one per height—but the discourse in this subsection will be with respect to a single classifier, for
simplicity. For such a classifier, with weight vector w[t] ∈ ℝ^d, a classification of instance x[t] is then of the form ŷ[t] = sign (w[t] · x[t]). The term $\stackrel{{^}}{{\Delta }}$[t] = w[t] · x[t
] is often referred to as the prediction margin attained on instance x[t], and the magnitude of the margin |$\stackrel{{^}}{{\Delta }}$[t]| is a measure of confidence of the classifier in label
In the setting of a developmental robot interacting with nature, training instances are generated in a biased manner. They are not independent and identically distributed—the sampling/query process
depends on the learner's adaptive model [t]. However, their corresponding labels can be assumed to be generated from a linear stochastic model. Specifically, we make the following assumptions: 1) The
labels y[t] ∈ {−1, +1} are realizations of independent random variables Y[t] sampled from a stochastic source with a probability density function P(Y[t] |x[t]) continuous at all x[t]. This entails
that, if Δ[t] = 𝔼[Y[t] |x[t]] ∈ [−1, 1], then sign(Δ[t]) is the Bayes optimal classification. 2) There exists a fixed but unknown vector u ∈ ℝ^d for which u · x[t] = Δ[t] for all t. Hence u is the
Bayes optimal classifier under this noise model.
Note that when running our algorithms in a reproducing kernel Hilbert space (RKHS) Steinwart, 2002), the classifiers are implicitly non-linear, and Δ[t] is well approximated by f(x[t]), for some
non-linear function f ∈
The key elements in designing an online learning algorithm include the comparator class ^d, the loss function ℓ, and the update rule. For an arbitrary classifier v ∈ v; x[t], y[t]) its non-negative
instantaneous loss suffered on the current example (x[t], y[t]), and abbreviated by ℓ[t](v), i.e., ℓ[t](v) = ℓ(v; x[t], y[t]). We define the total loss of an adaptive learner x[t], y[t])}^T[t = 1] as
v as relative loss compared to the best linear hypothesis u:
for any sequence Azoury and Warmuth, 2001). A desired analysis step in designing online learners is then to prove upper bounds on such a relative loss. This bound should grow sublinearly in T, so
that it vanishes when T approaches infinity.
We use a modified version of the widely used regularized least square (RLS) classifier (Azoury and Warmuth, 2001; Cesa-Bianchi et al., 2009; Dekel et al., 2010)—a variant of the online
ridge-regression algorithm—as our online learner. As the name suggests, this class of algorithms uses the squared loss function, and possesses a proven relative loss bound under our label noise model
(Vovk, 2001; Dekel et al., 2012), with the desired sublinear growth. Established results for the algorithm will be used to derive our query condition (Section 2.6).
Given the sequence of queried (i.e., training) examples up to setting i, {(x[j], y[j])}^i[j = 1], the RLS classifier maintains a data correlation matrix, ${{A}}_{{i}}{=}{I}{+}{{\sum }}_{{j}{=}{1}}^
{{i}{-}{1}}{{x}}_{{j}}{{x}}_{{j}}^{{\top }}$, with I the d × d identity matrix and A[1] = I. For the i-th queried instance x[i], the weight vector can be updated as w[i + 1] = A^−1[i + 1](A[i]w[i] +
The inverse matrix A^−1[i + 1] can be updated incrementally using the Sherman-Morrison method,
Using the fact that A^−1[i + 1] x[i] = b[i]/(1 + c[i]), the weight vector update is simplified as:
An implementation-efficient pseudocode of this modified RLS update rule is presented in Algorithm 2.
2.6. Query Condition
Our query condition is greatly inspired by work in selective sampling, a “stream-based” setting of active learning (Atlas et al., 1989; Freund et al., 1997). In selective sampling, the learner has
access to an incremental stream of inputs and has to choose, for each datum in order, whether to query its label or not. State of the art methods in selective sampling, with theoretical performance
guarantees, include BBQ (Orabona and Cesa-Bianchi, 2011) and DGS (Dekel et al., 2012). These methods also use variants of the RLS algorithm (Azoury and Warmuth, 2001; Vovk, 2001; Auer, 2003;
Cesa-Bianchi et al., 2005; Cesa-Bianchi and Lugosi, 2006; Cavallanti et al., 2008; Strehl and Littman, 2008; Cesa-Bianchi et al., 2009), and maintain a data correlation matrix to calculate a
confidence interval or uncertainty level in their prediction, which is essentially an estimate of the variance of the RLS margin for the current instance.
The query condition must indicate when the outcome is statistically known or unknown. Here we derive a query condition for this purpose, based on the expected learning progress. Essentially, when the
learner is certain in what it predicts, it can ignore the instance, since, with high probability, its learning model will not get updated much on this example if it is queried. Inversely, only those
instances that the learner is uncertain in its prediction are worth querying for labels, since the model of the learner will undergo a large update on such training examples.
The following lemma from Orabona and Cesa-Bianchi (2011) defines χ[t], the uncertainty level, or confidence interval of the RLS prediction.
Lemma 1. Let δ ∈ (0, 1] be a confidence level parameter, h[δ, u](t) be a function of the form
where ||u|| is the unknown squared norm of the optimal Bayes classifier, and r[i] = x^⊤[i] A^−1[i + 1] x[i].
Now, define ${{\chi }}_{{t}}{=}\sqrt{{{c}}_{{t}}{{h}}_{{\delta }{,}{u}}{\left(}{t}{\right)}}$ with c[t] = x^⊤[t] A^−1[i + 1] x[t]. With probability at least 1 − δ, the following inequality holds
simultaneously for all t:
This inequality can be rewritten as,
which essentially implies that if |$\stackrel{{^}}{{\Delta }}$[t]| > χ[t], the learner is certain (with probability at least 1 − δ) that $\stackrel{{^}}{{\Delta }}$[t] and Δ[t] have the same sign
(i.e., $\stackrel{{^}}{{\Delta }}$[t] Δ[t] > 0), and there is no need to query for the true label. Inversely, when |$\stackrel{{^}}{{\Delta }}$[t]| ≤ χ[t], the learner is uncertain about its
prediction, and it needs to issue a query. Formally, the query condition is stated as follows:
where [·] denotes the indicator function of the enclosed event.
Now, from Lemma 1 we also have |Δ[t]| ≤ |$\stackrel{{^}}{{\Delta }}$[t]| + χ[t]. Combined with the query condition derived above, we have | Δ[t]| ≤ 2 χ[t] with probability at least 1 − δ when a query
is issued. When the magnitude |Δ[t]| of the optimal prediction margin is small, the instance label is almost certainly noise, i.e., the prediction is nearly a random guess. These instances are “hard”
or even “impossible” to learn, and the learner should instead focus on other instances that it can improve its prediction capability. We derive another query condition to reflect this insight, by
enforcing another threshold θ on the uncertainty level,
In implementation, a surrogate or proxy function is used to avoid dependency on the optimal yet unknown u. This takes the form,
where α is a tunable positive parameter, and
is a simplification of h[δ, u](t). Importantly, the confidence interval does not depend on the squared norm of the optimal but unknown Bayes classifier u. See Dekel et al. (2012) Equation (12) and
Lemma 7, notice the additional assumption of ||u|| ≤ 1. See also Orabona and Cesa-Bianchi (2011) Algorithm 2 for another proxy function.
3. Results
In all implementations we used the following parameter values: discount factor γ = 0.95, and query condition scaling factor α = 1. The confidence-interval threshold θ = 0.01 for simulations, while θ
= 0.1 was used in the real robot experiments.
3.1. Simulated Blocks-World Environment
We designed a stripped-down simulated version of the actual blocks-world, in order to test our system. In simulation, thousands of trials can be run, which would take far too long on the real robot.
Of course we cannot capture all aspects of the real-world robot setting, but we can capture enough so that the insights and conclusions arising from simulated results suffice to evaluate our system's
The simulated environment also allows us to use any number of blocks and any number of features. For any configuration of blocks, some set of heights will be available for the agent to place upon,
corresponding to the heights of the top blocks in the stack(s), and height zero. In the simulation, we use eight blocks, and 21 features. Each height's feature vector is of length 21 bits, with only
one bit set. All 21 feature vectors are available for each available height. The agent must select one of them. Unlike the actual robot setting, in simulation, the features do not correspond to any
physical aspect of the simulated world. In simulation, each of the 21 features are associated with a different probability of stability, which is randomly generated.
Each possible height s has a different weight vector u^s, which is the randomly generated “true model” for the result of placing a block upon it. This was done in order to generate simulated block
placement outcomes in an easy-to-implement way. There are 21 components^4 of each u^s, which are randomly generated in the range [ −1, 1]. An outcome (stable/falling) is generated using the
corresponding height's true (probabilistic) model, where the actual outcome label sign(u · x[t]) is flipped with probability $\frac{{1}{-}{|}{u}{·}{{x}}_{{t}}{|}}{{2}}$. For the purpose of generating
orderly plots in Section 3.2, we re-order the 21 feature vectors of each height in ascending order of their likelihood of stability, then re-assign their feature indices from 1 to 21. Thus, the
smaller the feature index, the lower likelihood the placement will be stable. For an outcome of falling, there is a chance that the entire stack underneath the placement position collapses, in which
case all blocks in that stack are reset to height one.
The eight blocks' configuration is represented by vector q. The absolute value of each element |q[j]| is the height of the corresponding block j. We set sign(q[j]) = −1 if block j is occluded
(stacked upon), while sign(q[j]) = 1 means block j is on the top of its stack, which means its both graspable and another block can be placed upon it. The set of different positive elements of q
constitute the set of current available states (heights to place upon) in addition to height zero (which is always available). For example, vector q = (−1, −2, −3, 4, −1, 4, −2, −3) means the
configuration has two different stacks of height four, having block IDs 4 and 6 on top of the two stacks. Here, the set of available placement heights is height zero and height four.
After selecting the state and action, the agent picks an “available” top block, and “places it.” By available, we mean it is the top block of another stack. Another block in the stack (if any) of the
block that is grasped becomes a top block. If the placement is stable, the highest block in the placement stack has its sign reversed, and the placed block becomes the top block of that stack. If the
placement outcome turns out to be unstable, a “toppling” event occurs, where one randomly selected block in the stack of placement, with a lower height, becomes a top block of the remaining stack,
with blocks below unchanged. The (unsuccessfully) placed block and the other, higher blocks in the stack topple to the surface, and their values are all set to +1.
3.2. Results in Simulated Blocks-World
Figure 4 shows the averaged exploration behavior of our system over time, for all different heights. “Direct exploration” refers to settings where the query condition is true, while “planning
experience” refers to settings where the algorithm has to execute a planned action (since the query condition is always false for that setting). On the y-axis, “cumulative experience” is a count of
the number of times these types of actions are generated. The different colored lines indicate different heights. The vertical lines are from a single run, and indicate when, during that run, the
learner switches from direct exploration of one height to planning exploration of higher heights.
FIGURE 4
These plots show the developmental stages of the learning agent, where easier problems, such as direct exploration at height one, are learned first, and more difficult problems are learned later.
They also show cumulative learning, as the acquired knowledge at lower heights is exploited for planning, and this planning helps the agent get to the higher heights, in order to acquire more
knowledge. The difficulty of this problem is shown by the time the learner needs to spend to fully explore its environment, especially in achieving the highest heights. For instance, to even get to
height six to do experiments, the agent first needs to stack blocks from lower heights each time the stack collapses, which is a regular occurrence.
The agent does not necessarily explore a single height until everything at that height is statistically known. There are sometimes situations where several heights worth exploring are available
simultaneously in the environment. In such cases, the agent starts with the height having the largest “future exploration value” as estimated by LSPI. The planning step helps to trade off
“easy-to-get” small learning progress rewards with “harder-to-get” larger ones. As shown in Figure 4, the exploration at higher heights does, in fact, start before the direct exploration of lower
heights terminates.
Figure 5 shows the learning progress, measured with Kullback-Leibler (KL) divergence between the learned models and the true models. These distances tend to diminish exponentially with experience,
and they diminish faster at lower heights, where experience is easier to get. When each line in the graph saturates, it corresponds to the associated knowledge being “known” and ready for
exploitation in planning. The saturation levels are non-zero due to the noise level in the training labels, the query condition scaling factor α, and the confidence-interval threshold θ.
FIGURE 5
Figure 5. KL-divergence between learned models and ground-truth models (averaged over 10 runs). Best viewed in color.
Figure 6 shows how the exploration focus changes over time, for height one. In each subgraph row, the figure on the left shows the distribution of the experience up until the timestep in the
subfigure title. The shaded area between the two vertical lines represents the “unknown” region of input features that is deemed to still be worth exploring. This will be the “exploration focus” of
the agent, in subsequent interactions. Regions outside of this shaded area are considered “known” by the learning agent, and not worth exploring any more. Going from the top to the bottom of Figure 6
, note that the query region shrinks with the amount of experience. Additionally, note that the middle features, associated with the most uncertain outcomes (as mentioned in Section 3.1) stay
interesting longer than the others.
FIGURE 6
Figure 6. How the focus of the self-generated exploration goals at height 1 changes over time as the learned predictive model gets closer to the true one.
An interesting observation that is worth elaborating on, is as follows. At timestep #2000, when every prediction is statistically known, the agent starts to exploit the acquired knowledge for
planning (i.e., taking its estimated “best” action #16 to reach height two). It also keeps on refining the learned model, which reveals, as a result of generalization in learning that the optimal
action (i.e., the most stable placement position) is action #20 instead. Afterwards, the agent switches its optimal policy for this height, as shown in timesteps #3000 and #4000.
The plots on the right shows the learned predictive model (blue dashed lines), with two thin black lines representing the confidence intervals for each prediction. As more data are observed, the
associated confidence interval will shrink, reflecting the learning progress. Note that as a result of generalization, the neighboring area of the input feature space also gets improved, indirectly,
in its confidence interval. Recall that we re-arranged the input feature indices so that their prediction margin (hence, probability of stable/unstable outcomes) are in ascending order.
A measure of the difficulty of a learning problem is the sample complexity needed to achieve some desired level of confidence. The shaded regions (i.e., “unknown” and worth exploring) shrink with
experience, toward the input feature values with small prediction margin ground-truth. These feature values correspond to the input subspace with prediction outcomes close to noise, i.e., hard to
predict. However, these instances lying close to the decision boundary are the most informative instances for constructing a good decision plan. Our system first explores much of the input space,
then quickly shifts its attention to this “hard-to-learn” input region, where most of its exploration effort is spent. As a result, the learned predictive model gets closer to the true model over
time. Note that for “known” regions outside the shaded area, even though the number of experiences is small, and the confidence interval (i.e., uncertainty level) is large, the learning algorithm is
still confident that its prediction (sign of the margin) is close to the optimal one with high probability. Thus, these regions are not worth exploring any more.
The same exploration behavior is observed when we analyze the data for other heights, as shown in Figure 7 for height two, and Figure 8 for the first six heights when exploration terminates. In all
the experiments, the agent first explores the whole input feature space, then focuses on subspaces of input features that are informative but for which high confidence is hard to achieve, then on
features that are useful for planning. This typically occurs for each height in turn. As a result of learning how to plan, which necessarily entails reliably transitioning from one state (height) to
another, the skill of block stacking is achieved.
FIGURE 7
Figure 7. How the focus of the self-generated exploration goals at height 2 changes over time as the learned predictive model gets closer to the true one.
FIGURE 8
To further analyze the effectiveness of our method, we compare its performance to three other methods. The comparison measure is the KL-divergence with respect to the true model. The first method
simply is uniform random action selection, which results in undirected, babbling-like, behavior. The second method, which we call Conf (Ngo et al., 2012), uses confidence intervals χ[t] of the
prediction margin directly as phantom rewards to generate the exploration policy through planning. Intuitively, this is also an informed exploration method since it promotes exploration in parts of
the environment with high uncertainty. The main difference is the confidence intervals are used themselves as rewards, instead of using a query condition. The third method is a variant of our
proposed method, but the exploration policy is updated (i.e., planning) after every 10 observations, instead of on-demand whenever exploration planning is invoked. We denote this variant as Q10, and
our proposed method as Q1.
The results are shown in Figure 9, with each subgraph showing the KL-divergence between learned models and their ground-truth at each timestep. Inspecting carefully the subgraph for height one and
two, we see that Q1 gets close to the true model exponentially fast in the first 1000 timesteps, then saturates. The random method, on the other hand, though making much slower progress than Q1 and
Q10 in the first 1000 timesteps, keeps improving its learned models and achieves the best models for height one and two, among the four methods. However, for the other five higher heights, its
learned models are much worse compared to the rest. This can be explained by the fact that the blocks-world environment naturally generates unbalanced experience distribution among all the states
under random action selection, and lower heights will get much more learning experience compared to higher ones. This undirected exploration behavior makes random exploration the least efficient
method compared to the other three (informed) exploration methods, as shown in the overall results in the last subgraph at the bottom-right corner. The confidence-based method performs much better
than random method, but is still inferior compared to query-based methods Q1 and Q10. The overall performance of Q1 is the best, closely followed by Q10, which is less efficient due to less frequent
planning updates.
FIGURE 9
Figure 9. A comparison of exploration methods in terms of the KL-divergence between the learned predictive models at each time step and their ground-truth models. Results are averaged over 10 runs.
3.3. Results on the Real Robot
Now, we show the learning behavior on the real robot. Figures 10–12 show a snippet of experience consisting of 12 consecutive experiment sequences. In each frame, one should focus on the
configuration of the blocks in the workspace and track the changes from the previous frame. Each sequence starts with i) a fovea-based search for the desired placement in the current block
configuration (i.e., either the query condition returns “unknown” or the best planned action is selected), as shown in the first column, followed by ii) an action picking a block unrelated to the
placement experiment (second column), then iii) placing the block at the desired height, orientation, and relative position with respect to the stack below (third column). The sequence ends with an
observation process to self-generate the label (last column). The end of one sequence is also the beginning of the next sequence. Since the robot has already had some prior experience before
continuing from sequence #1 of the snippet, it now focuses on exploring height two. Specifically, from all the 12 sequences, we find that the robot gradually shifted its attention (from the second
sequence in Figure 11 to the second last sequence in Figure 12 to trying actions A[3] and A[4] (corresponding to relative placement positions with two and three bits set), which are actually the
actions with the most uncertain placement outcomes among the six actions. Note that with tower height four, the robot arm does not have many feasible workspace points for the pick and place task.
Hence we limit the maximum height to three.
FIGURE 10
FIGURE 11
FIGURE 12
Figure 13 shows the predictive models the Katana robot arm acquired in a single run with 30 interactions (see demo video at www.idsia.ch/~ngo/frontiers2013/katana_curious.html; the last 12
interactions shown in Figures 10–12 start from 1:52).
FIGURE 13
Figure 13. Learning progress of the Katana robot arm's predictive models at height 1 and 2 after 30 settings. Action 1 (no bits set) is the most unstable. Action 6 (all bits set) is the most stable.
See earlier discussion on the features and Figure 2.
Figure 14 shows a “tricky” situation for the robot, which it can overcome if it has learned the model well. Here, the robot must demonstrate its block stacking skill, as an externally imposed goal.
FIGURE 14
Figure 14. A “tricky” situation to test the robot's stacking skill. We show this case to illustrate the value of exploring to learn how the world works. Consider the robot is faced with a task to
build a stack of blocks as fast as possible from this initial setting. Given its learned model of the world, the robot will decide to start stacking from height 1 instead of height 2, as with high
probability the stack of two blocks will fall after placing another block upon them.
4. Discussion
4.1. Systematic Exploration
This work was conceived with pure exploration in mind, which is contrasted with the treatment of exploration in classical RL. There, exploration is discussed in terms of the exploration-exploitation
tradeoff. On the one hand, the agent should exploit the acquired knowledge by selecting the current best (greedy) action, thereby not spending too much time in low-value areas of the state space. On
the other hand, it needs to explore promising actions to improve its estimation of the value function, or to build a more accurate model of the environment.
The most widely used method for balancing exploration and exploitation is the ϵ-greedy algorithm (Watkins and Dayan, 1992; Sutton and Barto, 1998). At each state, with probability of 1−ϵ the agent
selects the greedy action with respect to the estimated value function, and with a small probability of ϵ it selects a random action for exploration. Optimistic initialization is another common
method for exploration (Sutton and Barto, 1998). By initializing the value function for all states with high values, the agent will try to reach less visited states until their values converge to
near-optimal ones, which is much lower than the initial values. The initial values strongly affect the exploration time. Progress-driven artificial curiosity is a more general method for balancing
exploration and exploitation which 1. removes the reliance on randomness—the exploration is informed, instead of relying on randomness (uninformed), and 2. promotes exploration of states where
learning can occur over states where not much can be learned. To contrast, in optimistic initialization, every state is equally worth exploring.
Somewhat recently, several algorithms modifying optimistic initialization have been proposed that guarantee to find near-optimal external policies in a polynomial number of time steps (PAC-MDP).
These algorithms, such as E^3 (Kearns and Singh, 2002) and R-max (Brafman and Tennenholtz, 2003), maintain a counter for the number of times each state-action pair is tried. When this number exceeds
some threshold, the estimated state-action value is quite accurate, and the state-action pair will be considered “known”—thus with high probability the greedy action will be near-optimal
(exploitation). Otherwise, the value is replaced with a highly optimistic one, encouraging the agent to explore such “less-selected” state-action pairs. Recent work in this model-based line of
research extends R-max in several aspects. Rao and Whiteson (2012) give a better estimate of the optimistic reward using a weighted average between experienced and optimistic ones, resulting in the
V-MAX algorithm that is capable of exploiting its experience more quickly. Lopes et al. (2012) propose to replace the counter of visits to a state with expected learning progress based on
leave-one-out cross-validation on the whole interaction history. Our method for estimating learning progress is, in contrast, instantaneous and online. Furthermore, it is able to generalize across
different actions, instead of treating them separately.
The common theme in many intrinsically motivated RL approaches is that the estimated learning progress is used as secondary to external rewards. The purpose of the behavior (i.e., the policy) of the
agent has a goal of achieving external rewards. Exceptions include, for instance, Şimşek and Barto (2006), where the agent's behavior is based on a second value function using an intrinsic reward
signal, which is calculated based on the changes in value estimates of external rewards.
Besides our preceding work (Ngo et al., 2012), which this work is an extension of, some recent work in the pure exploration setting also uses planning. Yi et al. (2011) develop a theoretically
optimal framework based on the Bayesian methods, in which the agent aims to maximize the information gain in estimating the distribution of model parameters. An approximate, tractable solution based
on Dynamic Programming is also described. Hester and Stone (2012) present results on simulated environments, where two progress-based intrinsic reward signals are used for exploration: one based on
the variance in predictions of a decision tree model, and one based on the “novelty” of the state-action pair, to promote the exploration focus to shift toward more complex situations. In our system,
we use a single curiosity reward signal based on the derived query condition, and our approach has been shown to be more effective than the previous variance-based approaches, since observations with
large variance will not be worth querying if the learner is confident about its predictions.
In all the aforementioned work with pure exploration, planning is used to generate exploration policies, which must be invoked at every timestep. It has been observed (Gordon and Ahissar, 2011; Luciw
et al., 2011) that quickly learning agents do not update their exploration policies fast enough to achieve the intrinsic rewards they expect to achieve. In such cases, learning progress-based
exploration is no better than random action selection or various simple heuristics. In other words, the update speed of the policy generation must be much greater than the learning speed of the
underlying learner. This can be computationally demanding. It can also be wasteful, when the intrinsic reward that the agent plans to achieve is, while non-zero, quite small.
Our approach allows the agent to choose the most informative observations (possibly several steps ahead) to sample, and only invoke expensive planning when the current situation is already “known.” A
statistically “known” prediction means the agent knows with high probability that its prediction is almost as correct as that of the Bayes optimal predictor. Due to this approach, the computational
demands are reduced compared to a regular planner, and further, the agent will know when to stop its planning efforts—when everything is “known.”
4.2. Conclusion
Goal-driven exploration is very common in the traditional RL setting. In the pure-exploration setting, self-generated goals are needed. The agent described here generates goals based on its
confidence in its predictions about how the environment reacts to its actions. When a state-action outcome is statistically unknown, the environment setting where that experience can be sampled
becomes a goal. The agent uses planning to manipulate the environment so that the goal is quickly reached. Without planning, only local, myopic exploration behavior can be achieved. The result is a
sample-efficient, curiosity-driven, exploration behavior, which exhibits developmental stages, continual learning, and skill acquisition, in an intrinsically-motivated playful agent. Key
characteristics of our proposed framework include: a mechanism of informed exploration (with no randomness involved), a clear distinction between direct and planned exploration (i.e., planning is
done only when all local instances are statistically known), and a mathematically-solid way of deciding when to stop learning something and when to seek out something new to learn.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We would like to thank the reviewers for their very useful comments that helped improve this paper.
This work was funded through the 7th framework program of the EU under grants #231722 (IM-CLeVeR project) and #270247 (NeuralDynamics project).
1. ^For more information on subspace planning, see related work in relational RL by Lang and Toussaint (2009).
2. ^A more general framework would consider the multiclass and regression cases, which we leave for future extension.
3. ^Note that the terms weight vector, linear hypothesis, classifier, and learner are fairly interchangeable for the purposes of this article.
4. ^To allow generalization in learning, each weight vector is extended with one extra bias component, corresponding to an extra augmented feature of 1. Thus, |u| = |w| = |x[t]| = 22 in the
implementation of the simulated environment, and |w| = |x[t]| = 7 in the implementation on the real robot.
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Genome-wide estimation of gender differences in the gene expression of human livers: Statistical design and analysis
Gender differences in gene expression were estimated in liver samples from 9 males and 9 females. The study tested 31,110 genes for a gender difference using a design that adjusted for sources of
variation associated with cDNA arrays, normalization, hybridizations and processing conditions.
The genes were split into 2,800 that were clearly expressed (expressed genes) and 28,310 that had expression levels in the background range (not expressed genes). The distribution of p-values from
the 'not expressed' group was consistent with no gender differences. The distribution of p-values from the 'expressed' group suggested that 8 % of these genes differed by gender, but the estimated
fold-changes (expression in males / expression in females) were small. The largest observed fold-change was 1.55. The 95 % confidence bounds on the estimated fold-changes were less than 1.4 fold for
79.3 %, and few (1.1%) exceed 2-fold.
Observed gender differences in gene expression were small. When selecting genes with gender differences based upon their p-values, false discovery rates exceed 80 % for any set of genes, essentially
making it impossible to identify any specific genes with a gender difference.
Liver toxicity is the most common adverse event associated with the introduction of a new drug despite extensive pre-clinical toxicity testing. The failure to predict this toxicity is attributed to
differences among species in the metabolism and disposition of certain chemicals and drugs. This spawns an interest in in vitro tests that use human hepatocytes. The scarcity of primary human
hepatocytes and the unsuitability of many human cell lines, which were derived from liver cancer cells, are a serious limitation for developing such tests. In addition, primary hepatocytes
differentiate quickly in culture, restricting their use to short term studies [1]. The National Center for Toxicological Research (NCTR) embarked upon a program to develop conditionally immortalized
cell lines as potential in vitro models to evaluate the liver toxicity of new drugs [2,3]. A further incentive for this approach is the potential to study mechanisms of liver toxicity from different
genders and/or ethnic populations. As a start and proof of principle, a study was proposed to develop and characterize conditionally immortalized human primary hepatocyte cell lines from female and
male donors.
It is desirable to quantify in some way that an immortalized cell line retains functions characteristic of primary hepatocytes. Since cDNA arrays can screen thousands of genes for expression
differences, they are attractive as an evaluation tool. Once some immortalized cell lines are characterized with respect to primary hepatocytes, cDNA arrays could monitor the persistence of gender
differences in expression across these immortalized cell lines, thereby showing retention of some functions without using primary hepatocytes. Toward these ends, this study scanned the genome for
expression differences in the livers between 9 males and 9 females.
The use of cDNA arrays to assay for gender difference encounters two statistical problems that are not simple to deal with. First, gender comparisons relying upon array technologies are subject to
biological and technical sources of variation [4]. The experimental design needs to avoid confounding technical variation within treatments. This study modified an experimental design, which was
previously employed for two-dye per array hybridizations [5], to ^33P-labeled filter arrays that are stripped and reused. Second, there is a potential for excessive false positive rates because of
the number of genes evaluated. For our purposes, a set of genes is needed for which the false positive rate is acceptably low. The false positive rates associated with potential sets were evaluated
using recently developed post hoc methods based upon the empirical distribution of the observed p-values [6,7].
Human Liver
Segments of human liver were obtained from Dr. Fred Kadlubar, Division of Molecular Epidemiology, NCTR (Jefferson, AR) and Dr. Steven Strom, the University of Pittsburgh (Pittsburgh, PA). This
project was approved by the Research Involving Human Subjects Committee of the Food and Drug Administration (FDA). Nine pairs, a male paired with a female, were formed from available subjects. Pairs
were processed concurrently to control variation from technical sources associated with sample preparation and measurement, and this was the major reason for pairing subjects. In forming pairs, we
also attempted to match the age, race, and smoking/drinking habits of subjects as much as possible. However, this matching was not rigorous. The age of each subject was known (range: 25–58). For some
subjects, information concerning their race (Caucasian and Hispanic) and their smoking and/or drinking habits was available although this information was not complete. In addition, several of these
subjects are known to have died in a hospital where they were administered drugs in a failed attempt to stabilize their condition.
RNA Isolation
Total RNA was isolated from each liver sample using TRIzol (Life Technologies, Rockville, MD) according to the manufacturer's recommendations. Purified RNA was then treated with DNAse to remove
residual DNA contamination. One tenth volume of 10X DNAse buffer (0.4 M Tris-HCl, pH 7.9; 0.1 M NaCl, 60 mM MgCl2, 1.0 mM CaCl2) was added to a reaction containing 50 to 100 μg of purified RNA and
one unit RQ1 RNAse-free DNAse (Promega, Madison, WI). The reaction was then incubated for 15 min at 37°C, extracted once with an equal volume of phenol/chloroform, precipitated with ethanol and
finally resuspended in RNAse-free dH[2]O. RNA yields were determined by spectrophotometric analysis. RNA integrity was confirmed by gel electrophoresis.
Filter Information
The filters used in this experiment were GF200, GF201, GF203, GF204, GF205 and GF206 (Invitrogen, Carlsbad, CA). Each filter was spotted with 5,184 expressed sequence tags (ESTs) representing human
Filter Array Analysis
Pre-wetted filters were prehybridized at 42°C for 2 hr in 0.75 M NaCl, 0.17 M NaPO[4 ]buffer (pH 7.0), 0.15 M Na[4]P[2]O[7 ]• 10 H[2]O, 5X Denhardt's solution, 2.0% SDS, 100 μg/ml denatured salmon
sperm DNA, 50% formamide and 5.0 μg human Cot-1 DNA. Five micrograms of total RNA were combined with 2.0 μl of 1.0 μg/ml oligo dT primer (LifeTechnologies) in a total volume of 10.0 μl and then
incubated for 10 min at 70°C. The reaction was quick-chilled on ice for 2 min. The following components were added to the oligo dT-primed RNA; 6.0 μl of 5X first strand buffer (Clontech, Palo Alto,
CA), 1.5 μl of 20 mM dNTPs (dGTP, dTTP, dCTP) (Invitrogen), 1.0 μl of 0.1 M DTT, 1.5 μl of PowerScript reverse transcriptase (RT) (Clontech) and 10 μl of α-^33P dATP (>3000 Ci/mmol) (ICN, Irvine,
CA). The reaction was incubated for 90 min at 42°C. Unincorporated nucleotides were removed by column purification using Bio-spin 6 columns (Biorad, Hercules, CA). Incorporation of label for all
targets ranged ± 20% from the mean. The radiolabeled target was denatured by boiling for 3 min and added to 5 ml of prehybridization solution. The filters were hybridized with the denatured target
for 18–20 hr at 42°C. After hybridization, the filters were washed twice in 2X SSC, 1% SDS at 68°C for 30 min and twice in 0.5X SSC, 0.5% SDS at 68°C for 30 min
Data Imaging
The washed, hybridized filters were sealed in plastic sheet protectors and exposed on a Molecular Dynamics phosphor-screen (Amersham, Piscataway, NJ) for 72 hr. The screens were imaged with a Storm
Phosphorimager (Amersham) at a resolution of 50 microns. The median pixel intensity for each spot was determined using ArrayVision software (Research Imagine, Ontario, Canada). Each filter was
stripped after imaging as recommended by the manufacturer. Briefly, boiling 0.5% SDS was poured into a large glass dish. Hybridized filters were placed in the hot solution and agitated for one hour
without additional heating. The filters were then imaged for four hr on a phosphor screen (Amersham Biosciences) at a resolution of 200 microns. Each filter was stripped five times.
Statistical Design
This study examined gene expression in liver tissue from 9 male subjects and 9 female subjects. Each male was paired with a female during the assay of gene expression in an effort to control
technical variation associated with arrays, hybridizations and processing conditions. Each liver sample was hybridized to two arrays. First, one of the pair was assigned to an array, and the other
sample was assigned to the other array. After the initial hybridization, both arrays were stripped and the array assignments of the samples were swapped for the second hybridization. These four
expression measurements form a 'block'. Intensities were recorded at development times of 16 and 72 hours yielding 8 observed intensities for a block. The 9 blocks yielded 72 intensities per
interrogated spot. With this design, we estimate the effects of blocks, effects of arrays within blocks, effects of hybridization (first or second) within blocks, and effects of subjects within
blocks (Table 1). The pair of samples, which form a block, was processed concurrently. Thereby, variation associated with conditions and reagents involved in mRNA extraction, reverse transcription,
hybridization, and washing steps are presumed to be smaller within blocks. This design mimics the simultaneous hybridization of two-dye platforms by taking advantage of the capability for membrane
arrays to be reused. This allows the estimation of an array effect for each spot, which has been recognized as one of the largest contributors to intensity variability in the radio-labeled platform [
Table 1. Analysis of covariance model that was applied to the data for an interrogated spot. This table gives the typical degrees of freedom and the approximate expected mean squared errors for the
sources of variation estimated under the experimental design. The reported F-ratios are the median of the 32,112 analyses. This median is the vertical red line in the box of Figure 1. The p-value is
for the tabled F-ratio with numerator degrees of freedom as tabled and 34 denominator degrees of freedom.
Analysis of Covariance
An analysis of covariance was fit to the log-intensity data for each spot. No background correction was applied. This model estimated the difference between the male subject's log-intensities and the
female subject's log-intensities, i.e., this analysis produced an estimate of the sex difference in every block. These 9 estimates are adjusted for the factors in the experimental design and they are
normalized by the median. In addition, a similarly adjusted and normalized average magnitude of the log-intensities was estimated.
Table 1 is a typical analysis of variance table for the statistical model that was fit to each spot. The median of all the spot intensities that were observed at each array-hybridization-time was
first computed. These medians were entered as covariates to normalize the log-intensities [9] and their effect in the model is similar to a global normalization. The least squares estimate of the
difference in log-intensities between the male sample and female sample was computed for each block. These estimates are normalized by the median and they are also adjusted for the main effects of
time, block, array, and hybridization. An 'average adjusted log-intensity' was also computed for each spot. These estimates are the least squares means evaluated at 'median = 10' and the average
levels of the categorical factors. This analysis was implemented using 'PROC GLM' [10].
Loess Regression
Within each array type (5352 spots) and block, the estimates of the gender difference were plotted against their estimate of the average magnitude, e.g., Figure 2. Observed trends were removed by
Loess regression using 'PROC LOESS' [10]. This program allows one to specify several parameters that govern the degree of smoothing. Herein, we selected a quadratic equation, a bandwidth of 10% of
the data (about 500 observations), and applied the smoothing algorithm three times to mitigate the influence of 'outliers'. Other combinations of these smoothing parameters were also tried, and they
did yield differences in details, which we elaborated in the Discussion.
Selecting Expressed Genes
The adjusted average log-intensity for many of the interrogated genes evidenced little if any expression. Genes that are not expressed cannot be differentially expressed. So, it is useful to separate
"expressed" genes from "not expressed" genes in analyses. Genes were partitioned into "expressed" and "not expressed" groups based on their adjusted average log-intensity. Essentially, high
intensities are unlikely to have resulted from cross hybridization or other background sources, while low intensities are likely to represent a substantial amount of cross hybridization. The
empirical distribution of the adjusted average log-intensity estimates was examined in a normal probability plot to determine a reasonable cut point. In liver samples that do not contain any mRNA
matching a spotted cDNA sequence, i.e., a gene that is not expressed, the observed hybridization log-intensity is a background level arising from cross hybridization plus measurement error. When a
large number of genes are not expressed in all of the liver samples, their intensities being of similar magnitude produce an obvious mode at the low end of the empirical distribution. Values less
than this mode are
entirely from "not expressed" genes. We also assumed that the distribution is symmetric about this mode and approximated this component of the empirical distribution by a normal distribution
], which can be estimated directly from the normal probability plot. The genes were partitioned into "expressed" genes and "not expressed" genes based on a cutoff, which gives a low probability that
larger values arise from the normal distribution. Genes with values greater than the cutoff were classified as "expressed" and the rest were classified as "not expressed".
Selecting Genes with Gender Differences in Expression
A few genes were spotted more than once. The study examined 32,112 spots representing 31,110 genes (distinct Gene Bank accession numbers). The analysis of covariance/Loess regression generated 9
smoothed estimates of log-fold changes for each spot. Estimates from replicated spots were averaged so that there was one estimate per block and gene. Likewise, replicated estimates of the adjusted
average log-intensities were averaged. This resulted in 9 estimates of the gender difference and an estimate of the average magnitude for each interrogated gene.
The smoothed estimated log-fold changes were averaged
There were 31,110 tests of the hypothesis that there was no gender effect. Simply selecting genes where the p-values are less that 0.05 would lead to an excessive number of false positives. Our
strategy for dealing with the false-positive problem is elaborated elsewhere [7]. P-values order genes according to the evidence for the null hypothesis. Genes having gender differences in expression
are more likely to have small p-values and this is seen in a departure of their empirical distribution from its uniform expectation under the null [7,12]. Herein, the observed distribution was
assumed to be a mixture distribution with a proportion of the values having a uniform distribution, i.e., no gender difference in the expression, and the remainder having a Beta distribution, i.e.,
sexes differed. The mixing proportion and Beta parameters were estimated by maximizing the likelihood of this mixture distribution [6]. The estimated mixture components were used to estimate false
discovery rates for subsets of genes classified as 'having a gender difference' because their p-value is less than a specified value [7].
Data Completeness
This study interrogated 32,112 cDNA spots using six types of arrays, each having 5352 spots. For each spot, the data are typically 72 observations, i.e. log-intensities from 9 blocks × 2 arrays × 2
hybridizations (hyb) × 2 development times. With no missing values, there would be 32,112 × 72 (2,312,064) observations. About 2 % of the data was discarded because the quality of the image from the
phosphorimager was judged to be unsatisfactory, 48,168 observations: data from 6 of the 16 hr development times and 3 of the 72 hr development times. All block-array-hybridization combinations have
data from at least one development time and all blocks have at least 7 observations out of the 8 that were planned for. Thus, gender differences were estimable for all blocks and genes.
Scatter plots of the accepted data suggest that there may be a few outlier values on some arrays. We did not attempt to remove 'outliers'. Most occurred in spots with background levels of expression
and any apparent gender differences in these genes were classified as false positives because the gene was essentially 'not expressed' in this study. The few wider confidence bounds seen in Figure 6
may represent a contribution from an outlier.
Analyses of Covariance
The data for a spot were partitioned into six sources of variation as outlined in Table 1. The residual variation is the sum of squared differences between the 16 hour and 72 hour intensities after
adjusting for 'median' and 'time'. This source largely measures variation associated with aligning the data-capture template with the actual cDNA spots and the process of counting radioactive decays.
In particular, it does not have any variation due to subject differences, array differences, sample preparation differences or hybridization differences (Expected mean squared errors, Table 1).
Conceptually, the residual is a lower bound on measurement errors. The ratio of the respective mean squared errors with the residual mean squared error (F-ratio, Table 1) give the relative magnitudes
of variation as partitioned in this study. Table 1 reports the median of the 32,112 F-ratios for each source along with the p-value for an F-ratio with the table's degrees of freedom. Figure 1
summarizes these ratios from all spots as box plots. The dominant source of variation is associated with the regression using the median as a covariate. This is the median of the log-intensities of
the 5,352 spots that were interrogated on an array. The log[10](F ratio) is essentially greater than 2 for all spots with a median value of 3.23. The remaining sources generally have log[10](F ratio)
s that exceed 0 but usually do not exceed 1. Because the EMS for the source, 'Blocks', includes variance components from arrays, hybridizations, and subjects, the F-ratios for 'Blocks' should be
larger than those for 'Array(Block)', 'Hyb(Block)', or 'Sex(Block)', and this is the case in Figure 1. The smallest source of variation is 'Sex(Block)', median log[10](F ratio): 0.24. Since the box
plot for 'Sex(Block)' is not centered over 0, this source usually exceeds the residual variance implying that ^0.24 = 1.74 with 9 and 34 degrees of freedom has a p-value of 0.12.
Figure 1. Box plots summarizing the logarithm of F-ratios computed in the 32,112 analyses of covariance. The F-ratios for six sources of variation are each represented by a box plot. The box encloses
the range between the first and third quartile. The interior line is the median (Table 1). The dashed blue line encloses the interior 95% of the observations. More extreme values are plotted with a
plus (+) symbol; a few values for 'Time' less than -4 and values for 'Median' greater than 4 are not shown.
Figure 2. Scatter plot of estimated fold-changes before (a) and after (b) Loess smoothing. Figure 2a plots 5,352 estimates of the gender difference in expression from the analyses of covariance.
These estimates are for 'Block 5' and the genes interrogated on array type, GF201. The red line is the trend estimated by Loess regression. Figure 2b plots these data after removing the trend.
In the analysis of covariance, least squares estimates of the logarithm (base 2) of the fold-change in gene expression, males/females, were computed for each block and spot. These are hereafter
referred to as "estimated log-fold changes". Likewise, the least squares estimates of the expected log-intensity evaluated at median = 10 and the mean levels of the other factors, i.e., block, time,
hyb, and array, were computed for each spot. We refer to these estimates as "adjusted average log-intensities".
Adjustment by Loess regression
The upper panel of Figure 2 plots estimated log-fold changes from block 5 and array type GF201 (5352 spots) against the adjusted average log-intensities. This figure is representative of trends
observed over blocks and array types in the sense that the estimates exhibit systematic deviations from a horizontal line at 0 and these deviations tend to affect all spots within a neighborhood. The
magnitude and direction of these deviations differ by block and array type. So, it is unlikely that these deviations represent gender differences. Such trends were removed by Loess regression
computed within each block and array type, e.g., lower panel of Figure 2, yielding smoothed estimated log-fold changes.
Selecting expressed genes
The 32,112 spots represent 31,110 unique Genebank accession numbers (genes). Replicate estimates of adjusted average log-intensities were averaged to yield a single estimate for a gene. Figure 3 is a
normal probability plot of the 31,110 adjusted average log-intensities. The dashed line indicates that the lower values can be approximated by a normal distribution. We
that this distribution models the hybridization that occurs when the samples do not contain any mRNA matching the spotted cDNA sequence, i.e., genes that are not expressed in the sample. Under this
normal model for 'not expressed' genes, values exceeding 12 are unlikely,
> 2.1] = 0.018, to arise when a gene is not expressed in at least some of the samples. This cut point partitioned the interrogated genes into 2,800 'expressed' genes and 28,310 'not expressed' genes.
Most of the genes for cytochrome P450 enzymes were classified as 'not expressed'. This probably reflects a limited ability to discern low average levels of expression from background.
Figure 3. Normal probability plot of the estimates of the adjusted average log-intensities. The red line, actually 31,110 points, is a normal probability plot of the adjusted average log-intensities.
The dashed line indicates a normal distribution that roughly approximates the lower values, and it was used to model the background distribution of log-intensities. Our interpretation was that
adjusted average log-intensities exceeding 12 represent expressed genes.
Selecting genes with gender differences in expression
A p-value assessing the evidence of 'no gender effect' was computed for each gene. Figure 4 plots these p-values (1 - p) against their expectation under a uniform distribution. In this plot,
departures from the diagonal indicate that the p-values are not uniformly distributed. The p-values from the 'not expressed' genes are close to the diagonal, which corroborates our assumption that
these genes cannot differ because they are not expressed. The expressed genes depart from the diagonal. The observed distribution of p-values for the expressed genes was fit with a mixture model,
which estimates that 92% (2,576 genes) of the expressed genes arise from a uniform distribution, i.e., no gender difference, and 8% (224 genes) of the expressed genes have a beta (1.82, 5.89)
distribution, i.e., gender difference.
Figure 4. Cumulative frequency distribution of 1-p (p-value plot) for expressed genes and 'not expressed' genes. The distribution for expressed genes is green and the distribution for 'not expressed'
genes is black. The p-values are from the t-tests of a gender difference. The dashed lines indicate a theoretical uniform distribution for p-values under the null hypothesis; the black line assumes
that all of the 'not expressed' genes fit the null hypothesis and the green line assumes that 92% of expressed genes fit the null hypothesis.
Figure 5 plots expected error rates for gene selections based upon their p-values. For example, 134 genes have p-values less than 0.05. The estimated false discovery rate for these 134 genes is
0.905, which implies that the expression for 121 of these selected genes does not actually differ by gender. The estimated false non-discovery rate is 0.079. That is, 211 genes having a sex
difference are expected among 2,576 genes that are not selected. The fraction not selected is 0.94, 211 out of the 224 genes that are predicted to differ between the sexes. Figure 5 indicates that
the false discovery rate (solid blue line) would exceed 80% for any set of genes selected because their p-values are smaller than a specified value.
Figure 5. Expected classification errors for genes that are selected based upon their p-value from the t-test for a gender difference. When the genes are ordered by their p-values from the t-test of
a gender difference, the horizontal axis indicates the set of genes selected as having a gender difference. The vertical axis plots associated estimates of the false discovery rate (solid blue line),
false non-discovery rate (dash-dotted green line), and proportion of affected genes not selected (dashed red line). These estimates assume that 8% of the 2800 expressed genes, 224 genes, have a
gender difference where the 8% was estimated by fitting a mixture of distributions model to the observed p-values.
Figure 6. Estimated fold-changes in gene expression of males relative to females for 2800 expressed genes. The black points are the averages of the 9 Loess-smoothed estimates of the logarithm (base
2) of the fold change for the 2,800 expressed genes. The estimates were ordered from smallest to larges and the horizontal axis gives the cumulative proportion. Blue points are upper and lower 95 %
confidence bounds.
The average of the Loess-smoothed estimates (black) and their 95% confidence bounds (blue) are plotted for the 'expressed' genes in Figure 6. The horizontal axis in this plot is the rank of the
average among the 2800 'expressed' genes. All of the observed gender differences in gene expression are small. Essentially all of the point estimates (99.7 %) are within the interval, [-0.5, 0.5].
That is, observed fold changes were less than
This study aimed to identify genes in human livers for which expression differed between the sexes. Expression was assayed for 31,110 genes of which 2,800 were classified as "expressed". The
remainder of the interrogated genes had observed expression intensities that were indistinct from background, and they are classified as "not expressed". However, most of the genes for the cytochrome
P450 enzymes were in this "not expressed" subset, which suggests that detection was limited by background and/or the sensitivity of the labeled target. Evidence of a gender difference was evaluated
by a t-test, and a mixture model was fit to the observed p-values from these tests (Figure 4). This model estimated that expression in 8 % [95 % CI: 7 % to 9 %] of the 2,800 "expressed" genes
differed by gender. However, the ability of this study to identify specific genes is poor with estimated false discovery rates exceeding 80 % for every partition of the 2,800 genes (Figure 5).
The study estimated the relative difference in expression for all interrogated genes. These estimates were plotted for the "expressed" genes (Figure 6). All estimates are less than 1.55 fold and they
generally have narrow confidence intervals. Any gender differences that might be detectable through these arrays would be small, which excludes their anticipated use to monitor the persistence of
gender differences across immortalized cell lines.
The experiment was designed to adjust estimated gender differences for several sources of variation (Table 1). Since this design made twice as many measurements – two arrays per sample, this yielded
more precise estimates of gender differences than would have been possible with one array per liver sample. This design was proposed because we had access to a limited number of liver samples, and
arrays were relatively inexpensive. Conceptually, one could have used the same number or arrays with twice as many samples. Figure 1 showed that components of variation associated with arrays and
hybridizations are somewhat larger than the variation associated with subjects. These components do not impact the variation in the estimated gender difference under the implemented design. However,
they would under a one array per sample design, and any precision gained in estimating the subject component would be offset by the addition of array and hybridization components. Because these two
designs would estimate the respective variances of the gender difference with different degrees of freedom, the better of the two designs would depend on the number of blocks. In all but cases with a
few blocks, the implemented design would be better.
Figure 2 illustrates a case where there was a systematic trend in the least squares estimates. There were substantial trends in about half of the block – array type combinations. However, the needed
correction was not similar either within an array type or within a sample block. Consequently, estimated gender differences would be much more variable without the Loess smoothing. We suspect that
these trends are caused by spatial variation in binding due to intrinsic properties of membranes and/or irregular distribution of labeled solution, besides it seems unlikely that real gender
differences would exhibit this behavior. Smoothing eliminates much of this variation, but it also reduces the estimated difference. We tried several smoothing levels ranging from no smoothing to very
local smoothing. Figure 2 represents an intermediate level of smoothing, which was adopted for this report as a representative example. The smoothing levels that we tried gave similar distributions
for the p-values, and the same general conclusions would be reached. Namely, there is evidence of a few small changes but the specific genes cannot be identified. However, the rank of a specific gene
in Figure 6 or the genes included in a 'significant' set (Figure 5) depends far too much on decisions about the smoothing parameters.
The estimate that 8 % of the "expressed" genes have gender differences relies on the assumption that the p-values from genes with no gender difference in expression have a uniform distribution. Since
these p-values are based on a t-test, this assumption requires that the mean gender difference for each gene have a normal distribution. This is not unreasonable on theoretical grounds. Further,
bootstrap estimates are largely within the expected range if they are considered as estimates of the t-test's p-values (data not shown). That is, the assumption of a symmetric distribution under the
null hypothesis gives a distribution for the mean that is well approximated by the t-distribution.
More problematic is the assumption that the 2,800 tests are independent. Correlations are induced through shared conditions by all genes on an array, the normalization step, and the Loess regression
step. Further, expression levels among some genes are expected to be correlated because they work in concert to achieve a specific cellular structure or function. Simulation studies have shown that
the estimated number of affected genes is not biased by correlations among tests, but correlations increase the variance of this estimate substantially [13,14]. The reported confidence bounds on the
proportion of affected genes assume independence and likely underestimate the actual variation, possibly by a substantial amount. Consequently, the statistical significance of the 8 % estimate is not
P-values were computed for all interrogated genes. Genes that are not expressed should not have intensities that depend on sex. The p-values for the "not expressed" subset show little departure from
the diagonal (Figure 4), which is "as expected" if they arise under the null distribution. These genes also have correlations induced by shared conditions, normalization and Loess regression.
Apparently, these correlations were insufficient to disrupt the uniform distribution for these p-values.
We estimated that the gene expression of 224 genes differed between sexes. The observed gender differences in expression were small. False discovery rates exceed 80 % for every set of genes selected
by their p-values, essentially making it impossible to identify any specific genes with a gender difference.
Authors' contributions
RRD and CV developed the statistical design, analyzed the data, and wrote the manuscript. SD carried out the preparation of the liver samples and the cDNA array hybridizations. AJH conceived of the
study, participated in its design and coordination, obtained the grant and helped to draft the manuscript. All authors read and approved the final manuscript.
This study was funded by the Food and Drug Administration's Office of Women's Health and the National Center for Toxicological Research. The normal human livers used in this study were obtained
through the Liver Tissue Procurement and Distribution System, Pittsburgh, Pennsylvania which was funded by NIH Contract #N01-DK-9-2310. CV was supported by an Oak Ridge Institute of Science and
Education (ORISE) fellowship at NCTR during the early development of this research.
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Chapter 17 - Homework Reflections
Chapter 17 - Homework Reflections
Homework is an essential part of a mathematics class. Students are expected to do homework, because teachers know that students learn best when they work on problems, and practice their skills.
Hopefully, each homework assignment is discussed in class, so that the students find if they have any errors in their work. Teachers know that it is important that students not only recognize their
errors, but also learn how to do those problems correctly so that they will not make those errors again. Writing corrections to their homework assignments is a valuable task, one that will reinforce
the students' understanding of the concepts.
In my writing-intensive geometry class, I was also interested in hearing how the students felt about their homework assignments, their struggles, their errors, and their triumphs. I asked them to
select a few homework corrections for their portfolio, and to write reflections on those assignments: why they chose the ones the picked, and what (if anything) they learned from the correction
Of course a few always wrote about how they thought homework corrections were "a pain", and that they didn't really like to do them; but most of the students felt it was important that they find out
exactly what their error had been, in each case, and exactly why they had made that mistake. They agreed with me when I said that if we did not find the source of our errors, we were doomed to repeat
them. This also allowed them a way to vent their frustration at those errors they, themselves, called "stupid mistakes". (One wonders if there are "smart mistakes"!)
In her Homework Reflections, Malia wrote: "I chose to put this piece in my portfolio because I feel that homework is something that shows the amount of effort you put into a partucular class on your
own time. I am proud to say that I have always done my homework, and if I did not understand a problem, I made sure it was explained by a classmate or the teacher. I should have taken the time to
draw an accurate diagram. If I had just drawn the diagram below, I would have gotten the problem right. I sure won't make that mistake again!"
Keenan wrote "Although I have to admit it, I think homework is a great factor in how well you do in class. Homework also reflects how much effort a student puts into the work. If I feel that a
particular assignment is challenging or easy to forget, I circle it in my homework reflections. Then I know exactly which problems to review before the next test."
Shelly had some excllent ideas about methods for handling homework. She wrote "I keep a notebook with each homework assignment, and I write all the solutions clearly for each problem, step by step.
Then, when we go over them in class, I circle in red the ones I got wrong. I write notes to myself saying what I did wrong, like 'forgot to square it' or 'I was thinking area and it was supposed to
be perimeter'. (I think it's dumb to write something like "I made an arithemetic mistake" - the point is, what was the mistake, exactly!) Then I study these before the next test."
Jan began her corrections with the comment "In general, proofs are not my favorite part of math, but I've learned ways to get better at them. Mostly, writing clear notes explaining (to myself)
exactly where and how I went wrong is what works for me. Then, before the next test, I study what I wrote so I can do better the next time."
"It is easier to square the circle than to get round a mathematician."
Augustus De Morgan (1806-1871)
Go To Homepage Go To Introduction
1) Constructions 2) Clock Problem 3) Test Corrections 4) ASN Explain 5) Thoughts About Slope 6) What is Proof?
7) Similar Triangles 8) Homework Corrections 9) Quads Midpoints 10) Quads Congruence 11) Polygons
12) Polygons Into Circles 13) Area and Perimeter 14) Writing About Grading 15) Locus 16) Extra Credit Projects
17) Homework Reflections 18) Students' Overall Reflections 19) Parents' Evaluate Method 20) In Conclusion | {"url":"http://mathforum.org/sanders/exploringandwritinggeometry/hwreflections.htm","timestamp":"2014-04-21T00:28:54Z","content_type":null,"content_length":"6723","record_id":"<urn:uuid:7388f41b-b198-44a4-948b-160f704bb05e>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00174-ip-10-147-4-33.ec2.internal.warc.gz"} |
Some Important Features of unit Quaternions for Animation Programming
In the previous post, Euler angles and Quaternions were compared and some important reasons which causes the unit Quaternions to become the dominant rotation system in graphics and game engines were
studied. Now we know that we can't run away from quaternions if we want to become an animation programmer, gameplay programmer or graphics programmer, so lets check out two important feature of
First lets check out the multiplication of a quaternion to a vector. One vector can be transformed by being multiplied to a quaternion. This multiplication can both scale and rotate the vector. If we
multiply an unit quaternion to a vector, it just rotates it and no scale occurs. This is why all the graphics and game engines normalize quaternions before multiplying it to a vector. So after
normalizing a quaternion, a vector can be rotated with this equation:
Result = q * v * inverse(q);
Where q is an unit quaternion and v is our vector which we want it to be rotated and Result is the vector v after being rotated by q. One most important feature of quaternion multiplication is that
it's not commutative. So q1*q2 is not equal to q2*q1. This order of multiplication is really important for many animation algorithms like animation blending techniques. For example you can seek the
importance of this rule in additive animations. Additive animations are one type of animation which are the difference of at least two animations. Mostly they are used for asynchronous events. For
example you can create a breathing additive animation in which only character's spine bone is rotating in and out and other bones have no transformation. This additive animation can be added to any
animation like idle aiming, running and many more. Now if we want to add an additive animation to an existing one, we should notice about the order of quaternion multiplication. First the main
animation should be calculated, then the additive animation comes up on it so the rotations should be calculated in this order.
Now let's consider a simple example in which q1 is the rotation of main animation and q2 is the rotation of additive animation. the order of additive animation blending should be like this:
1- First apply q1 to the current vector (v) :
Result1 = q1 * v * inverse(q1)
2- Second apply q2 to the Result1:
Result2 = q2 * Result1 * inverse (q2) = q2 * q1 * v * inverse(q1) * inverse(q2)
So you can see if you want to add an animation to another you have to multiply them in reverse order like:
This means your vector first rotates by q1 and then q2, q3 ..., qn
Just note that most of the graphics and game engines overload the quaternion-vector multiplication with operator '*', so you can replace the 'q * v * inverse(q)' with just 'q * v'. If you are using
an engine or API which has overloaded quaternion-vector multiplication then you can apply the multiplication order mentioned above, like this:
Now lets consider another important feature of unit quaternions. You can consider the imaginary vector part of a unit quaternion as the axis which your vector wants to rotate around and the scalar
part is some value shows the amount of rotation around that axis. The imaginary vector part has a great feature and that is, its magnitude is equal to sin(a/2) where a is the rotation degree or
radian which you want your vector to rotate around the imaginary vector part of your unit quaternion. Also there is another important feature for unit quaternions and that is the the scalar part is
equal to cos(a/2). So whenever you want to create an unit quaternion which can rotate your object around an axis [x,y,z] with a degree equal to 'a', you can follow these steps in order:
1- First normalize your rotation axis:
[x,y,z]/ length( [x,y,z] )
2- Multiply the normalized rotation axis to sin(a/2) and use the result as your imaginary vector part.
3- Use cos(a/2) as your quaternion scalar part.
Now for a better understanding, lets consider an example in which you want to rotate your object around y-axis with 90 degrees. First you have to normalize your rotation axis which is [0, 1, 0]. In
this example, our rotation axis is already normalized so we should not normalized it again. Second, we should create our imaginary vector part by multiplying the rotation axis to sin( 90/2 ):
sin (90/2) = sin (45) = 0.7071
Imaginary vector part = [0, 1, 0] *0.7071 = [0, 0.7071, 0]
At the third step, we should calculate the scalar part of our quaternion which is equal to cos (90/2):
w = cos (45) = 0.7071
The final quaternion should be like this:
[ 0.7071, 0, 0.7071, 0]
You can write it as its mathematical form:
0.7071 + 0i + 0.7071j + 0k = 0.7071 + 0.7071j
This can be considered inversely, for the times you have an unit quaternion and you want to know how much it can rotates your vector. In this situation, for finding the desired degree you can do
DesiredDegree = 2 * ArcCos(w)
Don't forget that a unit quaternion can just rotate an object between 0 and 180 degrees because it uses ArcCosine function to represent rotations. So if you want to rotate an object more than 180
degrees through time, you have to do it with more than one rotation. For example if you want to rotate your object with 240 degrees linearly through time, you can first Slerp it it with 120 degrees
at t/2 and after that, Slerp it again with another 120 degrees at next t/2.
Most of the game and graphics engines use unit quaternions for rotations. Learning to work with them is very important. Some people prefer to use Euler angles for rotations because they are most
understandable but the fact is that the used graphics or game engine converts Euler angles to an unit quaternion because of the reasons i mentioned in this
. So by working directly with unit quaternions the conversion step of an Euler angles rotation to unit quaternions can be omitted.
In this post two important feature of quaternions and unit quaternions were considered. These two important features are using frequently in Animation, Gameplay or Graphics programming so its good to
keep them in mind. | {"url":"http://peyman-mass.blogspot.com/2013/05/some-important-features-of-unit.html","timestamp":"2014-04-19T18:02:45Z","content_type":null,"content_length":"62825","record_id":"<urn:uuid:54d077f6-474f-424d-8596-185626ddec06>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00322-ip-10-147-4-33.ec2.internal.warc.gz"} |
Can some one help explain cross correlation analysis?
February 26th 2013, 01:45 PM
Can some one help explain cross correlation analysis?
I was wondering if someone could help explain cross correlation to me with the data i have available.
I have two time series
One is how variable X changes each month over 133 months
the other is how variable Y changes month over 133 months
I'm using mini tab and i've set the LAG to 25% (33) as i wasn't sure what it should be and it produces a graph that i've copied in.
Can someone give me an insight into what i'm looking at?
I know this sounds really stupid but i'd love for someone to explain what the chart is actually demonstrating.
February 26th 2013, 03:30 PM
Re: Can some one help explain cross correlation analysis?
I was wondering if someone could help explain cross correlation to me with the data i have available.
I have two time series
One is how variable X changes each month over 133 months
the other is how variable Y changes month over 133 months
I'm using mini tab and i've set the LAG to 25% (33) as i wasn't sure what it should be and it produces a graph that i've copied in.
Can someone give me an insight into what i'm looking at?
I know this sounds really stupid but i'd love for someone to explain what the chart is actually demonstrating.
Hi joshnathan! :)
The cross correlation indicates how much X and Y are related and in particular how much variable Y lags with respect to X.
In the diagram you see that there is a peak is about 5 months.
This means that Y is similar to X, but lags about 5 months behind X.
This is not very clear though, because we see a high correlation between 0 up to 33 months.
However, we see specifically that Y is not really ahead of X, since the cross correlation is low there.
The LAG of 33 that you specified limits the graph to 33 months behind up to 33 month ahead.
February 26th 2013, 03:39 PM
Re: Can some one help explain cross correlation analysis?
Hello thanks with the useful information,
would it be worthwhile for me to produce one with a lag of 133 to see if it changes at any point?
This way i can analyse if there is a greater lag in the future.
Based on what you've said there is very little i can draw from this really as the correlation is relatively high for a very large period.
One thing i also wanted to confirm was that cross correlation treats both variables as being in a time series correct as these 133 events for x and y occur 1 month after each other? sorry if it
seems a bit stupid just i know that normal correlation doesn't observe the time series nature of the data.
February 26th 2013, 10:03 PM
Re: Can some one help explain cross correlation analysis?
Hello thanks with the useful information,
would it be worthwhile for me to produce one with a lag of 133 to see if it changes at any point?
This way i can analyse if there is a greater lag in the future.
Based on what you've said there is very little i can draw from this really as the correlation is relatively high for a very large period.
One thing i also wanted to confirm was that cross correlation treats both variables as being in a time series correct as these 133 events for x and y occur 1 month after each other? sorry if it
seems a bit stupid just i know that normal correlation doesn't observe the time series nature of the data.
A longer lag than say 25% does not necessarily give more information though.
If the overlap in time of the series becomes too low, the numbers won't mean much. | {"url":"http://mathhelpforum.com/statistics/213876-can-some-one-help-explain-cross-correlation-analysis-print.html","timestamp":"2014-04-17T09:16:36Z","content_type":null,"content_length":"8946","record_id":"<urn:uuid:0809c4bb-f995-4bb6-b382-a3a3ff2c026b>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00291-ip-10-147-4-33.ec2.internal.warc.gz"} |
Solving Rational Inequalities
November 7th 2012, 12:46 PM
Solving Rational Inequalities
I'm having a hard time solving this question:
(2t-10)/t > t + 5
I multiplied by the squared lowest common denominator value and tried to solve for x, except that I cannot find any real solutions. I'm not sure what else to do?
November 7th 2012, 01:01 PM
Re: Solving Rational Inequalities
The numerator has no real roots (the discriminant is negative), so we only have the critical number $t=0$. So, test the expression on the two intervals:
$(-\infty,0)$ and $(0,\infty)$. If the expression is negative on either interval, then that interval is the solution. | {"url":"http://mathhelpforum.com/algebra/206987-solving-rational-inequalities-print.html","timestamp":"2014-04-19T20:28:45Z","content_type":null,"content_length":"5200","record_id":"<urn:uuid:98c45ede-0b9e-4372-b2ab-f1ad6a2edde1>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00231-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Measuring quantum systems with a tunnel junction
Abstract (Summary)
This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale
manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a
nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will
be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description
of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement
process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise
on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a
non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the
oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the
junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator
frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and
the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry
of a nanomechanical oscillator.
Bibliographical Information:
School:Umeå universitet
School Location:Sweden
Source Type:Doctoral Dissertation
Keywords:NATURAL SCIENCES; Physics; quantum mechanics; quantum measurement; tunnel junction; qubit; nanomechanics; noise
Date of Publication:01/01/2006 | {"url":"http://www.openthesis.org/documents/Measuring-quantum-systems-with-tunnel-420190.html","timestamp":"2014-04-18T10:38:04Z","content_type":null,"content_length":"10280","record_id":"<urn:uuid:3ca3312f-1177-41d2-a7c9-ed324d4600cf>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00214-ip-10-147-4-33.ec2.internal.warc.gz"} |
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HELP!! for representing a fraction with the line betwn the numbers as a horizontal line?
Using AWK What command would display the contents of the file with line numbers for each line..
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If writing an essay about a poem, do I have to cite line numbers when quoting?
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Need help with a number line and finding the product of two numbers?
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a line is a collection of infinite numbers of points. but infinite times zero is zero. there must be no lenght?
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need help.Lithuanian,Latvia,Estonia - mobile & land line Telephone numbers.
what some good help line numbers?
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can we have the hot line numbers in the Philippines that we could call/contact, in case of suspected H1N1?
I'm looking to do my key skills level 2 application of numbers. is there any courses on line?
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by java Write a program that displays all prime numbers between100 and 1000 Print ten numbers per line?
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fuel line connectors part numbers on a 1972 mercury 500 50hp?
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2 land line phones. can i get an extension between the 2 different numbers?
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free northern california party line numbers?
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How do you plot a trend line (line of best-fit) in iWorks' 08 Numbers (Mac version of Excel)?
How do i get the numbers i have phone on a BT land line.
How do you plot a trend line (line of best-fit) in iWorks' 08 Numbers (Mac version of Excel)?
website.. with the play Julius Caesar including line numbers...
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What is the puzzle called that is a grid that has numbers that tell you how many squs colored per line?
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Where can I find the full text of The Aeneid by Vergil with the line numbers?
just dial dream 2 All board line numbers fasted and prayed!
What some chat line numbers for s?
(java) how can i output a line of numbers, without them being added?
does any one know los angeles party line numbers?
how to find a decimal numbers in between 2 numbers on a number line?
free html simple text editors(with colors and line numbers)?
Who currently dominates the unemployment line highest in numbers people who vote Democratic or Republicans?
Why doesn’t Java have line numbers?
Who created the offensive line numbering system in american football?
Using a linear model (for example, a number line, a ruler) to compre the pairs of rational numbers that follow?
Storing a line of numbers to a variable in c?
Is there anybody know how to revise two phones numbers to use in one phone line?
how to unblock blocked phone numbers on a land line?
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What do I do when citing a play without line numbers?
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How do you change the font of line numbers in Microsoft Word?
does a number line only have whole numbers?
Storing a line of numbers to a variable in c?
Using AWK What command would display the contents of the file with line numbers for each line..
Any way to put line numbers on Microsoft Word?
How to represent irrational numbers on the number line?
Anyone know any chat line numbers?
C program to find the largest of three numbers using command line argument?
Java question - how to get numbers to line up?
How can I create line numbers in MS Excel?
Loooking for info website/ telephone numbers for Phone Sx Chat Line Jobs In Ireland?
What the Daily Mails lucky line numbers?
excel vba coding line numbers?
In which year was the last CL final where all the players from starting line up had the numbers from 1 to 11?
how do I make a number line using these numbers in Microsoft Excel.
PLEASE HELP?? HOW do you quote the line numbers of POETRY?
do u know any party line numbers?
How to graph the solution set all real numbers on a number line?
what is the line and numbers from a grid system that allow us to describe the location on earth?
How do you receive multiple different business numbers to one phone line?
Does anybody now any party line phone numbers?
do u no any bi or lisbean chat line numbers?
internal rhyme in canterbury tales prologue?? pls give line numbers?
Circle or Line? How all numbers represented?
How do you find the distance between a pair of points (numbers) on a number line?
where can i find the most official version of Romeo and Juliet with line numbers?
how do i find a line joining 2 complex numbers?
excel vba coding line numbers?
How do I type the symbol for all real numbers on microsoft word? It looks like the letter R with a line?
Does anyone know of any doctor hot line numbers?
do you guys know any free chat line numbers?
Places the numbers 1 to 9 and so that each line of 3 numbers add 13?
If i put 40 lines on the lottery what my chances of getting 3 numbers on one line?
free html simple text editors(with colors and line numbers)?
I dont know how to find a point on a line without any given numbers. Help?
need to know where to look on line for residents phone numbers for grimsby and cleethorpes?
In the play, Julius Caesar, when does the line numbering start over?
Why isn't there a straight line of composite numbers?
Is there any online directory for mobile phone numbers in India?
what the line numbers for the following lines in shakespes 12th night?
party line numbers?
What the numbers to any Party line gay/bi/straight?
any 1 no of any 1800 chat line numbers for 17 and under?
what happens to the numbers on the line of laude as you move further away from the equator?
Are there any web sites that let you look up cell and land line phone numbers at no charge?
Whats the free chicago chat line numbers ?
what is the meaning of the three numbers given as a baseball players batting line?
C program to find the largest of three numbers using command line argument?
How do I display the line numbers when printing an Excel 07 doent?
Local Chat Line Numbers?
Numbers on each line of my word doent?
Copy a file character by character to another file adding line numbers to each line in Java 2.5?
If writing an essay about a poem, do I have to cite line numbers when quoting?
What the numbers for line 5 on the vision test at the dmv?
I have to write a paper on Oedipus Rex. How am i supposed to do quotes if there no line numbers?
Numbers on each line of my word doent?
any body know a free chat line numbers?
Craps table with additional numbers on the Place line?
Is there a website for plotting rational numbers on a number line?
Is it true Pres Obama is intoducting a line in the budget that would get rid of the numbers 1 and 2?
I received a personal check that had a strange MICR line. I want to know what the last set of numbers .
when do you have to start using npi numbers and what line of the hcfa 1500 form does it go on?
what happens to the numbers on the line of laude as you move further away from the equator?
CALC: How do i determine the numbers btw 0 and 2pi where the line tangent to a curve is horizontal???
do any of u know any good chat line numbers for the sacramento a?
Noble Eagle IA line numbers?
In the olympics track races is the finish line the blue line or the line with all the numbers in front of it?
I have created a chart in excel 2007, and copied two sets of numbers to a line chart. problem is they in ?
How line numbers in the Air Force work?
Proper fractions on the number line exist between what numbers?
Who currently dominates the unemployment line highest in numbers people who vote Democratic or Republicans?
Look cfully at each line of numbers in the number pyramid.What number should replace the question mark in t?
On guitar tab what does it mean when I have a sloping line connecting to numbers? ?
a can you help me find some party line numbers?
Can I get contact numbers/Deptt issuing below proverty line certificates.What is the criteria for the same.
I can't attach my address numbers to my address plaque because the holes don't line up. How can I attach them?
how do i put line underneath numbers?
MS Word 2007 line numbers help?
In the olympics track races is the finish line the blue line or the line with all the numbers in front of it?
when graphing numbers on a number line, does the solid dot mean the number above is not included?
How to add line numbers in a file?
what the line numbers for the following lines in shakespes 12th night?
what is the free chat line numbers for west palm beach florida?
Do line numbers vary from print edition to edition?
by java Write a program that displays all prime numbers between100 and 1000 Print ten numbers per line?
Land line where I can store many numbers?
what is the strategy used to solve missing numbers on a number line?
how do you find home and cell phone numbers on line?
How can i put numbers on top of a line?
What is a light green bar shaped pill with Watson on one side and the numbers 395 then line and 50 over 0.5?
Is the Euro line Enron in its fudged numbers and could have this contributed to our crisis?
Look cfully at each line of numbers in the number pyramid.What number should replace the question mark in t?
can you call 1-800 numbers from a local only phone line?
where can i find the romeo and juliet play with the line numbers for reference on the side of each line(row)?
Where can I find the whole text of The Tragedy of Julius Caesar with the line numbers?
Why and how is Oedipus Rex not guity of and insest....line numbers please..if not its ok?
Where could I go to use phone line that allows me to call 1-900 numbers?
If real numbers can be presented on a number line...
what websites show the line numbers for romeo and juliet along with the full translation?
do any of u know any good chat line numbers for the sacramento a?
Who the people who call into these TV shows on premium line numbers?
Can I get contact numbers/Deptt issuing below proverty line certificates.What is the criteria for the same.
How do you configure 'grep' to not add line numbers?
How do I cite a play with no line numbers or scenes?
Is there a way to put line numbers on Microsoft works?
When checking the lotto max ticket to win do the numbers have to be in one line to win?
Dose anyone know any wierd phone numbers other than the rejection line?
How do I reset the numbers on Linux command line prompt?
determine the length of the straight line from A to B to three significant numbers?
Where is on-line mathematical tool to find functional relationship from sequence of numbers?
Treat a block of numbers in excel as one line?
Where online can I get the book "Love's labours lost" with the line numbers (free)?
What some chat line numbers for s?
in java programming, there ways to use big int in a program for Fibonacci numbers with command line input?
can you call 1-800 numbers from a local only phone line?
what line is the stage direction "exit pursued by a bear" on?
Free Cleveland Ohio Chat-line Numbers?
does anyone know any chat line telephone numbers?
What's the pattern of this set of numbers and what is the next line?
Think of the number line of irrational numbers...
Craps table with additional numbers on the Place line?
MTA Line Numbers?
what is the free chat line numbers for west palm beach florida?
What all the rejection hot line numbers?
does it list incoming calls and phone numbers on your land line phone bill?
What some TS chat line phone numbers?
Craps table with additional numbers on the Place line?
How to add line numbers in a file?
How do I get tabs, bullets, and numbers to stay on the line I want without getting them on lines before it?
when do you have to start using npi numbers and what line of the hcfa 1500 form does it go on?
how to view line numbers along with the code in microsoft visual studio?
MTA Line Numbers?
write a program that will print out the numbers from 53 to 48, backwards,all on one line.Print Starting & Done
where can i find the most official version of Romeo and Juliet with line numbers?
Excel Formating: Turn a column of numbers into a horizontal line (example in details)?
What line numbers these lines from Shakespe's A Midsummer Night's Dream?
Why and how is Oedipus Rex not guity of and insest....line numbers please..if not its ok?
What do you call the straight line between the two numbers in a fraction?
a program that prints the numbers 1 to 4 on the same line with each pair of adjacent numbers separated by one?
a line is a collection of infinite numbers of points. but infinite times zero is zero. there must be no lenght?
does anyone know any good free chat line numbers ? i am very bored?
Has anyone got the numbers on what percentage of people must stay below the poverty line to keep?
how to format in a c++ program the output so there between 5 to 10 numbers per line when executing a loop?
If you can have negative numbers, can you have a negative scale as well as flavors of number line?
PETS/Dogs/Is anyone familiar with the American Canine Association and how to research official numbers on-line?
Which mobile should I buy if I want to barr particular mobile numbers or land line numbers?
i need a softw that can identify four numbers out of six numbers from a full list of 1000 lines; each line?
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Where I can get important help line numbers for dindigul?
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How much do you think my $1 bill with all double digit numbers on the serial line could sell for on Ebay?
[Phone codes] How to dial land-line numbers from mobile?
free date line numbers dose any 1 know any?
Does anyone know any phone numbers for child services or family services, or just any hot line. Thanks?
life line numbers?
Where can i find Hamlet online with line numbers?
Where can I get the free party line numbers for my a 831?
does anyone know any chat line telephone numbers?
free chat line numbers for the stockton and sacramento as?
does the president direct line or personal line has 7 numbers like any telephone number in the U.S?
Does anyone know any local free trial chat line numbers in Virginia?
how to find a decimal numbers in between 2 numbers on a number line?
I want to get Land line Telephone numbers with address in Washigton DC? Is there any idea to get access?
add the numbers on the number line from zero both ways as far as they go?
Why were the numbers 911 chosen for the emergency hot-line?
What is the option Word (vista) to insert line numbers in a doent?
Party Line numbers please?
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Is the Euro line Enron in its fudged numbers and could have this contributed to our crisis?
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Where can I read Romeo and Juliet online in full with line numbers?
Why all the useful finite numbers on the zero side of the number line?
What is the command that causes line numbers to appear in vi. How do you enter the command.
Do line plots have to have numbers?
How do I cite a play with no line numbers or scenes?
How to plot whole numbers AND decimals on a number line?
Can anybody help me find an online version of The Scarlet Letter with page and line numbers?
Proper fractions on the number line exist between what numbers?
Using a linear model (for example, a number line, a ruler) to compre the pairs of rational numbers that follow?
Can someone tell me if the usage of the line numbers is correct?
How do I find the geographic telephone number of companies who insist you phone them on premium line numbers?
Do you know any phone chat line numbers with free trials?
free date line numbers dose any 1 know any?
How to get line of best fit on iWorks numbers?!
How to add line numbers in word but only to certain parts of the text, not the whole doent ?
Copy a file character by character to another file adding line numbers to each line in Java 2.5?
two differnt phone numbers and one line?
need to read the Odyssey online with line numbers?
How can we ign a position to irrational numbers(eg.Root2,Pi) on the number line even the value is not known?
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How do you write Numbers like √12 On a number line?
Is this normal with dedicated data line numbers?
Where can i find Hamlet online with line numbers?
does the president direct line or personal line has 7 numbers like any telephone number in the U.S?
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Who came up with and why the numbers for the emergency line, "9" "1" "1" ?
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Has anyone got the numbers on what percentage of people must stay below the poverty line to keep?
where do you find the odyssey with line numbers?
How do I write the equation of a line with a Domain of all real numbers and a range of 2?
i need a softw that can identify four numbers out of six numbers from a full list of 1000 lines; each line?
how to unblock blocked phone numbers on a land line?
Does anyone know any phone numbers for child services or family services, or just any hot line. Thanks?
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Do line numbers vary from print edition to edition?
show me some bsnl land line numbers?
free chat line numbers for the stockton and sacramento as?
hi does anyone know how i can stop land line numbers showing up as blocked on my iphone?thanks?
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fuel line connectors part numbers on a 1972 mercury 500 50hp?
Is there any online directory for cell phone numbers in India?
with a sky line rental, can you see the numbers of incoming international calls?
Does anyone know any gay help line numbers so I can stop being gay? | {"url":"http://okay.so/en/list/line+numbers/0/","timestamp":"2014-04-17T15:42:09Z","content_type":null,"content_length":"88119","record_id":"<urn:uuid:3e883e43-d895-48b1-a822-c612d0e5df5f>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00326-ip-10-147-4-33.ec2.internal.warc.gz"} |
Posts from December 9, 2008 on The Unapologetic Mathematician
We know that we can take direct sums of vector spaces. Can we take representations $\rho:A\rightarrow\mathrm{End}(V)$ and $\sigma:A\rightarrow\mathrm{End}(W)$ and use them to put a representation on
$V\oplus W$? Of course we can, or I wouldn’t be making this post!
This is even easier than tensor products were, and we don’t even need $A$ to be a bialgebra. An element of $V\oplus W$ is just a pair $(v,w)$ with $v\in V$ and $w\in W$. We simply follow our noses to
The important thing to notice here is that the direct summands $V$ and $W$ do not interact with each other in the direct sum $V\oplus W$. This is very different from tensor products, where the
tensorands $V$ and $W$ are very closely related in the tensor product $V\otimes W$. If you’ve seen a bit of pop quantum mechanics, this is exactly the reason quantum system exhibit entanglement while
classical systems don’t.
Okay, so we have a direct sum of representations. Is it a biproduct? Luckily, we don’t have to bother with universal conditions here, because a biproduct can be defined purely in terms of the
morphisms $\pi_i$ and $\iota_i$. And we automatically have the candidates for the proper morphisms sitting around: the inclusion and projection morphisms on the underlying vector spaces! All we need
to do is check that they intertwine representations, and we’re done. And we really only need to check that the first inclusion and projection morphisms work, because all the others are pretty much
the same.
So, we’ve got $\iota_1:V\rightarrow V\oplus W$ defined by $\iota_1(v)=(v,0)$. Following this with the action on $V\oplus W$ we get
But this is the same as if we applied $\iota_1$ to $\left[\rho(a)\right](v)$. Thus, $\iota_1$ is an intertwiner.
On the other hand, we have $\pi_1:V\oplus W\rightarrow V$, defined by $\pi_1(v,w)=v$. Acting now by $\rho$ we get $\left[\rho(a)\right](v)$, while if we acted by $\rho\oplus\sigma$ beforehand we’d
Just as we want.
The upshot is that taking the direct sum of two representations in this manner is a biproduct on the category of representations.
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Portfolio analysis
1. 470182
1) During the past year, you had a portfolio that contained U.S. government T-bills, long-term government bonds, and common stocks. The rates of return on each of them were as follows: U.S.
government T-bills 5.50%, U.S. government long-term bonds 7.50%, U.S. common stocks 11.60%. During the year, the consumer price index, which measures the rate of inflation, went from 160 to172 (1982
- 1984 = 100). Compute the rate of inflation during this year. Compute the real rates of return on each of the investments in your portfolio based on the inflation rate.
2) Assume that the consensus required rate of return on common stocks is 14 percent. In addition, you read in Fortune that the expected rate of inflation is 5 percent and the estimated long-term
real growth rate of the economy is 3 percent. What interest rate would you expect on U.S. government T-bills? What is the approximate risk premium for common stocks implied by these data?
3) a) Someone in the 15 percent tax bracket can earn 10 percent on his investments in a tax exempt IRA account. What will be the value of a $10,000 investment in 5 years? 10 years? 20 years?
b) Suppose the preceding 10 percent return is taxable rather than tax-deferred. What will be the after tax value of his $10,000 investment after 5, 10, and 20 years?
4) Assume that the rate of inflation during all these periods was 3 percent a year. Compute the real value of the two tax-deferred portfolios in problems 4a and 5a.
Calculating the Rate of Inflation, risk premium on common stock, after tax value, etc | {"url":"https://brainmass.com/business/the-role-of-government-and-regulation/470182","timestamp":"2014-04-19T20:27:10Z","content_type":null,"content_length":"29552","record_id":"<urn:uuid:c15eb64d-d1d8-43b4-be68-255dc3809c3e>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00585-ip-10-147-4-33.ec2.internal.warc.gz"} |
Converting 2D array from C to MIPS assembly language (Beginner)
08-03-2012 #1
Join Date
Aug 2012
Hi there guys,
I am trying to understand how 2D arrays are implemented in MIPS assembly. Now I tried looking online for a few examples but they have no MIPS code so its hard for me to understand the logic
behind implementing 2D arrays in MIPS.
Heres a random question I picked from a source.
On first glance, the question is easy to implement in C, C#, C++ and java however, when it comes to MIPS I get confused.
If someone can give me a sample code in MIPS then I would really appreciate it.
Step 1 is write this as a 'C' function (not main).
Step 2 is compile it with "gcc -S prog.c"
Step 3 is study prog.s
Step 4 is read your MIPS assembler reference manual and try to match up the assembler you see with MIPS instructions.
If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
If at first you don't succeed, try writing your phone number on the exam paper.
I support http://www.ukip.org/ as the first necessary step to a free Europe.
I mean I dont want to convert it without understanding it. I was wondering if someone can explain me the MIPS code after conversion.
Do you have MIPS code for it already?
> I mean I dont want to convert it without understanding it.
There is very little danger of you arriving at MIPS code which works without you understanding it.
If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
If at first you don't succeed, try writing your phone number on the exam paper.
I support http://www.ukip.org/ as the first necessary step to a free Europe.
No I was wondering if someone can convert it to MIPS and explain whats happening =(
If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
If at first you don't succeed, try writing your phone number on the exam paper.
I support http://www.ukip.org/ as the first necessary step to a free Europe.
There are a TON of sites brought up by Google for MIPS assembly language programming:
Including this gem:
Programmed Introduction to MIPS Assembly Language
What you want is not really C language help, so that's one problem. (many of us never learned, or have long since forgotten what we were taught about MIPS assembly language).
Second problem is we try to help people with THEIR work - it's a really rare day that we actually DO code up a problem, unless it's VERY trivial or interesting, and can't be readily discussed
without having a program to show what we mean. Note that this is not the case with your problem.
Third, your "random question" is not exactly "Hello World" is it? A first program with a 2D array in MIPS a.l., it seems to me, should consist of something far simpler.
There are a TON of sites brought up by Google for MIPS assembly language programming:
Including this gem:
Programmed Introduction to MIPS Assembly Language
What you want is not really C language help, so that's one problem. (many of us never learned, or have long since forgotten what we were taught about MIPS assembly language).
Second problem is we try to help people with THEIR work - it's a really rare day that we actually DO code up a problem, unless it's VERY trivial or interesting, and can't be readily discussed
without having a program to show what we mean. Note that this is not the case with your problem.
Third, your "random question" is not exactly "Hello World" is it? A first program with a 2D array in MIPS a.l., it seems to me, should consist of something far simpler.
Hi there, Yes I understand basic MIPS and even implementing a 1D array. But just having difficulty with 2D arrays
Look into indexed addressing. That's how 2D arrays are usually done in assembly.
You know that this is not an ASM board, let alone a MIPS ASM board. I strongly suggest you ask your question over on an ASM board, with a far simpler example question - and please forget the name
I can't begin to tell you how often students and lazy programmers drop requests for help similar to yours, just to get someone to do their code up for them.
Aren't all arrays (under the hood), done by using a base address + an increment on a pointer?
Last edited by Adak; 08-06-2012 at 05:12 AM.
Isn't that EXACTLY what we were saying to you anyway? This isn't C, at all, and this is a C forum. You want to know how something would appear in MIPS assembly, but haven't tried to write it like
that yourself. You're not interested in seeing working MIPS assembler as a compiler would churn out, either. You want someone on a C forum to bypass C entirely and write their own MIPS assembly
directly to solve a stated problem which looks like a class exercise to me.
I suggest you do your own homework and never darken this forum with your presence again. But, of course, you'll have some insightful and witty comeback ready to hand, no doubt.
- Compiler warnings are like "Bridge Out Ahead" warnings. DON'T just ignore them.
- A compiler error is something SO stupid that the compiler genuinely can't carry on with its job. A compiler warning is the compiler saying "Well, that's bloody stupid but if you WANT to ignore
me..." and carrying on.
- The best debugging tool in the world is a bunch of printf()'s for everything important around the bits you think might be wrong.
Well, I don't recall much about assembly, since I barely spent any time with it, but it won't matter.
That kind of language isn't up to our board's standards, so you will soon be booted off the forum.
I posted this on a C forum because its easy to implement this in C, C#, C++ etc but you can use a compiler to convert it to assembly if you didnt know.
Obviously, you can use a compiler to convert C code to assembly, since most C compilers do that as an intermediate step. However, your question is really about MIPS, not C, regardless of how easy
it is to implement in C.
If you had provided the requisite C code that you were trying to convert and posted your best attempt, then perhaps your thread would be marginally on topic, but as it is, this whole thread is
off topic.
Furthermore, your behaviour in this thread is against the forum rules. Hence, consider this an official warning.
*thread closed*
C + C++ Compiler: MinGW port of GCC
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Look up a C++ Reference and learn How To Ask Questions The Smart Way
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On This Day in Math - July 7
Probability is a mathematical discipline whose aims are akin to those,
for example, of geometry of analytical mechanics.
In each field we must carefully distinguish three aspects of the theory:
(a) the formal logical content,
(b) the intuitive background,
(c) the applications.
The character, and the charm, of the whole structure cannot be appreciated without
considering all three aspects in their proper relation.
William Feller, An Introduction to Probability Theory and its Applications
The 189th day of the year; the product of the primes in a prime quadruplet always end in 189, except for the very first quadruplet 3x5x7x11.(
A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form {p, p+2, p+6, p+8} you can see some of the smaller ones listed here
1339 There was an annular-total eclipse, with the total part of the track finding its way between the Orkney and Shetland Islands without touching either. At this location the track of totality was
only 1 km wide, with a duration of 1 second! Presuming that you could position a boat to an accuracy of 1 km, totality must have been a ring of Baily's Beads. *NSEC
1668, Sir Isaac Newton received his M.A. from Trinity College in Cambridge.*TIS
1742 Goldbach's conjecture was sent in a letter to Leonhard Euler on 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime
numbers." It has been checked by computer for vast numbers - up to at least 4 x 10
- but still remains unproved. *TIS
1747 Johann Sebastian Bach dedicated his Musikalisches Opfer (Musical Offering) to Frederick the Great. For a discussion of the mathematical significance of this cerebral music, see Godel, Escher,
Bach: An Eternal Golden Braid by Douglas R. Hofstadter. *VFR
1777 Johan Bernoulli, then astronomer Royal, Berlin, is paid a sum of 84 pounds for the Sexcentenary tables. "To Mr. John Hyacinth Magellan....for the use of Mr. Bournoulli .. as a reward for his
care and trouble in constructing a manuscript Book of Tables for facilita."
Two years later they would pay 28.35 pounds to Dr. Charles Hutton for translating the preface of the tables.
1823 William Rowan Hamilton passed into Trinity College, Dublin. He was easily first out of the 100 candidates. *VFR
1847 Lassel discovered a satellite of Neptune. *VFR (this date does not concur with other dates on these discoveries) In 1846 Lassell discovered Triton, the largest moon of Neptune, just 17 days
after the discovery of Neptune itself by German astronomer Johann Gottfried Galle. In 1848 he independently co-discovered Hyperion, a moon of Saturn. In 1851 he discovered Ariel and Umbriel, two new
moons of Uranus.*Wik
1855, a letter from Michael Faraday in The Times newspaper, London, described the polluted state of the River Thames he had observed on a boat trip: "The whole of the river was an opaque pale brown
fluid. In order to test the degree of opacity, I ... dropped [pieces of card] into the water at every pier the boat came to; before they had sunk an inch below the surface they were
indistinguishable, though the sun shone brightly at the time." His words, he said, were no exaggeration, they were "the simple truth." He asserted, "If there be sufficient authority to remove a
putrescent pond from the neighborhood of a few simple dwellings, surely the river which flows for so many miles through London ought not to be allowed to become a fermenting sewer." *TIS I wrote a
few years ago about the
return of the seahorse
to the muddy waters of the Thames.
1638 Francois or Francois Bertrand Barrême Barrême,(7 July 1638, Tarascon, France - 1703, Paris France) is considered one of the founders of accounting . After having engaged in trading in Italy , he
moved to Paris where he gave lessons in bookkeeping and became a protégé of Colbert . Expert for the accounts of the Accounting Chamber of Paris and King's ordinary arithmetician, he is the author of
books of mathematical conversions. His books were so common that today his name is used for what was once in English called a "ready reckoner", a table of numbers used to facilitate simple
calculations, esp one for applying rates of discount, interest, charging, etc, to different sums . *Wik
1746 Giuseppe Piazzi (July 7, 1746 - July 22, 1826) an Italian mathematician and astronomer. He discovered the asteroid Ceres and established an observatory at Palermo, now the Osservatorio
Astronomico di Palermo – Giuseppe S. Vaiana. (for more detail see the source article) *
Today in Astronomy
1752 Joseph-Marie Jacquard born (7 July 1752 – 7 August 1834). *VFR French silk weaver, (born Lyons), inventor of the Jacquard programmable power loom for brocaded fabric. His loom would mechanically
produce any pattern, controlled by perforated control cards (1805). This served as the impetus for the technological revolution of the textile industry and is the basis of the modern automatic loom.
The concept of using punched cards was later applied by Hollerith to keeping track of the 1890 US census data. The idea futher evolved to computer input punched cards. *TIS
1816 Rudolf Wolf Swiss (7 July 1816 – 6 December 1893) astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of
its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and
sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte
Carlo methods.*TIS
1888 Archibald Goldie (7 July 1888 in Glenisla, Angus, Scotland - 24 Jan 1964 in London, England) studied at the universities of St Andrews and Cambridge. He served in the Meteorological Service of
the British Army in World War I and continued to work in various branches of the Meteorological Office.*SAU
1906 Birthdate of the probabilist William Feller (July 7, 1906 – January 14, 1970). He once said that multiplication, especially before breakfast, is seldom commutative. He died in 1970. *VFR
Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States.
In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the
Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By
stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller
contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the
theory of "Feller operators".*Wik
1900 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *VFR
1927 Magnus Gustaf Mittag-Leffler died (16 March 1846 – 7 July 1927) . Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to
mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus,
analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the
analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem.*TIS
1930 Sir Arthur Conan Doyle (22 May 1859 – 7 July 1930) Scottish novelist, physician, spiritualist. His fictional detective, Sherlock Holmes, emulates the scientist, diligently searching through data
and to make sense of it. "It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." *TIS
1942 William Henry Young (London, 20 October 1863 - Lausanne, 7 July 1942) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series
in general.*SAU
1975 William Hodge (17 June 1903 – 7 July 1975) studied at Edinburgh and Cambridge Universities. After some time at Bristol and in the USA he returned to Cambridge and became Lowndean Professor of
Astronomy and Geometry. His main interests were in Algebraic Geometry and Differential Geometry. He became an honorary member of the EMS in 1954. He was knighted in 1959. *SAU His discovery of
far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on
subsequent work in geometry. *Wik
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell | {"url":"http://pballew.blogspot.de/2012/07/on-this-day-in-math-july-7.html","timestamp":"2014-04-21T14:41:08Z","content_type":null,"content_length":"109398","record_id":"<urn:uuid:a7a4eb54-abc6-4306-9737-254e862850b3>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00558-ip-10-147-4-33.ec2.internal.warc.gz"} |
A Possible Polymath Project?
May 12, 2011
An interesting old problem of Erdős
Leo Moser was a mathematician who worked in combinatorics. He created, among many other things, a notation for extremely large numbers, and worked on the problem of coloring the plane.
Today I want to talk about an old Diophantine problem he worked on that may be ripe for some progress.
The other problem, which is probably not ripe for progress, is the the plane coloring problem first stated by Ed Nelson:
How many colors are needed to assign each point of the plane a color so that no two points exactly distance ${1}$ apart have the same color?
The value is known to be either ${4}$, ${5}$, ${6}$, or ${7}$; the lower bound is due to Moser and the upper bound is due to John Isbell.
The following graphic used by Wikipedia shows both.
The graph is called the Moser spindle, and its seven vertices with unit-distance edges shown require four colors. The hexagons are somewhat less than unit-distance across, but with more than unit
distance to the nearest of the same color, so seven colors suffice. The seven color sets are translations of each other, and Hugo Hadwiger in 1945 had used the same pattern to give an upper bound of
7 on the related problem of tessellating the plane by congruent sets, whose best-known lower bound is 5. Paul Erdős and Nicolaas de Bruijn employed the Axiom of Choice to show that the true value is
enforced by some finite unit-distance graph—which need not be a planar graph, though the Moser spindle is planar. It is known that any 4-coloring of the plane must involve color set(s) that are not
Lebesgue measurable, while recent work indicates that forms of choice would be required for any 4-coloring. Thus this problem goes deep in a hurry.
I cannot resist to add that I knew Isbell, since I once took a course on projective geometry from him when I was an undergraduate at Case Western Reserve. He later moved from Case in 1969 to the
University at Buffalo, where he stayed until he retired in 2002. Ken did not know him there—it is a small world—but not that small. I will write soon about him and my adventure into projective
geometry, which was one of the hardest courses I have ever taken. But that is another story, for another day.
The Problem
The problem is a Diophantine conjecture, raised by Erdős around 1950 in a letter to Moser. The conjecture is that there are no solutions to the equation
$\displaystyle 1^{k} + 2^{k} + \cdots + (m-1)^{k} = m^{k},$
where ${k \ge 2}$ and ${k,m}$ are natural numbers. This is a typical style of question that Erdős would raise over and over. In 1953 Moser made partial progress on it, and proved that there is no
“small” solution:
Theorem: Any solution with ${k \ge 2}$ must have ${m > 10^{10^{6}}}$.
A recent paper by Pieter Moree in the American Mathematical Monthly explains the conjecture’s history, gives a improved bound, and explains in detail how it is proved. The best known lower bound now
Theorem: Any solution with ${k \ge 2}$, must have ${m > 10^{10^{9}}}$.
The paper of Moree shows how to prove a weaker bound via elementary means. As usual “elementary” does not mean simple, but means that only basic number-theory tools are used. The main ingredients
• Basic properties of congruences.
• The Chinese Remainder Theorem.
• The simple fact that
$\displaystyle \sum_{k=1}^{m} \frac{1}{p_{k}}$
is never an integer if ${p_{1},\dots, p_{m} }$ are distinct primes. Do you see why?
• The behavior of the function ${p(\alpha)}$, which is defined to be the smallest ${x}$ so that
$\displaystyle \sum_{p \le x} \frac{1}{p} \ge \alpha.$
The sum is over primes.
The latter function is well defined since Leonhard Euler proved that
$\displaystyle \sum_{p \le x} \frac{1}{p} = \ln\ln x + O(1).$
Since the sum grows very slowing, computing the function ${p(\alpha)}$ exactly is a serious computational challenge. For example, the record appears to be
$\displaystyle p(4) = 1801241230056600467.$
This result is due to Eric Bach and Jonathan Sorenson.
One Idea
The thought I have is that the equation should yield a tight bound on ${k}$ vs ${m}$. This will not solve the problem, but may allow us to get some additional insights into the possible solutions.
Assume that ${(k,m)}$ is a solution, then
$\displaystyle \frac{1^{k}}{m^{k}} + \frac{2^{k}}{m^{k}} + \cdots + \frac{(m-1)^{k}}{m^{k}} = 1.$
This is equal to,
$\displaystyle \sum_{\ell =1}^{m-1} (\frac{m-\ell}{m})^{k},$
and this is the same as,
$\displaystyle \sum_{\ell =1}^{m-1} (1-\frac{\ell}{m})^{k}.$
The latter should show that
$\displaystyle \sum_{\ell =1}^{m-1} \exp(-k\ell/m) \approx 1.$
The thought I have is that the equation should yield a tight bound on ${k}$ vs ${m}$. This will not solve the problem, but it should imply that ${k}$ must be almost equal to ${m}$, and I hope that
this inequality will allow us to make some progress on the conjecture. I have not tried to work out the approximation, but I believe that some useful information could come from this. The reason we
feel it is a good candidate for a PolyMath project is that investigating these equations and approximations may require computer algebra, with cases that can be worked on in parallel by different
Open Problems
Is this a possible problem? Can we at least improve the bound somewhat?
Whenever we see a hard Diophantine problem we should think about what happens over polynomials instead of the integers. That is are there polynomials ${f(x)}$ so that
$\displaystyle f(x-1)^{k} + f(x-2)^{k} + \cdots + f(x-(m-1))^{k} = f(x)^{k},$
for ${k \ge 2}$? This appears to be easy to resolve: there are no solutions. Just repeatedly differentiate the equation with respect to ${x}$. Divide out by ${f'(x)}$ as long as it is non-zero. It
seems that this must lead to
$\displaystyle g(x-1) + g(x-2) + \cdots + g(x-(m-1)) = g(x),$
for some non-zero ${g(x)}$. But this is impossible—look at the leading term of ${x}$.
1. May 12, 2011 2:26 pm
Hi Dick,
For the polynomial equation, your approach of “look at the leading coefficient” applies to the given (supposed) identity directly, leading to a contradiction to the existence of such a
2. May 12, 2011 2:54 pm
I think the “m-vs-k” argument is that for f monotone on [0,1], $\frac{1}{m}\sum_{l=0}{m-1}f\left(\frac{l}{m}\right) \leq \int_0^1 f(x) dx \leq \frac{1}{m}\sum_{l=1}{m}f\left(\frac{l}{m}\right).$
For $f(x) = x^k$ you get $\frac{m}{k+1} - 1 \leq \sum_{l=0}{m-1}\left(\frac{l}{m}\right)^k \leq \frac{m}{k+1}$, so if the sum in the middle is 1 you find $k+1 \leq m \leq 2(k+1)$.
One can probably make this argument more accurate.
3. May 13, 2011 3:57 am
Your sum of exponentials can be summed to infinity as a further approximation leading to
k/m ~ ln 2
You could look at the next term in the approximation and see if this requires a good rational approximation to ln 2
□ May 13, 2011 8:11 am
This sounds right. If true it would eliminate some cases in the proof from the Math Monthly paper—I think.
4. May 13, 2011 11:12 am
Sum(from n=0 to N) of n^k
is for any given integer k doable in closed form, and you can express it in terms of an
asymptotic series by using the Euler-Maclaurin summation formula EQ 23.1.30 of
Abramowitz+Stegun. (And the series converges, since it terminates.)
I get for the first 4 terms
N^k [ N/(k+1) + 1/2 + k/(12N) - (k^2-3k+2)k/(720N^3) + O(k^5 / N^5) ]
and if your diophantine is to hold then this must be equal to
(N+1)^k =
= N^k [ 1 + k/N + (k-1)k/(2N^2) + (k-2)(k-1)k/(6N^3) + (k-3)(k-2)(k-1)k/(24N^4)
+ O(k^5 / N^5) ]
where the rightmost = is from Newton binomial theorem.
If k<>N
is not possible because then (N+1)^k >> N^k+(N-1)^k+…
So this proves k must be bounded between two positive constants times N.
Given that N and k are both large and k=cN for some positive constant c, these
expressions simplify to
N^k [ 1/c + 1/2 + c/12 - c^3/720 + c^5/30240 - c^7/1209600 + c^9/47900160
- 691c^{11}/1307674368000 + c^{13}/74724249600 + ... ]
N^k [ 1 + c + c^2/2 + c^3/6 + c^4 / 24 + ... ] = N^k exp(c)
If I solve this numerically [truncating the O(c^19) terms of the series to 0] for c, I find
that the only real root of the resulting polynomial equation is
c = 0.6931471806 to 10 decimals.
Oddly enough,
ln(2) = 0.6931471806
I therefore conjecture that k must be asymptotic to ln(2)N.
Assuming this conjecture can be established, we can now use known bounds on “how irrational”
ln(2) is to make further progress.
□ May 13, 2011 1:42 pm
OK, using the operator derivation of the Euler Maclaurin sum formula
[JOHN BORIS MILLER:
THE EULER-MACLAURIN SUM FORMULA
A CLOSED DERIVATION
J. Austral. Math. Soc. (Series A) 37 (1984), 128-138
but I'm sure there are better cites than this, probably N.Norlund's book]
one can demonstrate that (i) the series converge in my derivation above and (ii) that
c=ln(2) is exactly correct.
This yields the correct leading asymptotic.
More challenging would be to determine the non-leading asymptotics, which I suspect should
also be doable in closed form at least for the first few terms.
Concerning “how irrational” ln(2) is,
see Yu.V.Nesterenko, Math’l Notes 88,4 (2010) 530-543
where he provides a new proof that
|P/Q – ln2| > Q^(-3.57455391)
for all integers P,Q except for a finite set.
So a possible strategy to almost-solve your diophantine problem would be to
show the full asymptotics would imply an infinite set of too-good diophantine
approximations to ln2, hence therefore the diophantine can have at most a finite set of
solutions. Probably this strategy will not work because the bounds won’t be strong enough,
but you cannot tell until you do it.
5. May 13, 2011 4:04 pm
Dick, we have published a full paper on this. The citation is
E. Bach, D. Klyve, and J. Sorenson, Computing Prime Harmonic Sums,
Mathematics of Computation 78 (2009), 2283-2305.
□ May 13, 2011 4:40 pm
Sorry missed that. Will look at paper right away.
6. May 14, 2011 1:25 am
Another line of attack is to use modulo arithmetic. Try the case where k is prime or one less than a prime and use Fermats little theorem to add up mod k. Given that k/m ~ ln 2 you can see that
these cases can be eliminated. You would need some strict inequalities to make it rigorous.
There may also be possibilities mod m, or mod factors of m.
7. April 14, 2012 3:05 pm
Jonathan Sondow and I have been making good progress on this conjecture since I discovered it in 2008 — you might find our papers useful.
In particular, they use math which is both elementary *and* simple, while obtaining some fairly spectacular results. For example, in , induction is the most difficult technique we use to [re]
prove that in any solution to the more general equation
1^k + 2^k + … + (m-1)^k = am^k, a ≥ 1,
m must be odd.
We’ve got another paper in preparation which might also be of interest to you when we’re done with it.
Best regards,
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How does the area change of a polyhedra as the number
General Question
How does the area change of a polyhedra as the number of faces go up but circumference stays the same?
So imagne we have a very simple polyhedra, I’m not too sure if they would concider an edge from one vertex to another and back again a polyhedra, if not start off with a triangle.
The circumference of this equalatral trangle is 1.
Increase the number of sides keeping all sides the same length and at the same angle.
So next a square then a pentagon and so on.
Is there a graph to show me how the area changes with each face?
Observing members: 0 Composing members: 0
4 Answers
Hint: Imagine a tetrahedron encased in a sphere. Now imagine a cube in a sphere of the same size. Now a dodecahedron. Notice that as the number of faces goes up, the closer the polyhedron
approximates a sphere. (It may be easier to imagine a polygon in a circle, but the same principle applies).
Also—the parameters you set out in your question are impossible as you’ve worded them, and triangles do not have circumferences. Framing the problem correctly is half the battle.
First a clarification. Since you are talking about 2 dimensional objects, the correct term is polygon. Polyhedra are 3 dimensional, like cubes and tetrahedrons.
I don’t know how much schooling you have had, but if you are familiar with trigonometry, there is a simple formula for the area. Just connect the center with segments to each of the vertices. Take
one of the triangles and drop a perpendicular from the top vertex at the center of the triangle. The lengths of the sides are r sin theta and r cosine theta where theta is 360/2n and n is the number
of sides. That gives the area as 2n *½ * r ^2 cos theta sin theta =
n cosine theta sine theta.
In the limit, sin theta = sin 2 pi/ 2n, approximately equal to pi/n and cos theta approaches 1, so the limit would be pi r^2 , the area of the circle. You can see intuitively that as the number of
sides increases, the sum of the lengths of the triangles approaches the circumference of the circle and the altitude of the triangles approaches r, so the sum of the areas of the triangles again
appraches pi r^2,
This isn’t quite what you asked, since the circumference changes, but almost.
Answer this question
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THIS WEEK’S SEMINARS
Monday 1^st May
Seminar: Sixth Kuwait Fund Lecture (Lecture 1)
Location & Time: Mill Lane Lecture Rooms, Room 3 at 5.00 p.m.
Speaker: Professor K. Kato
Title: Classical Iwasawa theory and its generalization to elliptic curves and modular forms
Seminar: Geometric Topology Seminar
Location & Time: Meeting Room 12, CMS Wilberforce Road at 2.30 p.m.
Speaker: Professor W.B.R. Lickorish
Title: SU(n) skein theory and TQFT
Tuesday 2^nd May
Seminar: Sixth Kuwait Fund Lecture (Lecture 2)
Location & Time: Mill Lane Lecture Rooms, Room 3 at 11.00 a.m.
Speaker: Professor K. Kato
Title: Classical Iwasawa theory and its generalization to elliptic curves and modular forms
Seminar: Number Theory Seminar
Location & Time: Seminar Room 1, (Mill Lane) DPMMS at 4.00 p.m.
Speaker: O. Venjakob
Title: On the structure of Selmer groups over p-adic Lie extensions
Wednesday 3^rd May
Seminar: Sixth Kuwait Fund Lecture (Lecture 3)
Location & Time: Mill Lane Lecture Rooms, Room 3 at 11.00 a.m.
Speaker: Professor K. Kato
Title: Classical Iwasawa theory and its generalization to elliptic curves and modular forms
Seminar: Algebra Seminar
Location & Time: Seminar Room 1, (Mill Lane) DPMMS at 4.30 p.m.
Speaker: Dr I. Grojnowski
Title: Rigid structure on the symmetric group
Thursday 4^th May
Seminar: Sixth Kuwait Fund Lecture (Lecture 4)
Location & Time: Mill Lane Lecture Rooms, Room 3 at 11.00 a.m.
Speaker: Professor K. Kato
Title: Classical Iwasawa theory and its generalization to elliptic curves and modular forms
Seminar: Number Theory Seminar
Location & Time: Seminar Room 1, (Mill Lane) DPMMS at 4.00 p.m.
Speaker: O. Venjakob
Title: On the structure of Selmer groups over p-adic Lie extensions II
Friday 5^th May
Seminar: Sixth Kuwait Fund Lecture (Lecture 5)
Location & Time: Mill Lane Lecture Rooms, Room 3 at 11.00 a.m.
Speaker: Professor K. Kato
Title: Classical Iwasawa theory and its generalization to elliptic curves and modular forms
Seminar: Number Theory Seminar
Location & Time: Seminar Room 1, (Mill Lane) DPMMS at 2.30 p.m.
Speaker: Dr Y. Ochi
Title: On the structure of Selmer groups over p-adic Lie extensions III | {"url":"https://www.dpmms.cam.ac.uk/Seminars/Weekly/1999-2000/Seminar1May.html","timestamp":"2014-04-18T20:42:32Z","content_type":null,"content_length":"4044","record_id":"<urn:uuid:04b60dfc-b7b0-4b7a-ad93-a00ee66e4f74>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00331-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Trace of sphere in the coordinate planes
Question: A sphere is trapped inside the box whose walls are the following six planes:
x = 2; x = 8; y = 0; y = 10; z = 3; z = 13
(a) Find an equation for the sphere, in the form of a level surface of a 3-variable function: g(x; y; z) = C.
(b) Find a function z = f(x; y) whose graph is the bottom half of the sphere.
(c) Describe the trace of the sphere in each of the coordinate planes (possibly the empty set).
(d) Find the point(s) of intersection of the sphere with the line defined by {y = 1, z =2x + 8}
Question: The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, -10 ≤ y ≤ 10 is given by the function T(x, y) = 100 – x² - y²
(a) Provide f(x, y) and the equation g(x, y, z) = c.
(b) Sketch isothermal curves (curves of constant temperature) for T = 100°C, T = 75°C, T = 50°C, T = 25°
C, and T = 0°C.
(c) A heat-seeking bug is put down at a point on the xy-plane. In which direction should it move to increase its temperature fastest? How is that direction related to the level curve through that
Ref. No:-
Its really helpful guide for me.
Posted on: December 12, 2012
Thanks a lot for your expert's assistance..
Posted on: Feb 2, 2013 | {"url":"http://www.tutorsglobe.com/question/trace-of-sphere-in-the-coordinate-planes-564.aspx","timestamp":"2014-04-18T10:35:05Z","content_type":null,"content_length":"21575","record_id":"<urn:uuid:66d4dd57-7e7f-4cc3-941f-2318224c7abf>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00371-ip-10-147-4-33.ec2.internal.warc.gz"} |
Early draft of naturalistic reflection paper - Machine Intelligence Research Institute
Early draft of naturalistic reflection paper
Update: See Reflection in Probabilistic Logic for more details on how this result relates to MIRI’s research mission.
In a recent blog post we described one of the results of our 1st MIRI Workshop on Logic, Probability, and Reflection:
The participants worked on the foundations of probabilistic reflective reasoning. In particular, they showed that a careful formalization of probabilistic logic can circumvent many classical
paradoxes of self-reference. Applied to metamathematics, this framework provides (what seems to be) the first definition of truth which is expressive enough for use in reflective reasoning.
In short, the result described is a “loophole” in Tarski’s undefinability theorem (1936).
An early draft of the paper describing this result is now available: download it here. Its authors are Paul Christiano (UC Berkeley), Eliezer Yudkowsky (MIRI), Marcello Herreshoff (Google), and
Mihaly Barasz (Google). An excerpt from the paper is included below:
Unfortunately, it is impossible for any expressive language to contain its own truth predicate True…
There are a few standard responses to this challenge.
The first and most popular is to work with meta-languages…
A second approach is to accept that some sentences, such as the liar sentence G, are neither true nor false…
Although this construction successfully dodges the “undefinability of truth” it is somewhat unsatisfying. There is no predicate in these languages to test if a sentence… is undefined, and there
is no bound on the number of sentences which remain undefined. In fact, if we are specifically concerned with self-reference, then a great number of properties of interest (and not just
pathological counterexamples) become undefined.
In this paper we show that it is possible to perform a similar construction over probabilistic logic. Though a language cannot contain its own truth predicate True, it can nevertheless contain
its own “subjective probability” function P. The assigned probabilities can be reflectively consistent in the sense of an appropriate analog of the reflection property 1. In practice, most
meaningful assertions must already be treated probabilistically, and very little is lost by allowing some sentences to have probabilities intermediate between 0 and 1.
Another paper showing an application of this result to set theory is forthcoming.
Is there a preferred arena for reviews/discussion?
I am concerned about the one-way arrow in the reflection principle. It seems like a “quotation principle” without a “dequotation principle”, very similar to theories of truth which satisfy A=>T(“A”)
without satisfying T(“A”)=>A (so-called glut theories). Is there anything which makes this nicer than those theories? Is there anything which stops us from setting our truth value to 1 for all
statements of the form P(“a<P('A')<b")=1? This would trivially satisfy the reflection principle stated.
The preferred arena for discussion is here (as you’ve already discovered): | {"url":"http://intelligence.org/2013/03/22/early-draft-of-naturalistic-reflection-paper/","timestamp":"2014-04-18T13:10:51Z","content_type":null,"content_length":"33796","record_id":"<urn:uuid:220d5990-8f8f-4dd0-90d0-0bbc4f3d943b>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00434-ip-10-147-4-33.ec2.internal.warc.gz"} |
Cutting Cake with Geometry
Date: 2/4/96 at 4:37:18
From: Mittledorf Joshua J
Subject: Geometry puzzle
Here's a cute geometry puzzle that came to me from a very public
source, which I'm too embarrassed to credit:
A cake is square when viewed from the top. Height is unspecified.
It is iced on top and the four vertical sides. How can the cake be
divided in 5 pieces such that each piece has the same amount of cake and
the same amount of icing? How can you minimize the number of cuts you
have to make in the cake and still meet this target? Alternatively, how
can you minimize the total length of the cuts you make in the cake?
- Josh Mitteldorf
Date: 2/12/96 at 12:46:37
From: Doctor Ken
Subject: Re: Geometry puzzle
Hello -
You listen to Car Talk too?
When I heard this puzzle on National Public Radio, I thought of this
solution: the cake has a certain perimeter whn viewed from the top. Let
the perimeter be called "P." Then find five points around the perimeter
such that they divide the perimeter into five equal parts (each with the
same length, in other words). Now if you cut the cake into five
pieces, and make sure that the corners of the pieces are these five
points and the tops of the five pieces have the same surface area, then
you'll have done it!
The other parts of the puzzle can be gotten by drawing pictures and
messing around with them: for example, you know it's going to take at
_least_ three cuts, because two cuts can only get you four pieces.
-Doctor Ken, The Math Forum | {"url":"http://mathforum.org/library/drmath/view/56453.html","timestamp":"2014-04-17T13:29:03Z","content_type":null,"content_length":"6884","record_id":"<urn:uuid:f5ed609d-7b62-4293-9169-245cd11d3293>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00222-ip-10-147-4-33.ec2.internal.warc.gz"} |
Weekly Problem 16 - 2012
Copyright © University of Cambridge. All rights reserved.
'Weekly Problem 16 - 2012' printed from http://nrich.maths.org/
I have some strange dice: the faces show the numbers 1 to 6 as usual, except that the odd numbers are negative (i.e. -1, -3, -5 in place of 1, 3, 5). If I throw two such dice, which of the following
totals cannot be achieved?
A) 3
B) 7
C) 8
Clcik here for a poster of this problem
If you liked this problem,
here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
View the previous week's solutionView the current weekly problem | {"url":"http://nrich.maths.org/2462/index?nomenu=1","timestamp":"2014-04-21T09:46:05Z","content_type":null,"content_length":"3652","record_id":"<urn:uuid:cee9b00e-040b-45c4-8591-6b348a2316dc>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00575-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Primes, Modular Arithmetic, and Public Key Cryptography
Back to Number Theory and Cryptography
Primes, Modular Arithmetic, and Public Key Cryptography
(April 15, 2004)
Every cipher we have worked with up to this point has been what is called a symmetric key cipher, in that the key with which you encipher a plaintext message is the same as the key with which you
decipher a ciphertext message. As we have discussed from time to time, this leads to several problems. One of these is that, somehow, two people who want to use such a system must privately and
secretly agree on a secret key. This is quite difficult if they are a long distance apart (it requires either a trusted courier or an expensive trip), and is wholly impractical if there is a whole
network of people (for example, an army) who need to communicate. Even the sophisticated Enigma machine required secret keys. In fact, it was exactly the key distribution problem that led to the
initial successful attacks on the Enigma machine.
However, in the late 1970's, several people came up with a remarkable new way to solve the key-distribution problem. This allows two people to publicly exchange information that leads to a shared
secret without anyone else being able to figure out the secret. The Diffie-Hellman key exchange is based on some math that you may not have seen before. Thus, before we get to the code, we discuss
the necessary mathematical background.
Prime Numbers and Modular Arithmetic
Recall that a prime number is an integer (a whole number) that has as its only factors 1 and itself (for example, 2, 17, 23, and 127 are prime). We'll be working a lot with prime numbers, since they
have some special properties associated with them.
Modular arithmetic is basically doing addition (and other operations) not on a line, as you usually do, but on a circle -- the values "wrap around", always staying less than a fixed number called the
To find, for example, 39 modulo 7, you simply calculate 39/7 (= 5 4/7) and take the remainder. In this case, 7 divides into 39 with a remainder of 4. Thus, 39 modulo 7 = 4. Note that the remainder
(when dividing by 7) is always less than 7. Thus, the values "wrap around," as you can see below:
0 mod 7=0 6 mod 7=6
1 mod 7=1 7 mod 7=0
2 mod 7=2 8 mod 7=1
3 mod 7=3 9 mod 7=2
4 mod 7=4 10 mod 7=3
5 mod 7=5 etc.
To do modular addition, you first add the two numbers normally, then divide by the modulus and take the remainder. Thus, (17+20) mod 7 = (37) mod 7 = 2.
Modular arithmetic is not unfamiliar to you; you've used it before when you want to calculate, for example, when you would have to get up in the morning if you want to get a certain number of hours
of sleep. Say you're planning to go to bed at 10 PM and want to get 8 hours of sleep. To figure out when to set your alarm for, you count, starting at 10, the hours until midnight (in this case,
two). At midnight (12), you reset to zero (you "wrap around" to 0) and keep counting until your total is 8. The result is 6 AM. What you just did is to solve (10+8) mod 12. As long as you don't want
to sleep for more than 12 hours, you'll get the right answer using this technique. What happens if you slept more than 12 hours?
Here are some exercises for you to practice modular arithmetic on.
Did you notice something funny about the last 5 exercises? While, usually, when we take powers of numbers, the answer gets systematically bigger and bigger, using modular arithmetic has the effect of
scrambling the answers. This is, as you may guess, useful for cryptography!
Diffie-Hellman Key Exchange
The premise of the Diffie-Hellman key exchange is that two people, Alice and Bob, want to come up with a shared secret number. However, they're limited to using an insecure telephone line that their
adversary, Eve (an eavesdropper), is sure to be listening to. Alice and Bob may use this secret number as their key to a Vigenere cipher, or as their key to some other cipher. If Eve gets the key,
then she'll be able to read all of Alice and Bob's correspondence effortlessly. So, what are Alice and Bob to do? The amazing thing is that, using prime numbers and modular arithmetic, Alice and Bob
can share their secret, right under Eve's nose! Here's how the key exchange works.
1. Alice and Bob agree, publicly, on a prime number P, and a base number N. Eve will know these two numbers, and it won't matter!
2. Alice chooses a number A, which we'll call her "secret exponent." She keeps A secret from everyone, including Bob. Bob, likewise, chooses his "secret exponent" B, which he keeps secret from
everyone, including Alice (for subtle reasons, both A and B should be relatively prime to N; that is, A should have no common factors with N, and neither should B).
3. Then, Alice computes the number
J = N^A (mod P)
and sends J to Bob. Similarly, Bob computes the number
K = N^B (mod P)
and sends K to Alice. Note that Eve now has both J and K in her possession.
4. The final mathematical trick is that Alice now takes K, the number she got from Bob, and computes
K^A(mod P).
Bob does the same step in his own way, computing
J^B (mod P).
The number they get is the same! Why is this so? Well, remember that K = N^B (mod P) and Alice computed K^A (mod P) = (N^B)^A (mod P) = N^BA (mod P). Also, Bob used J = N^A (mod P), and computed
J^B (mod P) = (N^A)^B (mod P) = N^AB (mod P).
Thus, without ever knowing Bob's secret exponent, B, Alice was able to compute N^AB (mod P). With this number as a key, Alice and Bob can now start communicating privately using some other
Why Diffie-Hellman Works
At this point, you may be asking, "Why can't Eve break this?" This is indeed, a good question. Eve knows N, P, J, and K. Why can't she find A, B, or, most importantly, N^AB(mod P)? Isn't there
some sort of inverse process by which Eve can recover A from N^A(mod P)?
Well, the thing Eve would most like to do, that is, take the logarithm (base N) of J, to get A, is confounded by the fact that Alice and Bob have done all of their math modulo P. The problem of
finding A, given N, P, and N^A (mod P) is called the discrete logarithm problem. As of now, there is no fast way known to do this, especially as P gets really large. One way for Eve to solve this
is to make a table of all of the powers of N modulo P. However, Eve's table will have (P-1) entries in it. Thus, if P is enormous (say 100 digits long), the table Eve would have to make would
have more entries in it than the number of atoms in the universe! Simply storing that table would be impossible, not to mention searching through it to find a particular number. Thus, if P is
sufficiently large, Eve doesn't have a good way to recover Alice and Bob's secret.
"That's fine," you counter, "but if P is so huge, how in the world are Alice and Bob going to compute powers of numbers that big?" This is, again, a valid question. Certainly, raising a
100-digit-long number to the power 138239, for example, will produce a ridiculously large number. This is true, but since Alice and Bob are working modulo P, there is a shortcut called the
repeated squaring method.
To illustrate the method, we'll use small numbers (it works the same for larger numbers, but it requires more paper to print!). Say we want to compute 7^29 (mod 17). It's actually possible to do
this on a simple four-function calculator. Certainly, 7^29 is too large for the calculator to handle by itself, so we need to break the problem down into more manageable chunks. First, break the
exponent (29) into a sum of powers of two. That is,
29 = 16 + 8 + 4 + 1 = 2^4 + 2^3 + 2^2 + 2^0
(all we're doing here is writing 29 in binary: 11101). Now, make a list of the repeated squares of the base (7) modulo 17:
7^1 (mod 17) = 7
7^2 (mod 17) = 49 (mod 17) = 15
7^4 (mod 17) = 7^2 * 7^2 (mod 17) = 15 * 15 (mod 17) = 4
7^8 (mod 17) = 7^4 * 7^4 (mod 17) = 4*4 (mod 17) = 16
7^16 (mod 17) = 7^8 * 7^8 (mod 17) = 16*16 (mod 17) = 1
Then, 7^29 (mod 17) = 7^16 * 7^8 * 7^4 * 7^1 (mod 17) = 1 * 16 * 4 * 7 (mod 17) = 448 (mod 17) = 6.
The neat thing is that the numbers in this whole process never got bigger than 16^2 = 256 (except for the last step; if those numbers get too big, you can reduce mod 17 again before multiplying).
Thus, even though P may be huge, Alice's and Bob's computers don't need to deal with numbers bigger than (P-1)^2 at any point.
Here's a worksheet to try this whole process out on. It may help to work with a few friends!
1. Will this method work if Alice and Bob don't know each other? What could Eve do if she were impersonating one of them? What if she were "in the middle", that is, what if Bob thought Eve was
Alice and Alice thought Eve was Bob?
2. How can Alice and Bob know that Eve hasn't jumped "in the middle"? That is, how can Alice really know that Bob is Bob? (This is called authentication.) Is there any way for Alice to know with
absolute certainty?
Other Links*
* These links are for informational purposes only and are from sources outside MEC and Cornell University | {"url":"http://www.math.cornell.edu/~mec/2003-2004/cryptography/diffiehellman/diffiehellman.html","timestamp":"2014-04-18T23:19:44Z","content_type":null,"content_length":"13147","record_id":"<urn:uuid:6d7b73d5-3a04-4dd1-9db8-5b3e342e032e>","cc-path":"CC-MAIN-2014-15/segments/1397609535535.6/warc/CC-MAIN-20140416005215-00152-ip-10-147-4-33.ec2.internal.warc.gz"} |
Tensor partial differentiation question...
July 10th 2010, 12:15 PM #1
Junior Member
Apr 2009
Tensor partial differentiation question...
Hi I have the following tensor (the Cauchy-Green deformation tensor)
$C = \begin{bmatrix}<br /> \lambda_{1}^2 & 0 & 0 \\<br /> 0 & \lambda_{2}^2 & 0 \\<br /> 0 & 0 & \lambda_{3}^2 <br /> \end{bmatrix}<br />$
and I have the following energy function
$W = D_{1}(I_{1}-3) + D_{2}(I_{2}-3) + f(\lambda)$
$I_{1} = tr C = \lambda_{1}^2+\lambda_{2}^2+\lambda_{3}^2$
$I_{2} = {(tr C)^2 - tr C^2 = \lambda_{1}^2\lambda_{2}^2+\lambda_{2}^2\lambda_{3 }^2+\lambda_{3}^2\lambda_{1}^2$
$\lambda_{3} = \frac{1}{\lambda_{1}\lambda_{2}}$
$D_{1}$ and $D_{2}$ are constants
(And $f(\lambda)$ is a piecwise function who's derivitives are already known but I can supply this information if it is needed.)
How do I calculate $\frac{\partial W}{\partial C}$?
Some version of the chain rule?
Thanks for any help in this matter, Nic
Since no one else has posted anything, I figure I'll give it a try.
Note: I'm not the strongest at matrix calculus so take this with a grain of salt.
You're taking the derivative of a scalar function with respect to a matrix (3 x 3). So our result is going to be a (3 x 3) matrix as well.
It looks like the difficulty here is finding $\frac{\partial I_1}{\partial C}$.
So we know that this derivative is a 3 by 3 matrix $\frac{\partial trC}{\partial C}=[\frac{\partial trC}{\partial C_{i,j}}]$.
And you say you have the derivative of $f(\lambda)$
So I think the rest should be doable?
This may help also
Matrix Calculus
July 12th 2010, 09:22 PM #2
Junior Member
May 2010 | {"url":"http://mathhelpforum.com/advanced-applied-math/150569-tensor-partial-differentiation-question.html","timestamp":"2014-04-19T03:11:34Z","content_type":null,"content_length":"35581","record_id":"<urn:uuid:99e94bc8-d25e-44be-bcf8-90e525eca178>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00243-ip-10-147-4-33.ec2.internal.warc.gz"} |
From HLWIKI Canada
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: dean.giustini@ubc.ca
To browse other articles on a range of HSL topics, see the A-Z index.
Last Update
See also Assessment | Data science portal | Finding medical / health care statistics online | Research tutorials on the web | Statistics for academic librarians
Biostatistics is a field that applies a subset of standard statistical techniques to clinical research in medicine, public health and epidemiology. Biostatistics is also oriented towards formulating
questions through observable clinical problems. In order to find solutions to clinical problems, quantitative data is gathered and examined using a combination of mathematics and careful reasoning.
This includes the measurement and analysis of data (descriptive, inferential), statistical graphs; clinical decision-making in the face of uncertainty (variability) making inferences from sample
populations (a cohort) to populations generally. According to Murad & Shi (2010), biostatistics "...is the application of statistical methods to medical and biological phenomena". Similarly, Jekel et
al (2007) say that "...biostatistics is a tool that is used to analyze, understand, and explain the variance in medical and epidemiological data.
The field of biostatistics encompasses the methodology and theory of statistics as applied to the life and biomedical sciences. Biostatisticians are specialists in the evaluation of data as
scientific evidence. They understand the construct of data and provide the mathematical framework to generalize the clinical findings. Their expertise includes the design and conduct of experiments,
the mode and manner in which data are collected, the analysis of data, and the interpretation of results.
Biostatistics, epidemiology, and evidence-based medicine are closely related disciplines. Epidemiology is defined as the study of disease within populations; epidemiology provides robust quantitative
evidence (data) for the practice of evidence-based health care. Biostatistics is simply the set of tools that are used to analyze and understand this data.
Population, sampling, analysis
In biomedical studies, research questions will describe or define the specific population that is being studied. The population being studied is called the target population. The target population
should be a well-defined population in order to collect representative data that can be used to gather data pertaining to the research question. Finding the actual answer to a research question
requires that the entire target population be observed, which is usually impossible. Further, since it is generally impractical to observe an entire population, biomedical researchers will examine a
subset of the population. A subset of the population is a sample, and may provide data but may not definitively answer the research question. Complete information on a target population is required
to answer a clinical question; since a sample is a subset of a population, it provides generalizable information about the problem. For this reason, statistics is often referred to as "the science of
describing populations in the presence of uncertainty."
Key associations & video
Descriptive statistics
An example of the use of descriptive statistics occurs in drug studies. In papers reporting human subjects, there is typically a table that states the sample size in subgroups (e.g. treatment or
exposure groups), and demographic or clinical characteristics such as average age, proportion of subjects in each gender and proportion of subjects with related comorbidities. In research involving
comparisons, an emphasis is placed on the significance level for the hypothesis that the two groups differ to a degree that is greater than would be expected by chance. This significance is
represented as a p-value or as a standard score of a test statistic. In contrast, an effect size is a descriptive statistic that conveys the estimated magnitude and direction of the difference
between groups. This is without regard to whether the difference is statistically significant. Reporting significance levels without effect sizes is criticized because large samples with small
effects can be highly significant statistically.
Inferential statistics
With inferential statistics, conclusions are made that go beyond the immediate data. For instance, inferential statistics are used to infer from sample data what a population might be thinking about
something. Or, inferential statistics are used to make judgments of the probability that an observed difference between groups is dependent on something happening, or might have happened by chance in
this study. Inferential statistics are used to make inferences from the data collected and used to describe what is probably happening. Most inferential statistics derive from a family of statistical
models known as the General Linear Model, and includes the t-test, Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA), regression analysis, and multivariate methods like factor analysis,
multidimensional scaling, cluster analysis, etc. It's a good idea for researchers to become familiar with GLM. Its discussion here is simplified and considers simple straight-line models only.
Key tools & websites
□ • How to calculate an odds ratio; confidence intervals; forest plots; meta-analysis; clinical significance | {"url":"http://hlwiki.slais.ubc.ca/index.php/Biostatistics","timestamp":"2014-04-21T05:17:58Z","content_type":null,"content_length":"28001","record_id":"<urn:uuid:ff31e28d-7389-436e-b9fc-cc8f8da8f6e9>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00020-ip-10-147-4-33.ec2.internal.warc.gz"} |
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A guessing game
A guessing game
I have an assignment to write a number guessing game. That I think I can do, but there's a catch. The assignment reads..
With each good guess out of 10 the player should be able to eliminate half of the numbers. Show why any number from 1 to 1000 can be guessed in 10 or fewer tries.
Can someone explain?
do a websearch or a board search for "binary search".
All will be revealed to you. Think about it first. How could you do it. And you can in your head quite easily.
what about if on the first error you give them an idea as to how much off they approximately are?
nope just a simple its this way and not that way
Originally posted by zbap
what about if on the first error you give them an idea as to how much off they approximately are?
Then they could simply add (or subtract) the number given to their number and find the answer.
Hey lyanette, think of it this way. If I said pick a number between 1 and 1000, what number would YOU pick? Why would you pick that number? If I said that number was too low, what number would
you pick next? Why did you pick that one? Keep going. That should answer your question. | {"url":"http://cboard.cprogramming.com/cplusplus-programming/37215-guessing-game-printable-thread.html","timestamp":"2014-04-19T02:05:05Z","content_type":null,"content_length":"8212","record_id":"<urn:uuid:41ee99f3-4ac7-438c-b106-71271c0b6105>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00445-ip-10-147-4-33.ec2.internal.warc.gz"} |
34-XX Ordinary differential equations
34Cxx Qualitative theory [See also 37-XX]
34C05 Location of integral curves, singular points, limit cycles
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory
34C11 Growth, boundedness, comparison of solutions
34C12 Monotone systems
34C14 Symmetries, invariants
34C15 Nonlinear oscillations, coupled oscillators
34C20 Transformation and reduction of equations and systems, normal forms
34C23 Bifurcation [See mainly 37Gxx]
34C25 Periodic solutions
34C26 Relaxation oscillations
34C27 Almost periodic solutions
34C28 Complex behavior, chaotic systems [See mainly 37Dxx]
34C29 Averaging method
34C30 Manifolds of solutions
34C37 Homoclinic and heteroclinic solutions
34C40 Equations and systems on manifolds
34C41 Equivalence, asymptotic equivalence
34C45 Method of integral manifolds
34C55 Hysteresis
34C60 Applications
34C99 None of the above, but in this section | {"url":"http://ams.org/mathscinet/msc/msc.html?t=34C15","timestamp":"2014-04-17T04:58:47Z","content_type":null,"content_length":"14408","record_id":"<urn:uuid:38a9a4fd-34c1-441e-8b58-c94381620dd2>","cc-path":"CC-MAIN-2014-15/segments/1397609526252.40/warc/CC-MAIN-20140416005206-00076-ip-10-147-4-33.ec2.internal.warc.gz"} |
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If you can't find the right transformer for your project at the right price, there is an easy solution—rewind one! As this article shows, the job is not as difficult as you might think.
DON A. MEADOR
Radio Electronics May 1983, pp. 77-80
One of the most important parts of a power supply, whether it be for a project or for your bench, is the transformer. If you've had much building experience, however, you know that getting the right
transformer—one with appropriate voltage and current ratings—can be difficult and/or expensive. That's doubly true if you need something other than a "standard" voltage.
The easiest and most economical way to solve those problems is to rewind a readily available or inexpensive transformer. This article focuses on two aspects of the task; specification, and the
general guidelines for rewinding transformers. Also, we'll look at a practical example—how to rewind a transformer with a rating of 18 volts at 2.5 amps into one with a rating of 7 volts at 4.5 amps.
Manufacturer's specifications
Transformer ratings are usually given in RMS values. A secondary rated at 12.6 volts center-tapped at 1 amp means 12.6 volts RMS is across the entire secondary and that no more than 1-amp RMS can be
drawn safely from it. The voltage from either end of the secondary to the center tap is half the voltage across the entire secondary, or, in this case, 6.3 volts RMS. The current that can be supplied
by each part of the secondary simultaneously is equal to the current rating of the entire secondary, or in this case, the halves of the secondary can supply 1-amp RMS each.
The secondary's output ratings are based on the assumption that a particular RMS voltage will be applied to the primary of the transformer. Favorite values used by manufacturers are 110-, 117-, and
120-volts RMS. Note that while any transformer you buy new will have the ratings stamped either on it or its packaging, surplus or salvaged transformers usually will not. For the remainder of our
discussion we will assume that the input to the primary is 117-volts RMS.
Since the maximum power capability of a transformer depends on the cross-sectional area of the iron core, the maximum power that a transformer can deliver is a constant. But any combination of
voltage and current is possible provided that the voltage times the current is less than or equal to the transformer's wattage rating. Thus, if the manufacturer rates the secondary for 25.2 volts at
0.5 amps, it means that the transformer can supply 12.6 watts (P = V × I = 25.2 volts × 0.5 amps = 12.6 watts), It also means that the transformer can handle any combination of voltage and current,
so long as the product of the two is less than or equal to 12.6 watts—6 volts at 2.1 amps for example.
Besides the wattage rating, the cross-sectional area of the wire used in the transformer puts a limitation of the amount of current that it can supply. If a transformer's secondary is rated for 22.5
volts at 2 amps, the manufacturer has told us that the wire used in the secondary will safely supply 2 amps RMS at any voltage, provided the transformer is capable of handling the resultant power.
Finding specifications on your own
If you have a salvaged transformer, information about its voltage, power, and current ratings is usually not available. That information is not that hard to find, however, if you follow these simple
To find the voltage rating of the secondary, first find which wire belongs to the primary winding. Most electronics handbooks provide a complete color code for the transformer's wires, but let's
sketch out the essentials here.
The two black wires on the transformer lead to the primary and are where the 117-volts RMS line-voltage is applied. The wires to each secondary have a different color set. The wires to one secondary,
for instance, may use a red color set—two solid red wires and another red wire with a different color stripe. The striped wire is the center tap of the secondary. If a secondary does not have a
center tap, only two wires will be found in that color set. With the primary and secondaries identified, you simply use an AC voltmeter to find the voltages required.
To do that, hook the transformer up to your household power line and measure the voltages on each winding. [Ed. note: Better yet use a step-down transformer to reduce the household line voltage to
much lower value—say 10 volts RMS—and place this lower value the primary. Doing so reduces the chance that you might overload your voltmeter should the secondary happen to step up the voltage
considerably. The lower voltages are much safer as well.] Be very careful in performing this step. The best way to go about it is to wire a plug to the primary, attach the AC voltmeter to the winding
you want to measure, and make sure that there are no exposed or touching bare wires before plugging in the transformer. To find the voltage simply plug in the transformer and read the voltage on the
meter. Take enough measurements so that you know the voltage across each secondary, the voltage to each center tap, and voltage applied to the primary. For safety, be sure to disconnect the power
before you switch the meter leads.
TABLE 1
FIG. 1—TO FIND
THE Cross-Sectional Area
cross-sectional (Square Inches) Power (Watts)
area of the 1.00 45
transformer 1.25 50
core, multiply 1.75 75
L × W. Be sure 2.00 120
to measure L 2.25 150
and W in 2.75 230
inches. 3.00 275
3.25 330
3.75 440
4.00 520
To find the power rating of the transformer, first find the cross-sectional area of the core by multiplying L × W as shown in Fig. 1. Be sure to measure L and W in inches so the cross-sectional area
is calculated in square inches. Then using Table 1. find the approximate wattage rating that corresponds to the cross-sectional area.
It is possible to reuse the wire from the original secondary for the new secondary. If the rating of that wire is not known and there is only one secondary, the maximum current that the wire can
safely handle is equal to the power capability of the iron core divided by the voltage of the winding. When there is more than one secondary, you would be better off to use the cross-sectional area
of the wire used in each secondary to determine its current-handling capability (more on that later).
Rewinding a transformer
Since rewinding a primary is a job that should be avoided if at all possible (suggestions for handling that messy task will be given later on), the best transformers to rewind are those in which the
primary is wound closest to the iron core. Transformers with a high-voltage secondary often have that winding wrapped next to the core, the primary wrapped on the outside of the high-voltage
secondary, and finally the low-voltage secondaries as the outermost layer. Transformers with only one low-voltage secondary (less than 110 volts) usually have the primary wound closest to the core
and secondary on the outside. There is no way of knowing where the secondaries are until you disassemble the transformer.
The first step in rewinding a transformer is to determine what size transformer you need. To calculate the power that is required, multiply the voltage you need by the current you need.
Using Table 1 you can approximate the core size you need. If the core size is not given in a catalogue, the total power capability of a transformer can be found simply by adding the power rating of
each secondary.
After you get the transformer, check the voltages using the technique we discussed earlier. The next step is to disassemble the unit. Take out the screws and anything else holding the transformer
together. Usually, the laminations are soaked in a special enamel and then baked. This is done to keep the transformer from buzzing and to seal it from the environment; it also makes the laminations
hard to remove. As each lamination is removed, the enamel holding it must be broken off; when doing so it is very easy to damage the transformer's wires, so great care must be taken.
The first few laminations are hardest to remove. To break the enamel seal, take a very small screwdriver and slip it between the outside edges of the laminations you are removing. If you ruin a few
laminations at first, don't worry—you won't be able to get all of them back in anyway when the transformer is reassembled. Set the transformer on a piece of plywood so that the lamination that you
are removing projects over the edge as shown in Fig. 2. Working alternately at either end of the exposed lamination, lightly tap the screwdriver until the enamel on the inside of the core breaks
loose. Then remove the lamination.
FIG. 2—TO
REMOVE THE FIG. 3—AFTER
laminations, A FEW
position the laminations
transformer are removed,
as shown, one of the
slip a small "I"-shaped
screwdriver laminations
under the can be used
first in place of
lamination, the
and tap screwdriver.
lightly with
a hammer.
After a few laminations are removed, one of the "I"-shaped laminations can be used to break the enamel seal on the remainder—the ones inside the coil—as shown in Fig. 3. You will still have to tap
lightly with a hammer, but the "I" piece will be easier to use and cause less damage than a screwdriver.
After removing the laminations, the next step is to unwind the secondary. As you unwind the wire, count the number of turns. When the secondary is completely unwound, calculate the turns-per-volt by
dividing the turns counted by the voltage previously measured on the secondary. For example, if the output from the secondary is 12.6 volts RMS and it has 40 turns, the turns-per-volt ratio is 3.175.
When there is more than one secondary, the turns-per-volt ration for each should be the same. If not, you have miscounted. In that case, use the average of the different values.
If the voltage measurements were made with something other than 117-volts RMS applied to the primary, you need to adjust the turns-per-volt value. Or, if the line voltage in your house was 112-volts
RMS when you measured the secondary voltage, but most times your line voltage is 120-volts RMS, you may want to calculate the turns-per-volt value with 120 volts RMS applied to the primary. The
following formula allows you to do that:
T[T] = ( E[MEAS] / E[NEW] ) x T[C]
where T[C] is the calculated turns-per-volt, E[MEAS] is the voltage applied to the primary when the values were measured for the T[C] calculation, E[NEW] is the voltage you are recalculating for, the
T[T] is the turns-per-volt ratio with E[NEW] applied to the primary.
The next step is to determine the number of turns you need by multiplying the turns-per-volt calculated above by the voltage you want. In the above example, if you want 6-volts RMS, then you need 19
turns (6 volts × 3.175 turns-per-volt). Keep in mind that the wire you use must be capable of handling the maximum current you desire.
The amount of current that a wire can handle, whether used for the primary or secondary, depends on the wire's cross-sectional area. The easiest way to determine its current-handling capability is to
use one of the wire tables found in most complete electronics handbooks. Measure the wire's diameter in mils, using either a micrometer or a wire gauge, and using the table find the maximum current
that the wire is rated to handle. The cross-sectional area of a wire is measured in a unit called the circular mil (a circular mil is equal to the cross-sectional area of a wire with diameter of one
mil) and wire tables often include the data for a give wire diameter or gauge. Generally speaking, a cross-sectional area of 600 mils per ampere is satisfactory for small transformers, although areas
of 500 to 1000 mils are commonly used. If you are unsure about how heavy a wire you require, it is best to remember that the larger the cross-sectional area, the cooler the transformer will operate;
so choose as heavy a wire as is practical.
It's best to use new wire for the new secondary, but, as we previously mentioned, if you're careful the old secondary's wire may be serviceable. Bend old wire as little as possible, and do not use it
if there are any spots where the enamel has flaked off.
Once the proper wire has been chosen, the next step is to wrap the secondary. Wrap the wire without leaving any space between turns to get the maximum number of turns in the minimum amount of space.
Put wax paper, duct tape, or some other type of insulation capable of withstanding the maximum voltage of any one winding between each layer. The outside of the last layer should be covered extra
well and taped tightly for both your and the transformer's protection.
The last step is to reassemble the transformer. Fig 4 shows how to fit the "I"- and "E"-shaped laminations together. Most likely, there will be two to four "I" and "E" laminations left over—you will
not be able to squeeze those laminations back into the core, but that will not subtantially affect the power rating of the transformer.
FIG. 4—THE LAMINATIONS ARE reassembled as shown. Do not worry if a couple are left out—that is sure to happen but will not have any significant effect on the rewound transformer.
Rewinding a primary
Rewinding a primary becomes necessary if the primary on the transformer you have chosen is not wound closest to the iron core. That task is not recommended, but the the information is included here
for the industrious.
After the turns-per-volt ratio has been calculated, the number of turns on the primary can be determined by multiplying the turns-per-volt ratio by the primary voltage. Using the example of the
previous section and assuming the turns-per-volt was calculated with a primary voltage of 117 volts, the primary requires 371 turns (117 volts × 3.175 turns-per-volt). The alternative to that
procedure is to actually count the turns of the primary, which may lead to errors.
Under the secondary's and primary's wire there is usually a cardboard or plastic form. Wrap the new primary and secondary on that form so that the laminations will fit into the new windings. Use the
same gauge wire that the manufacturer used, but do not reuse the same primary wire. That's because that wire is usually a small gauge with enamel insulation that's apt to break off easily. Since the
primary wire is usually very long, it's very easy to develop shorts—when rewinding primaries, doing a lot of work for nothing is not that uncommon.
A practical example
Let's look at how we can rewind a transformer to deliver 8-volts DC at about 5 amps to a 5-volt regulator. That allows about 3volts across the regulator. Also, for the purposes of this example, let's
assume that we will use a bridge rectifier so that the transformer current would only need to be about 5 amps, since both halves of the AC cycle are used.
Using those specifications we get a pretty clear picture of exactly what kind of transformer is required. With a bridge rectifier a center tap is not needed on the secondary, but a bridge rectifier
drops the output voltage (voltage getting to the filter) by about 1.4 volts. The peak-value output of the transformer, therefore, has to be approximately 9.4 volts (8 volts + 1.4 volts). That means
that the transformer's power rating has to be about 47 watts (9.4 volts × 5 amps).
The transformer we'll choose to rewind has a secondary rated at 18 volts at 2.5 amps. Therefore, the transformer has a power rating of 45 watts, which is close enough for our purposes.
As the transformer is disassembled, make notes of its characteristics. First thing to do is to take the voltage measurements. For the transformer chosen for the example, the voltage from the center
tap to either end of the secondary measured about 8.1 volts, and the voltage across the primary was about 105 volts. When we disassembled the transformer, we found that the primary was next to the
core, the secondary from the outside end to the center tap had 51 turns in two layers, and that the wire from the center tap to the other end of the secondary was shorter but had the same number of
turns. Given those measured values, the turns-per-volt ratio was 6.3 (51 turns ÷ 8.1 volts). Using the correction formula, adjust that turns-per-volt ratio for 117 volts applied to the primary. The
corrected turns-per-volt ratio is therefore 5.65—105 volts ÷ 117 volts) × 6.3 turns-per-volt.
Knowing that, we can calculate the number of turns required for the secondary by multiplying the turns-per-volt by the voltage desired. The 9.4 volts peak translates to 6.65 volts RMS (9.4 volts ÷
√2) so 37.7 turns are needed (5.667 turns-per-volt × 6.65 volts). If the line voltage that the transformer is to be used with is normally below 117 volts, such as 105 volts, for instance, round the
number of turns up to 40.
Continuing with our example, since we are using a new transformer, it is reasonable to assume that the secondary wire will be in excellent condition and can be reused. But as we stated earlier, while
the wire is rated for 2.5-amps RMS, we want a transformer capable of handling 5-amps RMS. The wire can still be used, however, if two secondaries—wound for the same voltage and in parallel—are used.
With two parallel secondary, the transformer can handle the 5-volts RMS and no additional wire needs to be bought.
Cut the original secondary write at the the center tap. Use the shorter of that wire for one secondary, wrapping it on top of the primary in two layers of twenty turns each—duct tape should be placed
between the layers. For the other secondary, wrap the longer length of wire on top of the first secondary in the same manner—two layers of twenty turns each. Start that outer secondary winding at the
same place you started the first secondary and be sure to wind it in the same direction. The two secondaries must be wound in the same direction. Otherwise, the net effect of paralleling them is 0
The transformer is then reassembled, but before it can be used its specifications must be re-rated. Using the number of turns of the secondary divided by the turns-per-volt ratio at 117 volts, the
output voltage of the transformer is 7.06-volts RMS with 117 volts applied to the primary (40 turns ÷ 5.667 turns-per-volt). The current rating is not as easy to calculate. Let's look at the problem
from a power standpoint. The maximum power from the transformer is 45 watts. The maximum DC voltage is less than 9.98 volts (7.06 volts × √2), assuming full-wave rectification. The maximum DC current
that can be drawn is, therefore, 4.5 amps (45 watts ÷ 9.98 volts). For half-wave rectification you would divide that value in half.
The approach outlined here can be expanded to multiple-voltage secondaries with one more bit of information. The sum of the power required by each secondary must be equal to or less than the power
capability of the transformer itself.
One big advantage of winding your own transformers is the ability to compensate for house voltages that are slightly high or slightly low. You can also buy transformers that are on sale without
worrying about the output voltage. You only need be concerned about the power that the transformer can handle safely. | {"url":"http://home.comcast.net/~stphkeri/meader/rewinding_transformers.html","timestamp":"2014-04-18T23:57:16Z","content_type":null,"content_length":"23958","record_id":"<urn:uuid:afdc2c71-a7ea-423b-816c-5c78e196a9e8>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00549-ip-10-147-4-33.ec2.internal.warc.gz"} |
Labouchere System
The Labouchere betting system is very easy to understand and even easier to put into play, you will need a pen and a piece of paper and should aim to play it on a casino game such as roulette.
You now need to set yourself a win goal, you will then split this amount into a series of numbers and write this down, allow us to explain that in more detail.
Let's say you wish to win $10 in each cycle of the system, you then write down any series of numbers that add up to ten, this could be 2,3,5 or 1,1,1,1,1,5, the sequence of numbers is up to yourself
but the best way is to use smaller numbers.
You now need to sit down and start playing roulette. Your first wager will be the total of both numbers at the start and at the end of your sequence of numbers, so if you have 2,3 and 5 in your list
then your first wager will be 7 (2+5).
You then place 7 chips on your chosen even money wager. If this wager wins then you scratch off your list the two numbers and your next bet is 3 chips (the last remaining number of your list).
Labouchere in action
If your initial wager loses, then you need to add the loss to your list, so in effect the list 2,3,5 now becomes 2,3,5,7 and your next wager is, once again, the total of the two end numbers.
In our example this next wager will be 9 chips (2+7) if this wager wins then you knock off the 2 and 7 and your next wager will be 8 chips (3+5).
If that wager loses then the loss must be added onto your list and it will therefore become 2,3,5,7,9.
You keep on either adding losing numbers too your list or removing them accordingly.
Benefits of Labouchere
The idea and logic behind the Labouchere system is that you only need to win half as many wagers as you lose, and in a 50-50 proposition bet then this should be easily achievable.
Once you have completed each cycle of your number sequence you will have made (in our example) a ten unit profit.
Should the list of numbers get too big then experienced system players will then split this sequence down into much small lists of numbers in the hope that eventually everything will balance out and
they will end up in profit. | {"url":"http://www.learnbettingsystems.com/labouchere/","timestamp":"2014-04-18T15:38:52Z","content_type":null,"content_length":"12762","record_id":"<urn:uuid:dbb9548e-25a3-4724-9f07-66c640d06e5a>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00132-ip-10-147-4-33.ec2.internal.warc.gz"} |
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Followup to a derivatives question earlier: I'm told to find all critical points and specify which extrema are maxima or minima. I'm having trouble just chunking through the numbers. (Problem below).
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\[y = x ^{2/3}(x+2)\]\[y \prime = \frac{ 5x+4 }{ 3\sqrt[3]{x} }\]All critical points should occur at an endpoint or at y' = 0 or y' being undefined by the definition of a critical point. The
answers that satisfy the definition are \[x = 0, x = -\frac{ 4 }{ 5 }.\]Plugging the x values back into y itself, I am supposed to get\[y = 0, y =\frac{ 12 }{ 25 }10^{1/3}\]I have no idea how
that second one is gotten. First one, makes sense, everything is cancelled out by being multiplied by zero. Second one, you have \[(-\frac{ 4 }{ 5 })^{2/3}(-\frac{ 4 }{ 5 }+2)\]How the hell are
they ending up with that neat, fractional answer with that last bit?
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(Oh, and pardon me, i'm just horrible at algebra. Always have, will be marginally better with time. Eventually. Maybe.)
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y'(0) does not exist 5x + 4 = 0 when x = -4/5 so y'(-4/5) = 0 y'(-4/5) is your critical point
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y'(0) is still a critical point. It's undefined, but it doesn't not exist. And by the definition of a critical point [y'(0) is undefined, an end point within a defined interval or at a point
where y' = 0], it is a critical point. My book lists it as an answer word for word, and my book is definitely right.
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Well if x = 0 and x = -4/5 are you critical points, find f(0) and f(-4/5)
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f(0) = 0
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I found them above. I'm just having trouble numerically working out the second one.
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something is amiss
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What's amiss? I'm just bad with fractions being raised to fractional exponents less than one, especially when the base is also less than one, lol. I just don't understand how they're getting a
clean, fractional answer from it. Whenever I take the cube root of those fractions I just get an irrational slew of numbers, not a clean-cut, dandy little fraction.
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\[ (-\frac{ 4 }{ 5 })^{2/3}(-\frac{ 4 }{ 5 }+2) \] \[ (\frac{ 4^2 }{ 5^2 })^{1/3}(\frac{ 6 }{ 5 }) \] \[ (\frac{ 2\cdot 2^3 }{ 5^2 })^{1/3}(\frac{ 6 }{ 5 }) \] \[ (\frac{ 5\cdot 2\cdot 2^3 }{ 5 \
cdot 5^2 })^{1/3}(\frac{ 6 }{ 5 }) \] \[ (\frac{ 10\cdot 2^3 }{ 5^3 })^{1/3}(\frac{ 6 }{ 5 }) \] \[ 10^{1/3}(\frac{ 2 }{ 5 })(\frac{ 6 }{ 5 }) \] \[ 10^{1/3}\frac{ 12 }{ 25 }\]
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@phi , Line 4, did you just multiply the left portion by 5/5?
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yes, because it would be nice to have 5^3 in the bottom, so we can take its cube root.
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Makes sense, just making sure. Thanks so much, dude, this helps a lot.
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Help needed to perform bootstrap with matlab
March 5th 2009, 05:27 AM
Help needed to perform bootstrap with matlab
I have been given an m-file that amongst other things does a bootstrap calculation but I seem to be hitting a brick wall.
Here is the file I am using:
[nz,ntv] = size(obs);
% means
disp(' ')
mobs = mean(obs);
disp (['mean observed values = ' num2str(mobs)])
mest = mean(est);
disp (['mean estimated values = ' num2str(mest)])
% standart deviations
sdobs = std(obs);
disp (['std dev observed values = ' num2str(sdobs)])
sdest = std(est);
disp (['std dev estimated values = ' num2str(sdest)])
% assessment of goodness-of-fit
% correlation and coefficient of determination (explained variance)
[corre,p] = corrcoef([obs est]);R2=corre.^2;
disp (['R2 corre^2 = ' num2str(R2(1,2)) ' p = ' num2str(p(1,2))])
% mean absolute error
imae = sum(abs(obs-est))/ntv;
disp (['mae = ' num2str(imae)])
% root mean square error
rmse = sqrt(sum((obs-est).^2)/ntv);
disp (['rmse = ' num2str(rmse)])
disp(' ')
% Nash-Sutcliffe coeff of efficiency
E = 1-(sum((obs-est).^2)/sum((obs-mobs).^2));
disp (['N-Sut efficiency (E) = ' num2str(E)])
stat = bootstrp(500,@Nash_Sut,obs,est);
[a b]=ci95(stat);
disp ([ 'E 95% ci = ' num2str(a) ' ' num2str(b)])
disp (' ');clear stat
% log Nash-Sutcliffe coeff of efficiency
Elog = 1-(sum((log(obs)-log(est)).^2)/sum((log(obs)-log(mobs)).^2));
disp (['Elog = ' num2str(Elog)])
stat = bootstrp(500,@log_Nash_Sut,obs,est);
[a b]=ci95(stat);
disp ([ 'E 95% ci = ' num2str(a) ' ' num2str(b)])
disp (' ');clear stat
% Modified Nash-Sutcliffe coeff of efficiency
E1 = 1-(sum(abs(obs-est))/sum(abs(obs-mobs)));
disp (['N-Sut efficiency modified (E1) = ' num2str(E1)])
stat = bootstrp(500,@m_Nash_Sut,obs,est);
[a b]=ci95(stat);
disp ([ 'E1 95% ci = ' num2str(a) ' ' num2str(b)])
disp (' '); clear stat
% index of agreement
d = 1-(sum((obs-est).^2)/sum((abs(obs-mobs)+abs(obs-mobs)).^2));
disp (['Index of agreement (d) = ' num2str(d)])
stat = bootstrp(500,@I_agree,obs,est);
[a b]=ci95(stat);
disp ([ 'd 95% ci = ' num2str(a) ' ' num2str(b)])
disp (' '); clear stat
% Modified index of agreement
d1 = 1-(sum(abs(obs-est))/sum((abs(obs-mobs)+abs(obs-mobs))));
disp (['Index of agreement modified (d1) = ' num2str(d1)])
stat = bootstrp(500,@m_I_agree,obs,est);
[a b]=ci95(stat);
disp ([ 'd1 95% ci = ' num2str(a) ' ' num2str(b)])
disp (' '); clear stat
and this is the result:
mean observed values = 17.9477
mean estimated values = 17.7683
std dev observed values = 6.4146
std dev estimated values = 2.1859
R2 corre^2 = 0.034055 p = 0.32894
mae = 152.28
rmse = 34.3907
N-Sut efficiency (E) = 0.0088419
??? Error using ==> feval
Undefined command/function 'Nash_Sut'.
Error in ==> bootstrp at 77
thetafit = feval(bootfun,varargin{:});
Error in ==> goodfit2 at 53
stat = bootstrp(500,@Nash_Sut,obs,est);
Can anyone help me resolve the problem? It seems that matlab does not like Nash_sut and the rest as a Bootfun.
Secondly, and more to save time, how do I modify the m-file so that instead of running this for every obs and est file I have (there are 50+ of each), I could put them all into one file each ie
in columns and get the outputs for each individual column?
March 6th 2009, 12:08 AM
I have been given an m-file that amongst other things does a bootstrap calculation but I seem to be hitting a brick wall.
Here is the file I am using:
and this is the result:
Can anyone help me resolve the problem? It seems that matlab does not like Nash_sut and the rest as a Bootfun.
Secondly, and more to save time, how do I modify the m-file so that instead of running this for every obs and est file I have (there are 50+ of each), I could put them all into one file each ie
in columns and get the outputs for each individual column?
offending line is:
stat = bootstrp(500,@Nash_Sut,obs,est);
Where in Nash_Sut defined, and what is it?? If it is a function handel for an anonymous function then it does not need the @.
March 6th 2009, 01:21 AM
Hi CB,
from what I know nash_sut is the function above ie: E = 1-(sum((obs-est).^2)/sum((obs-mobs).^2)).
The idea is that by bootstraping one can determine the significance of E. How would I be able to correct the problem/rewrite the code to fix this?
March 6th 2009, 02:29 AM
Then what is the @ doing in that statement?
March 6th 2009, 02:57 AM
You got me! I have no idea, i am a relative newbie to matlab and definitly never used bootstrp before.
March 6th 2009, 03:22 AM
So if I want the bootfun to be the function mentioned how do I enter it into the bootstrp statement.
I tried to enter the entire function but that did not work, should I create a new m-file with the function, and then enter that m-file? | {"url":"http://mathhelpforum.com/math-software/77048-help-needed-perform-bootstrap-matlab-print.html","timestamp":"2014-04-17T05:39:16Z","content_type":null,"content_length":"11233","record_id":"<urn:uuid:44ef7852-643c-4d4b-874e-d095158d3bf1>","cc-path":"CC-MAIN-2014-15/segments/1397609526252.40/warc/CC-MAIN-20140416005206-00276-ip-10-147-4-33.ec2.internal.warc.gz"} |
Applications of the Integral
Problem : Suppose a dog named Tika is chasing a duck in a straight line. If the duck's speed is given by d'(t) = 5 feet per second and Tika's speed by T'(t) = 2t feet per second, how far has Tika
traveled when her speed is equal to the duck's speed? If the duck gets a 100 foot head start, how far has Tika traveled when she catches the duck?
Figure %: The Dog Tika Chasing a Duck
Tika's speed is equal the duck's speed after
seconds. To compute the distance she has traveled in this time, we integrate her speed from
To find how far Tika must run to catch the duck, we must find the functions that give the distance traveled by Tika and by the duck in the first
seconds. These are just antiderivatives of the velocity functions:
d (t) = 5t
T(t) = t ^2
. Since the duck gets a
foot head start, we should solve the equation
100 + 5t = t ^2
. The quadratic formula gives
t = (5 + 5
. Substituting into
, we find that Tika must run a total of about | {"url":"http://www.sparknotes.com/math/calcbc2/applicationsoftheintegral/problems_4.html","timestamp":"2014-04-17T15:35:27Z","content_type":null,"content_length":"53535","record_id":"<urn:uuid:6559e238-c299-4a0c-a3fc-d5105d8544d6>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00034-ip-10-147-4-33.ec2.internal.warc.gz"} |
Probability of randomly predicting the score of a baseball game
October 25th 2013, 09:49 PM #1
Oct 2013
Probability of randomly predicting the score of a baseball game
Hi there,
I'm writing a novel in which the main character receives the scoreboard to a baseball game from the future. It's right of course. He's a math whiz, and to verify that it's from the future he
calculates what the probability of it being a coincidence. Unfortunately it's beyond my simple grasp of permutations.
So here are your constraints: The final score is 7-4. The score during each of the nine innings is known. The losing team had three hits, the winning team had four. Let's assume an upper limit
for hits is 10 on both sides. The losing team had one error, and for our sake's we can assume an upper limit on errors of 5 on both sides. Here's the scoreboard:
Innings 1 2 3 4 5 6 7 8 9 R H E
Mariners 0 1 0 0 1 0 2 0 0 4 3 1
Athletics 0 2 0 1 1 0 1 2 0 7 4 0
So what would be the chance that if you knew what the score was, a person could guess, in correct order, how the game would score over 9 innings, and the correct number of hits and errors? I know
the number would be astronomical, but that's kind the point for my book. Also, if you can explain how you got your answer that would help a lot! Thank you! ~Chris
Re: Probability of randomly predicting the score of a baseball game
So here are your constraints: The final score is 7-4. The score during each of the nine innings is known. The losing team had three hits, the winning team had four. Let's assume an upper limit
for hits is 10 on both sides. The losing team had one error, and for our sake's we can assume an upper limit on errors of 5 on both sides. Here's the scoreboard:
Innings 1 2 3 4 5 6 7 8 9 R H E
Mariners 0 1 0 0 1 0 2 0 0 4 3 1
Athletics 0 2 0 1 1 0 1 2 0 7 4 0
So what would be the chance that if you knew what the score was, a person could guess, in correct order, how the game would score over 9 innings, and the correct number of hits and errors? I know
the number would be astronomical, but that's kind the point for my book. Also, if you can explain how you got your answer that would help a lot! Thank you! ~Chris
Knowing very little about baseball, I may not understand your question.
But have a look at this webpage.
It gives you the partitions of 7. As you can see there are 15 ways to get a seven.
A team could score all seven runs in one inning alone. That can be done in nine ways.
A team could score one run in each of seven innings. That can be done in 36 ways.
Or from your example: 2+2+1+1+1. That is scores in five innings. That can be done in $\frac{9!}{(2!)(3!)(4!)}=1260$ ways.
So what you are asking requires a lot of tedious workings.
Moreover, once it is done for seven then its must be done for four.
Multiply the two results together. Here are the partitions of 4. There are only five.
October 26th 2013, 07:34 AM #2 | {"url":"http://mathhelpforum.com/statistics/223506-probability-randomly-predicting-score-baseball-game.html","timestamp":"2014-04-19T12:13:14Z","content_type":null,"content_length":"37206","record_id":"<urn:uuid:3c26a06b-8919-4f9b-8409-fc9c9a19205e>","cc-path":"CC-MAIN-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00658-ip-10-147-4-33.ec2.internal.warc.gz"} |
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$C^2$-continuous solutions
An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T. (2013) ADI method based on C^2-continuous two-node integrated-RBF elements for viscous flows. Applied Mathematical Modelling, 37
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Kist, Alexander A. and Harris, Richard J. (2003) Using virtual SIP links to enable QoS for signalling. In: 11th IEEE International Conference on Networks (ICON 2003), 28 Sept - 1 Oct 2003 , Sydney,
3GPP SIP overlay networks
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adaptive filter
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Adaptive Fuzzy Logic Based Security Level Routing Protocol
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adaptive material
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65-95. ISSN 1526-1492
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2008) A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures. CMES: Computer Modeling in Engineering and
Sciences, 23 (3). pp. 209-222. ISSN 1526-1492
adaptive QoS guarantees
Zhou, Hong and Zhang, Zhongwei (2009) Adaptive end-to-end QoS provision for real-time multimedia applications in heterogeneous multi-hop wireless networks. In: 5th International ICST Mobile
Multimedia Communications Conference (MobiMedia'09), 7-9 September 2009, London, United Kingdom.
additive white Gaussian noise channel
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
adhesive wear and friction
Yousif, B. F. and Devadas, Alvin and Yusaf, Talal (2009) Adhesive wear and frictional behaviour of multilayered polyester composite based on betelnut fiber mats under wet contact conditions. Surface
Review and Letters, 16 (3). pp. 407-414. ISSN 0218-625X
ADI method
An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T. (2013) ADI method based on C^2-continuous two-node integrated-RBF elements for viscous flows. Applied Mathematical Modelling, 37
(7). pp. 5184-5203. ISSN 0307-904X
aerodynamic testing
Morgan, R. G. and McIntyre, T. J. and Jacobs, P. A. and Buttsworth, D. R. and Macrossan, M. N. and Gollan, R. J. and Capra, B. R. and Brandis, A. M. and Potter, D. and Eichmann, T. and Jacobs, C. M.
and McGilvray, M. and van Diem, D. and Scott, M. P. (2006) Impulse facility simulation of hypervelocity radiating flows. In: 2nd International Workshop on Radiation of High Temperature Gases in
Atmospheric Entry, 6-8 Sep 2006, Rome, Italy.
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Cai, Wenju and Cowan, Tim and Dix, Martin and Rotstayn, Leon and Ribbe, Joachim and Shi, Ge and Wijffels, Susan (2007) Anthropogenic aerosol forcing and the structure of temperature trends in the
southern Indian Ocean. Geophysical Research Letters, 34 (14). L14611. ISSN 0094-8276
aerospace engineering
Eichmann, T. N. and Khan, R. and McIntyre, T. J. and Jacobs, C. and Porat, H. and Buttsworth, D. and Upcroft, B. (2012) Radiometric temperature analysis of the Hayabusa spacecraft re-entry. In: 28th
International Symposium on Shock Waves (ISSW 28), 17-22 Jul 2011, Manchester, United Kingdom.
Buttsworth, David and Jacobs, Peter and Potter, Daniel and Mudford, Neil and D'Souza, Mary and Eichmann, Troy and Jenniskens, Peter and McIntyre, Tim and Jokic, Michael and Jacobs, Carolyn and
Upcroft, Ben and Khan, Razmi and Porat, Hadas and Neely, Andrew and Lohle, Stefan (2012) Super-orbital re-entry in Australia: laboratory measurement, simulation and flight observation [Keynote
lecture]. In: ISSW28: 28th International Symposium on Shock Waves, 17-22 Jul 2011, Manchester, United Kingdom.
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
aerothermodynamic measurements
Buttsworth, David R. and Stevens, Robert and Stone, C. Richard (2005) Eroding ribbon thermocouples: impulse response and transient heat flux analysis. Measurement Science and Technology, 16 (7). pp.
1487-1494. ISSN 0957-0233
affine scaling method
Eum, Suyong and Harris, Richard J. and Kist, Alexander (2006) Generalized Kruithof approach for traffic matrix estimation. In: 14th IEEE International Conference on Networks (ICON 2006), 13-15 Sep
2006, Singapore.
agriculatural machines
Wen, Peng and Kidd, Jason G. (2005) Electronic height indicator for agricultural machines. Australian Journal of Electrical and Electronics Engineering, 2 (1). pp. 13-20. ISSN 1448-837X
agricultural waste
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Yusaf, T. (2009) Potential of bioethanol production from agricultural wastes in Iran. Renewable and Sustainable Energy Reviews, 13 (6-7). pp.
1418-1427. ISSN 1364-0321
Donald, Alexis and Meinke, Holger and Power, Brendan and Maia, Aline de H. N. and Wheeler, Matthew and Stone, Roger C. and Ribbe, Joachim and White, Neil (2006) Near-global impact of the
Madden-Julian Oscillation on rainfall. Geophysical Research Letters, 33 (9). L09704. ISSN 0094-8276
air and fuel dilution
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Numerical investigation of influence of air and fuel dilution for open furnace MILD combustion burner. In: 2012 Qld Southern Regional
Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
air density
Stepanyants, Yury (2005) Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons. Proceedings of the Russian Academy of Engineering Sciences Series: Applied
Mathematics and Mechanics, 14. pp. 33-40.
air fuel ratio
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The air fuel ratio study for the mixture of biogas and hydrogen on mild combustion. In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5
Jul 2013, Sydney, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The study of air fuel ratio for open furnace MILD combustion of biogas on bluff-body burner. In: 2012 Qld Southern Regional Engineering
Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The modelling of the effect of air fuel ratio on unburned hydrocarbons for MILD combustion. In: 2nd Malaysian Postgraduate Conference (MPC
2012), 7-9 July 2012, Gold Coast, Australia.
air pollution
Sharifian, Ahmad (2012) The effect of direction of low speed winds on the performance of a split chimney. In: 23rd International Congress of Theoretical and Applied Mechanics (ICTAM 2012), 19-24
Aug2012, Beijing, China.
air quality
Zhou, Hong and Qi, Haixia and Banhazi, Thomas and Low, Tobias (2013) An integrated WSN and mobile robot system for agriculture and environment applications. In: MOBIQUITOUS 2013, 10th International
Conference on Mobile and Ubiquitous Systems: Computing, Networking and Services, 2-4 Dec 2013, Tokyo, Japan.
air sea interaction
Ribbe, Joachim (2001) Intermediate water mass production controlled by southern hemisphere winds. Geophysical Research Letters, 28 (3). pp. 535-538. ISSN 0094-8276
Tangalajuk Siang, Jeri and Sharifian, Ahmad (2013) Reducing the mass of the refrigerant in the capillary tube of a propane air-conditioner. In: 14th Asian Congress of Fluid Mechanics (14 ACFM), 15-19
Oct 2013, Hanoi-Halong, Vietnam.
aircraft turbofan
Buttsworth, D. R. and Davison, C. and MacLeod, J. D. and Strapp, J. W. (2007) Evaporator design for an isokinetic total water content probe in a naturally aspirating configuration. In: 16th
Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
aircraft wings
Saleh, Khalid and Buttsworth, David and Yusaf, Talal (2010) Development of a small icing wind tunnel for simulating the initial stages of solid phase ice accretion. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
alamouti code
Sileh, Ibrahim Khalil and Xiang, Wei (2012) Distributed space-frequency coding for OFDM-based hybrid relay selection. In: 12th International Symposium on Communications and Information Technologies
(ISCIT 2012), 2-5 Oct 2012, Gold Coast, Australia.
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
alternating current
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
alternating direction implicit (ADI)
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady
convection-diffusion equations. CMES: Computer Modeling in Engineering and Sciences, 89 (3). pp. 189-220. ISSN 1526-1492
alternative fuel
Yusaf, T. F. and Al-lwayzy, Saddam H. (2012) The use of microalgae biodiesel in diesel engine: production, extraction and engine performance. In: USQ Combustion Meeting, 21 Nov 2012, Toowoomba,
Australia. (Unpublished)
alternative fuel
Al-lwayzy, Saddam H. (2012) Alternative fuels from microalgae for diesel engine. In: USQ Combustion Meeting, 10 Oct 2012, Toowoomba, Australia. (Unpublished)
Najafi, Gholamhassan and Ghobadian, Barat and Yusaf, Talal and Rahimi, Hadi (2007) Combustion analysis of a CI engine performance using waste cooking biodiesel fuel with an artificial neural network
aid. American Journal of Applied Sciences, 4 (10). pp. 756-764. ISSN 1546-9239
Leis, J. and Martin, P. and Buttsworth, D. (2012) Simplified digital lock-in amplifier algorithm. Electronics Letters, 48 (5). pp. 259-261. ISSN 0013-5194
amplify and forward relay
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Multicast based dual amplify and forward relay scheme for 2 hop networks. In: LATINCOM 2009: 1st IEEE
Latin-American Conference on Communications, 10-11 Sep 2009, Medellin, Colombia.
amplitude expansion
Suslov, S. A. (2008) Two-equation model of mean flow resonances in subcritical flow systems. Discrete and Continuous Dynamical Systems Series S, Selected Topics, 1 (1). pp. 165-176. ISSN 1937-1632
analog network coding
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong and Huang, Tao (2011) Outage analysis of non-regenerative analog network coding for two-way multi-hop networks. IEEE Communications Letters, 15 (6). pp.
662-664. ISSN 1089-7798
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong and Huang, Tao (2011) Outage performance of analog network coding in generalized two-way multi-hop networks. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011) , 28-31 Mar 2011, Cancun, Mexico.
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Analysis of viscoelastic flow by a radial basis function networks method. In: 16th Australasian Fluid Mechanics Conference (AFMC 2007), 3-7
Dec 2007, Gold Coast, Australia.
Shiau, Jim and Al Abri, Mohammed (2011) A study on the failure mechanisms of horizontal plate anchors in clay. In: ICAGE 2011: International Conference on Advances in Geotechnical Engineering, 7-9
Nov 2011, Perth, Western Australia.
animal monitoring
Zhou, Hong and Wu, Huayi (2009) The integration of wireless sensor networks, remote sensing and geographic information systems for autonomous environmental and animal monitoring. In: IADIS
International Conference on Applied Computing 2009 (IADIS 2009), 19-21 Nov 2009, Rome, Italy.
animal welfare
Zhou, Hong and Qi, Haixia and Banhazi, Thomas and Low, Tobias (2013) An integrated WSN and mobile robot system for agriculture and environment applications. In: MOBIQUITOUS 2013, 10th International
Conference on Mobile and Ubiquitous Systems: Computing, Networking and Services, 2-4 Dec 2013, Tokyo, Japan.
anomalous diffusion
Langlands, T. A. M. and Henry, B. I. and Wearne, S. L. (2011) Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions. SIAM Journal on Applied
Mathematics, 71 (4). pp. 1168-1203. ISSN 0036-1399
anomalous subdiffusion
Henry, B. I. and Langlands, T. A. M. and Straka, P. (2010) Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces. Physical Review Letters, 105 (17).
17062-1-170602-4. ISSN 0031-9007
Langlands, T. A. M. and Henry, B. I. (2010) Fractional chemotaxis diffusion equations. Physical Review E: Statistical Nonlinear and Soft Matter Physics, 81 (5). pp. 1-12. ISSN 1539-3755
Henry, B. I. and Langlands, Trevor and Straka, P. (2010) An introduction to fractional diffusion. In: Proceedings of the 22nd Canberra International Physics Summer School, 8-19 Dec 2008, Canberra,
ANSYS Fluent 14.5
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Detail guide for CFD on the simulation of biogas combustion in bluff-body mild burner. In: 2nd International Conference of Mechanical
Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
ANSYS software
Dahmani, L. and Khennane, A. and Kaci, S. (2010) Crack identification in reinforced concrete beams using ANSYS software. Strength of Materials, 42 (2). pp. 232-240. ISSN 0039-2316
Sorensen, Jacob V. T. and Ribbe, Joachim and Shaffer, Gary (2001) Antarctic intermediate water mass formation in ocean general circulation models. Journal of Physical Oceanography, 31 (11). pp.
3295-3311. ISSN 1520-0485
antenna arrays
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
antenna gain mismatch
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
Zhang, Zhongwei (2009) An intelligent scheme of secure routing for mobile ad hoc networks. In: ICSPCS 2008: 2nd International Conference on Signal Processing and Communication Systems , 15-17 Dec
2008, Gold Coast, Australia.
Mai-Duy, N. and Tanner, R. I. (2005) Solving high-order partial differential equations with indirect radial basis function networks. International Journal for Numerical Methods in Engineering, 63
(11). pp. 1636-1654. ISSN 0029-5981
Mai-Duy, Nam (2005) Solving high order ordinary differential equations with radial basis function networks. International Journal for Numerical Methods in Engineering, 62 (6). pp. 824-852. ISSN
approximation theory
Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768
area-restricted search
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
arithmetic coding
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2012) Two-symbol FPGA architecture for fast arithmetic encoding in JPEG 2000. Journal of Signal Processing Systems, 69 (2). pp. 213-224. ISSN
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2010) An FPGA-based fast two-symbol processing architecture for JPEG 2000 arithmetic coding. In: ICASSP 2010: 35th International Conference on
Acoustics, Speech, and Signal Processing, 14-19 Mar 2010, Dallas, TX. USA.
artificial neural network
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Buttsworth, D. R. and Yusaf, T. F. and Faizollahnejad, M. (2009) Performance and exhaust emissions of a gasoline engine with ethanol blended gasoline
fuels using artificial neural network. Applied Energy, 86 (5). pp. 630-639. ISSN 0306-2619
Ghobadian, B. and Rahimi, H. and Nikbakht, A. M. and Najafi, G. and Yusaf, T. F. (2009) Diesel engine performance and exhaust emission analysis using waste cooking biodiesel fuel with an artificial
neural network. Renewable Energy, 34 (4). pp. 976-982. ISSN 0960-1481
Najafi, Gholamhassan and Ghobadian, Barat and Yusaf, Talal and Rahimi, Hadi (2007) Combustion analysis of a CI engine performance using waste cooking biodiesel fuel with an artificial neural network
aid. American Journal of Applied Sciences, 4 (10). pp. 756-764. ISSN 1546-9239
AS interfaces
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
Zhang, Zhongwei and Wang, Zhen (2006) Assessing and assuring trust in e-Commerce systems. In: International Conference on Intelligent Agents, Web Technologies & Internet Commerce (IAWTIC'06), 29 Nov
- 1 Dec 2006, Sydney, Australia.
Eichmann, T. N. and Khan, R. and McIntyre, T. J. and Jacobs, C. and Porat, H. and Buttsworth, D. and Upcroft, B. (2012) Radiometric temperature analysis of the Hayabusa spacecraft re-entry. In: 28th
International Symposium on Shock Waves (ISSW 28), 17-22 Jul 2011, Manchester, United Kingdom.
atkinson cycle
Malpress, Ray and Buttsworth, David (2010) A comparison between two-position variable compression ratio and continuously variable compression ratio engines using numerical simulation. In: ICEF 2009:
ASME Internal Combustion Engine Division Fall Technical Conference , 27-30 Sep 2009, Lucerne, Switzerland.
atmospheric circulation
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
atmospheric entry
Morgan, R. G. and McIntyre, T. J. and Jacobs, P. A. and Buttsworth, D. R. and Macrossan, M. N. and Gollan, R. J. and Capra, B. R. and Brandis, A. M. and Potter, D. and Eichmann, T. and Jacobs, C. M.
and McGilvray, M. and van Diem, D. and Scott, M. P. (2006) Impulse facility simulation of hypervelocity radiating flows. In: 2nd International Workshop on Radiation of High Temperature Gases in
Atmospheric Entry, 6-8 Sep 2006, Rome, Italy.
atmospheric radiation
Morgan, R. G. and McIntyre, T. J. and Jacobs, P. A. and Buttsworth, D. R. and Macrossan, M. N. and Gollan, R. J. and Capra, B. R. and Brandis, A. M. and Potter, D. and Eichmann, T. and Jacobs, C. M.
and McGilvray, M. and van Diem, D. and Scott, M. P. (2006) Impulse facility simulation of hypervelocity radiating flows. In: 2nd International Workshop on Radiation of High Temperature Gases in
Atmospheric Entry, 6-8 Sep 2006, Rome, Italy.
Wells, Colin G. and Ball, James A. R. (2006) Attenuation of a shielded rectangular dielectric rod waveguide. IEEE Transactions on Microwave Theory and Techniques, 54 (7). pp. 3013-3018. ISSN
Strunin, Dmitry V. (2007) Attractors in confined source problems for coupled nonlinear diffusion. SIAM Journal on Applied Mathematics, 67 (6). pp. 1654-1674. ISSN 0036-1399
Nguyen-Ky, T. and Leis, J. and Xiang, W. (2010) An improved new error estimation algorithm for optimal filter lengths for stereophonic acoustic echo cancellation. Computers and Electrical
Engineering, 36 (4). pp. 664-675. ISSN 0045-7906
Hashempour, Javad and Sharifian, Ahmad (2012) Potentials of metal mesh to contain bushfires. In: 2012 Qld Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Rahman, M. M. and Ismail, J., eds. (2012) Proceedings of the 2nd Malaysian Posgraduate Conference (MPC 2012). Education Malaysia, Sydney (EMAS), Gold Coast, Australia.
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2008) An interpretation of Australian rainfall projections. Geophysical Research Letters, 35 (2). L2072. ISSN 0094-8276
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
Faqih, Akhmad and Ribbe, Joachim and Meinke, Holger (2007) 20th century rainfall variability and the role of large scale climate events within Indo-Pacific region from IPCC AR4 models, reanalysis and
observations. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
You, John and Muller, Dietmar and Sdrolias, Maria and Herold, Nicholas and Ribbe, Joachim (2007) Sensitivity of middle Miocene climate and regional monsoon to palaeo-altimetry. In: 14th National
Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
Murphy, Bradley F. and Ribbe, Joachim (2004) Variability of southeast Queensland rainfall and climate indices. International Journal of Climatology, 24 (6). pp. 703-721. ISSN 0899-8418
Donald, Alexis and Ribbe, Joachim and Stone, Roger and Meinke, Holger and Harris, Graham and Power, Brendan and Wheeler, Matthew (2003) The influence of the Madden Julian Oscillation on Queensland's
rainfall. In: 15th Australian New Zealand Climate Forum, 19-21 Mar 2003, Palmerston, New Zealand.
Australian climate
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Lai, David Tai Wai (2010) Supporting secure services on dynamic aggregation of heterogeneous networks. [Thesis (PhD/Research)] (Unpublished)
auto-ignition process
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
automated vehicle classification
Xiang, Wei and Otto, Colin W. and Wen, Peng (2008) Automated vehicle classification system using advanced noise reduction technology. In: 1st International Conference on Signal Processing and
Communication Systems (ICSPCS 2007), 17-19 Dec 2007, Gold Coast, Australia.
automated vehicle classification system
Xiang, Wei and Otto, Colin W. and Wen, Peng (2009) Automated vehicle classification system for AUSTROADS standard based upon laser sensor technology. Australian Journal of Electrical and Electronics
Engineering, 5 (2). pp. 95-106. ISSN 1448-837X
Xiang, Wei and Pietrobon, Steven S. (2003) On the capacity and normalisation of ISI channels. In: 2003 IEEE International Conference on Communications (ICC2003), 11-15 May 2003, Anchorage, Alaska,
AWGN channel
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
axial flux machine cores
Hewitt, Andrew and Ahfock, Tony L. and Suslov, Sergey A. (2005) Magnetic flux density distribution in axial flux machine cores. IET Electric Power Applications, 152 (2). pp. 192-196. ISSN 1350-2352
axisymmetric simulation
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
Shiau, J. S. and Smith, C. A. (2011) Calculation of lateral earth pressures with layered backfill. In: Continuum and Distinct Element Numerical Modeling in Geomechanics, 14-16 Feb 2011, Melbourne,
background pressure
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
Hamid, H. A. and Yusaf, T. and Yusof, Z. M. (2006) An investigation on the improvement of the operation of Tenom Pangi HPP cooling power system. In: International Conference on Energy and Environment
2006 (ICEE 2006), 28-30 Aug 2006, Kajang, Malaysia.
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2008) Application of topological conservation to model key features of zero-torque multi-ply yarns. Journal of the Textile
Institute, 99 (4). pp. 325-337. ISSN 0040-5000
balance twisted yarn
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2006) Issues in processing unstable twisted fibre assemblies. In: 4th International Industrial Simulation Conference (ISC 2006),
5-7 Jun 2006, Palermo, Italy.
base station
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
battery sizing
Helwig, A. and Ahfock, A. (2011) Sizing nickel iron batteries for RAPS systems. In: 2011 IET Renewable Power Generation Conference (RPG 2011) , 6-8 Sep 2011, Edinburgh, UK.
Bayesian rule
Li, Yan and Wen, Peng (2005) Bayesian model for brain computation. In: 2005 International Conference on Complex Medical Engineering (CME 2005), 15-18 May 2005, Takamatsu, Japan.
bearing capacity
Shiau, J. S. and Merifield, R. S. and Lyamin, A. V. and Sloan, S. W. (2011) Undrained stability of footings on slopes. International Journal of Geomechanics, 11 (5). pp. 381-390. ISSN 1532-3641
Shiau, J. S. and Watson, J. F. (2008) 3D bearing capacity of shallow foundations located near deep excavation sites. In: 2008 International Conference on Deep Excavation: Challenges Risk Management
of Underground Construction (ICDE 2008), 10-12 Nov 2008, Singapore.
Smith, Catherine and Shiau, Jim S. (2007) Bearing capacity of footings near slopes. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane, Australia.
Mai-Duy, N. and Tanner, R. I. (2004) An efficient BEM for numerical solution of the biharmonic boundary value problem. In: International Conference on Computational and Experimental Engineering &
Sciences (ICCES 2004): Advances in Computational & Experimental Engineering & Sciences , 26-29 Jul 2004, Madeira, Portugal.
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
benchmark test problems
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
Phillips, D. G. and Tran, Canh-Dung and Fraser, W. B. and van der Heijden, G. H. M. (2010) Torsional properties of staple fibre plied yarns. Journal of the Textile Institute, 101 (7). pp. 595-612.
ISSN 0040-5000
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2008) Application of topological conservation to model key features of zero-torque multi-ply yarns. Journal of the Textile
Institute, 99 (4). pp. 325-337. ISSN 0040-5000
BER performance
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
Bernoulli's integral
Stepanyants, Yu. A. and Yakubovich, Evsey (2011) Scalar description of three-dimensional vortex flows of incompressible fluid. Doklady Physics, 56 (2). pp. 130-133. ISSN 1028-3358
BESO method
Nguyen, T. and Ghabraie, K. and Tran-Cong, T. (2014) Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour.
Computers and Geotechnics , 55. pp. 57-66. ISSN 0266-352X
Nguyen, T. and Ghabraie, K. and Tran-Cong, T. (2012) Tunnel reinforcement optimisation for nonlinear material. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012,
Gold Coast, Australia.
best partially disjoint paths
Kist, Alexander A. and Harris, Richard J. (2002) A heuristic to generate all best partially disjoint paths in a communications network. In: 8th International Conference on Communication Systems (ICCS
2002), 25-28 Nov 2002, Singapore.
best-relay position
Ran, Jie and Wang, Yafeng and Li, Chang and Yang, Dacheng and Xiang, Wei (2010) Joint power allocation and best-relay positioning for incremental selection amplify-and-forward relaying. In: 2010 IEEE
Vehicular Technology Conference (VTC 2010-Fall), 6-9 Sept 2010, Ottawa, Canada.
best-relay selection
Alajel, Khalid Mohamed and Xiang, Wei and Sileh, Ibrahim Khalil (2012) Best relays selection method for error-resilient 3-D video transmission. In: 12th International Symposium on Communications and
Information Technologies (ISCIT 2012), 2-5 Oct 2012, Gold Coast, Australia.
betelnut fiber mats
Yousif, B. F. and Devadas, Alvin and Yusaf, Talal (2009) Adhesive wear and frictional behaviour of multilayered polyester composite based on betelnut fiber mats under wet contact conditions. Surface
Review and Letters, 16 (3). pp. 407-414. ISSN 0218-625X
bi-direction unbalanced traffic
Zhou, Hong and Gyasi-Agyei, Amoakoh and Zhang, Zhongwei (2006) Performance of STT-Vegas in heterogeneous wired and wireless networks. In: 3rd International Conference on Quality of Service in
Heterogeneous Wired/Wireless Networks (QShine), 7-9 Aug 2006, Waterloo, Canada.
bi-directional communication
Long, Hang and Xiang, Wei and Liu, Hongmei and Shen, Shanshan (2012) Diversity analysis of two-way MIMO relaying system based on zero-forcing. In: IEEE International Conference on Communications (ICC
2012): Connect, Communicate, Collaborate, 10-15 Jun 2012, Ottawa, ON. Canada.
bifurcated reflected shock
Goozee, R. J. and Jacobs, P. A. and Buttsworth, D. R. (2006) Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. Shock Waves, 15 (3-4). pp. 165-176.
ISSN 0938-1287
Suslov, Sergey A. (2002) Flow patterns near codimension-2 bifurcation in non-Boussinesq mixed convection. In: Progress in Nonlinear Science, International Conference dedicated to the 100th
Anniversary of A.A. Andronov, 2-6 Jul 2001, Nizhniy Novgorod, Russia.
Sharifulin, Albert and Suslov, Sergey A. (2008) Bifurcations in convection of incompressible fluid in a rotated square cylinder. In: XXII International Congress of Theoretical and Applied Mechanics
ICTAM 2008, 24-29 August 2008, Adelaide, Australia.
biharmonic equations
Mai-Duy, Nam and Tran-Cong, Thanh (2008) Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks. In: 8th International Conference on Computational
and Mathematical Methods in Science and Engineering (CMMSE-2008), 13-16 June 2008, Murcia, Spain.
Mai-Duy, N. and Tanner, R. I. (2005) An effective high order interpolation scheme in BIEMs for biharmonic boundary value problems. Engineering Analysis with Boundary Elements, 29 (3). pp. 210-223.
ISSN 0955-7997
biharmonic Dirichlet problems
Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I. (2006) A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem. Engineering Analysis with Boundary Elements,
30 (10). pp. 809-817. ISSN 0955-7997
biharmonic equations
Mai-Duy, Nam and Ho-Minh, D. and Tran-Cong, Thanh (2009) A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations. International Journal
of Computer Mathematics, 86 (10-11). pp. 1746-1759. ISSN 0020-7160
Mai-Duy, N. and Tran-Cong, T. (2006) Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis With Boundary Elements, 30
(2). pp. 77-87. ISSN 0955-7997
Mai-Duy, N. and Tanner, R. I. (2004) An efficient BEM for numerical solution of the biharmonic boundary value problem. In: International Conference on Computational and Experimental Engineering &
Sciences (ICCES 2004): Advances in Computational & Experimental Engineering & Sciences , 26-29 Jul 2004, Madeira, Portugal.
biharmonic problems
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2009) A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical
Modelling, 33 (1). pp. 284-299. ISSN 0307-904X
Mai-Duy, Nam and Tanner, Roger I. (2007) A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. Journal of Computational and
Applied Mathematics, 201 (1). pp. 30-47. ISSN 0377-0427
binary gas flows
Buttsworth, David R. and Jones, Terry V. (2003) Concentration probe measurements in a Mach 4 nonreacting hydrogen jet. Journal of Fluids Engineering, 125 (4). pp. 628-635. ISSN 0098-2202
binomial coefficients
Li, Zhenquan and Roberts, A. J. (2007) Low-dimensional modelling of a generalised Burgers equation. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 203-218. ISSN 0973-1768
binomial Langevin model
Wandel, Andrew P. and Lindstedt, R. Peter (2009) Application of hybrid binomial Langevin-multiple mapping conditioning method to reacting jet flow. In: Australian Combustion Symposium 2009 (ACS09),
2-4 Dec 2009, Brisbane, Australia.
Al-lwayzy, Saddam H. (2012) Alternative fuels from microalgae for diesel engine. In: USQ Combustion Meeting, 10 Oct 2012, Toowoomba, Australia. (Unpublished)
Najafi, Bahman and Pirouzpanah, Vahab and Najafi, Gholamhassan and Yusaf, Talal and Ghobadian, Barat (2007) Experimental investigation of performance and emission parameters of a small diesel engine
using CNG and biodiesel. In: 13th Small Engine Technology Conference 2007, 30 Oct - 01 Nov 2007, Toki Messe, Niigata, Japan.
biodiesel production
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Yusaf, T. (2009) Potential of bioethanol production from agricultural wastes in Iran. Renewable and Sustainable Energy Reviews, 13 (6-7). pp.
1418-1427. ISSN 1364-0321
biodiesel-diesel blends
Najafi, Gholamhassan and Ghobadian, Barat and Yusaf, Talal and Rahimi, Hadi (2007) Combustion analysis of a CI engine performance using waste cooking biodiesel fuel with an artificial neural network
aid. American Journal of Applied Sciences, 4 (10). pp. 756-764. ISSN 1546-9239
biodiesel–diesel blends
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Buttsworth, D. R. and Yusaf, T. F. and Faizollahnejad, M. (2009) Performance and exhaust emissions of a gasoline engine with ethanol blended gasoline
fuels using artificial neural network. Applied Energy, 86 (5). pp. 630-639. ISSN 0306-2619
Ghobadian, B. and Rahimi, H. and Nikbakht, A. M. and Najafi, G. and Yusaf, T. F. (2009) Diesel engine performance and exhaust emission analysis using waste cooking biodiesel fuel with an artificial
neural network. Renewable Energy, 34 (4). pp. 976-982. ISSN 0960-1481
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Yusaf, T. (2009) Potential of bioethanol production from agricultural wastes in Iran. Renewable and Sustainable Energy Reviews, 13 (6-7). pp.
1418-1427. ISSN 1364-0321
Rahimi, Hadi and Ghobadian, Barat and Yusaf, Talal and Najafi, Gholamhasan and Khatamifar, Mahdi (2009) Diesterol: an environment-friendly IC engine fuel. Renewable Energy, 34 (1). pp. 335-342. ISSN
bioethanol feedstock
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Yusaf, T. (2009) Potential of bioethanol production from agricultural wastes in Iran. Renewable and Sustainable Energy Reviews, 13 (6-7). pp.
1418-1427. ISSN 1364-0321
Rahimi, Hadi and Ghobadian, Barat and Yusaf, Talal and Najafi, Gholamhasan and Khatamifar, Mahdi (2009) Diesterol: an environment-friendly IC engine fuel. Renewable Energy, 34 (1). pp. 335-342. ISSN
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2014) MILD combustion: the future for lean and clean combustion technology. International Review of Mechanical Engineering , 8 (1). pp. 251-257.
ISSN 1970-8734
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Numerical study of oxygen dilution and temperature distribution of biogas combustion in Bluff-body MILD burner. In: 7th Australian Combustion
Symposium (ACS 2013), 6-8 Nov 2013, Perth, Australia .
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The air fuel ratio study for the mixture of biogas and hydrogen on mild combustion. In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5
Jul 2013, Sydney, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Analysis of recirculation zone and ignition position of non-premixed bluff-body for biogas mild combustion. International Journal of
Automotive and Mechanical Engineering, 8. pp. 1176-1186. ISSN 2229-8649
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Detail guide for CFD on the simulation of biogas combustion in bluff-body mild burner. In: 2nd International Conference of Mechanical
Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Yusaf, Talal and Noor, M. M. and Wandel, Andrew P. (2013) Mild combustion: the future for lean and clean combustion. In: 2nd International Conference of Mechanical Engineering Research (ICMER 2013):
Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The analysis of recirculation zone and ignition position of non-premixed bluff-body for biogas mild combustion. In: 2nd International
Conference of Mechanical Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The study of air fuel ratio for open furnace MILD combustion of biogas on bluff-body burner. In: 2012 Qld Southern Regional Engineering
Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Investigation of Biogas Moderate or Intense Low Oxygen Dilution (MILD) combustion on open furnace bluff-body burner. In: USQ Combustion
Meeting, 29 Aug 2012, Toowoomba, Australia. (Unpublished)
Ng, S. K. and Carter, S. J. B. and Bullen, Frank (2006) A biomimicry approach to automating visual road surveys. In: 22nd ARRB Conference: Research Into Practice, 29 Oct - 02 Nov 2006, Canberra,
Sharifi, Behrooz and Leis, John (2010) Towards three-dimensional fusion of infrared guidance measurements for biopsy procedures: some preliminary results and design considerations. In: ICSPCS 2010:
4th International Conference on Signal Processing and Communication Systems, 13-15 Dec 2010, Gold Coast, Australia.
bit error probability
Alajel, Khalid Mohamed and Xiang, Wei and Sileh, Ibrahim Khalil (2012) Best relays selection method for error-resilient 3-D video transmission. In: 12th International Symposium on Communications and
Information Technologies (ISCIT 2012), 2-5 Oct 2012, Gold Coast, Australia.
bit error rate
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Performance analysis for coded cooperative multiple-relay in distributed turbo channels. In: IEEE 22nd International Symposium on
Personal Indoor and Mobile Radio Communications (PIMRC 2011), 11-14 Sep 2011, Toronto, Canada.
bit error ratios
Long, Hang and Kim, Kyeong Jin and Xiang, Wei and Shen, Shanshan and Zheng, Kan and Wang, Wenbo (2012) Improved wideband precoding with arbitrary subcarrier grouping in MIMO-OFDM systems. ETRI
Journal, 34 (1). pp. 9-16. ISSN 1225-6463
black body
McIntyre, T. J. and Khan, R. and Eichmann, T. N. and Upcroft, B. and Buttsworth, D. (2012) Visible and near infrared spectroscopy of Hayabusa re-entry using semi-autonomous tracking. In: 50th AIAA
Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition: Advancing the Science of Flight Technology (AIAA 2012) , 9-12 Jan 2012, Nashville, TN. United States.
blocking probability
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Throughput and proportional fairness in cognitive radio networks. In: ATC 2009: 2nd International Conference on Advanced
Technologies for Communications, 12-14 Oct 2009, Hai Phong, Vietnam.
Kist, Alexander A. (2007) Erlang B as a performance model for IP flows. In: ICON 2007: 15th IEEE International Conference on Networks, 19-21 Nov 2007, Adelaide, Australia.
Kist, Alexander A. and Lloyd-Smith, Bill and Harris, Richard J. (2005) A simple IP flow blocking model. In: 19th International Teletraffic Congress (ITC19), 29 August - 2 Sept. 2005, Beijing, China.
Kist, Alexander A. (2005) A flow blocking model for IP overflow traffic. In: 11th Asia-Pacific Conference on Communications, 3-5 Oct 2005, Perth, Australia.
Bluff-body burner
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Investigation of Biogas Moderate or Intense Low Oxygen Dilution (MILD) combustion on open furnace bluff-body burner. In: USQ Combustion
Meeting, 29 Aug 2012, Toowoomba, Australia. (Unpublished)
bluff-body MILD burner
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. (2013) Design and development of mild combustion burner. Journal of Mechanical Engineering and Sciences, 5. pp. 662-676. ISSN 2289-4659
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Numerical study of oxygen dilution and temperature distribution of biogas combustion in Bluff-body MILD burner. In: 7th Australian Combustion
Symposium (ACS 2013), 6-8 Nov 2013, Perth, Australia .
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Analysis of recirculation zone and ignition position of non-premixed bluff-body for biogas mild combustion. International Journal of
Automotive and Mechanical Engineering, 8. pp. 1176-1186. ISSN 2229-8649
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Detail guide for CFD on the simulation of biogas combustion in bluff-body mild burner. In: 2nd International Conference of Mechanical
Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The analysis of recirculation zone and ignition position of non-premixed bluff-body for biogas mild combustion. In: 2nd International
Conference of Mechanical Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The development of MILD combustion open burner experimental setup. In: 2nd International Conference of Mechanical Engineering Research (ICMER
2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
bodyworn antennas
Ziri-Castro, Karla and Scanlon, William and Evans, Noel (2004) Indoor radio channel characterization and modeling for a 5.2-GHz bodyworn receiver. IEEE Antennas and Wireless Propagation Letters, 3
(1). pp. 219-222. ISSN 1536-1225
bodyworn terminals
Ziri-Castro, Karla and Scanlon, William and Evans, Noel (2003) Measured pedestrian movement and bodyworn terminal effects for the indoor channel at 5.2 GHz. European Transactions on
Telecommunications, 14 (6). pp. 529-538. ISSN 1124-318X
Ziri-Castro, Karla and Scanlon, William and Feustle, R. and Evans, Noel (2003) Channel modelling and propagation measurements for a bodyworn 5.2 GHz terminal moving in the indoor environment. In:
12th IEE International Conference on Antennas and Propagation, 31 Mar - 3 April 2003, Exeter, United Kingdom.
border gateway protocol
Kist, Alexander A. and Harris, Richard J. (2004) Cost efficient overflow routing for outbound ISP traffic. In: 9th IEEE Symposium on Computers and Communications (ISCC 2004), 28 Jun - 1 July 2004,
Alexandria, Egypt.
Bose-Einstein condensation
Malomed, Boris A. and Stepanyants, Yury A. (2010) The inverse problem for the Gross-Pitaevskii equation. Chaos, 20 (1). ISSN 1054-1500
boundary condition
Crawford, Jagoda and Stepanyants, Yury (2005) Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps. ANZIAM Journal (Australian & New Zealand
Industrial and Applied Mathematics Journal), 46. C1104-C1125. ISSN 1446-8735
boundary conditions
Roberts, A. J. (2001) Holistic discretisation ensures fidelity to Burger's equation. Applied Numerical Mathematics, 37 (3). pp. 371-396. ISSN 0168-9274
boundary element
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
boundary element method
Mai-Duy, Nam and Tran-Cong, Thanh (2009) On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems. In: 31st International Conference on Boundary
Elements and Other Mesh Reduction Methods (BEM/MRM 31), 2-4 Sep 2009, New Forest, UK.
Mai-Duy, Nam and Tran-Cong, Thanh (2004) An effective RBFN-boundary integral approach for the analysis of natural convection flow. International Journal for Numerical Methods in Fluids, 46 (5). pp.
545-568. ISSN 0271-2091
Mai-Duy, Nam and Tran-Cong, Thanh (2003) RBF interpolation of boundary values in the BEM for heat transfer problems. International Journal of Numerical Methods for Heat and Fluid Flow, 13 (5/6). pp.
611-632. ISSN 0961-5539
boundary integral equation
Mai-Duy, Nam and Tran-Cong, Thanh (2003) RBF interpolation of boundary values in the BEM for heat transfer problems. International Journal of Numerical Methods for Heat and Fluid Flow, 13 (5/6). pp.
611-632. ISSN 0961-5539
boundary integral equation methods
Mai-Duy, N. and Tanner, R. I. (2005) An effective high order interpolation scheme in BIEMs for biharmonic boundary value problems. Engineering Analysis with Boundary Elements, 29 (3). pp. 210-223.
ISSN 0955-7997
boundary integral equations
Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I. (2006) A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem. Engineering Analysis with Boundary Elements,
30 (10). pp. 809-817. ISSN 0955-7997
boundary layer
Al-Falahi, Amir and Yusoff, M. Z. and Shuaib, N. H. and Yusaf, T. (2009) Flow instability in shock tube due to shock wave-boundary layer-contact surface interactions, a numerical study. European
Journal of Scientific Research, 30 (1). pp. 164-176. ISSN 1450-216X
boundary-integral-equation methods
Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I. (2006) A new high-order time-kernel BIEM for the Burgers equation. CMES: Computer Modeling in Engineering and Sciences, 16 (3). pp. 177-186. ISSN
Mai-Duy, Nam and Tran-Cong, Thanh and Tanner, R. I. (2006) A high-order time-kernel BIEM for the Burgers equation. In: International Conference on Boundary Element Techniques VII, 4-6 September 2006,
Paris, France.
box model
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
brain model
Li, Yan and Wen, Peng (2005) Bayesian model for brain computation. In: 2005 International Conference on Complex Medical Engineering (CME 2005), 15-18 May 2005, Takamatsu, Japan.
branch and bound algorithm
Shi, Chenggen and Lu, Jie and Zhang, Guangquan and Zhou, Hong (2006) An extended branch and bound algorithm for linear bilevel programming. Applied Mathematics and Computation, 180 (2). pp. 529-537.
ISSN 0096-3003
breakdown pressure
Golshani, Aliakbar and Tran-Cong, Thanh (2008) Simulation of hydraulic fracturing in brittle rocks. In: ISRM International Symposium 2008: 5th Asian Rock Mechanics Symposium, 24-26 Nov 2008, Tehran,
bridging law
Dai, Shao-Cong and Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Experimental study on z-pin bridging law by pullout test. Composites Science and Technology, 64 (16). pp. 2451-2457. ISSN
broadband wireless access
Zhou, Hong and Zhang, Zhongwei (2011) Examining QoS guarantees for real-time CBR services in broadband wireless access networks. In: Software engineering, artificial intelligence, networking and
parallel/distributed computing 2011. Studies in Computational Intelligence (368). Springer, Berlin, Germany, pp. 25-40. ISBN 978-3-642-22287-0
Zhou, Hong and Zhang, Zhongwei (2010) Differentiated statistical QoS guarantees for real-time CBR services in broadband wireless access networks. In: 6th International Conference on Wireless
Communications, Networking and Mobile Computing (WiCOM 2010), 23-25 Sep 2010, Chengdu, China.
brown dwarfs
Jenkins, J. S. and Jones, H. R. A. and Tinney, C. G. and Butler, R. P. and McCarthy, C. and Marcy, G. W. and Pinfield, D. J. and Carter, B. D. and Penny, A. J. (2006) An activity catalogue of
southern stars. Monthly Notices of the Royal Astronomical Society, 372 (1). pp. 163-173. ISSN 0035-8711
Brownian bugs
Young, W. R. and Roberts, A. J. and Stuhne, Gordan (2001) Reproductive pair correlations and the clustering of organisms. Nature, 412 (6844). pp. 328-331. ISSN 0028-0836
Brownian configuration field method
Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.
Brownian configuration fields
Tran, C.-D. and Mai-Duy, N. and Le-Cao, K. and Tran-Cong, T. (2012) A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 85 (6). pp. 499-519. ISSN 1526-1492
Tran, C.-D. and An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2011) An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 82 (2). pp. 137-162. ISSN 1526-1492
Tran, Canh-Dung and Phillips, David G. and Tran-Cong, Thanh (2009) Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique. Korea-Australia
Rheology Journal, 21 (1). pp. 1-12. ISSN 1226-119X
Tran, Canh-Dung and Tran-Cong, Thanh (2004) Element-free simulation of dilute polymeric flows using Brownian configuration fields. Korea-Australia Rheology Journal, 16 (1). pp. 1-15. ISSN 1226-119X
Brownian dynamics
Tran, Canh-Dung and Phillips, David G. and Tran-Cong, Thanh (2009) Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique. Korea-Australia
Rheology Journal, 21 (1). pp. 1-12. ISSN 1226-119X
Tran, Canh-Dung and Tran-Cong, Thanh (2004) Element-free simulation of dilute polymeric flows using Brownian configuration fields. Korea-Australia Rheology Journal, 16 (1). pp. 1-15. ISSN 1226-119X
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
Brownian simulation
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
brushless DC motors
Gambetta, D. and Ahfock, A. (2009) A new sensorless commutation technique for brushless DC motors. IET Electric Power Applications, 3 (1). pp. 40-49. ISSN 1751-8660
brushless motors
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
brushless permanent magnet motor
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
bubble flow
Mai-Cao, L. and Tran-Cong, T. (2006) A meshless level-set scheme for interfacial flows. In: 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi
Minh City, Vietnam.
buckling response
Nguyen-Van, H. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell
element with in-plane rotations. Computers and Structures, 89 (7-8). pp. 612-625. ISSN 0045-7949
building fire warning
Su, Gang and Zhou, Hong and Gao, Rui (2011) Intelligent building fire warning system with WSN. In: 4th IEEE International Conference on Computer Science and Information Technology, 10-12 Jun 2011,
Chengdu, China.
building foundations
Shiau, Jim S. and Watson, Joshua Francis and Arnold, Matthew David (2008) Numerical study of a shallow foundation located near 45 degree slopes. In: ASEM 2008: 4th International Conference on
Advances in Structural Engineering and Mechanics , 26-28 May 2008, Jeju, Korea.
bulk properties
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2010) Towards an analysis of shear suspension flows using radial basis functions. CMES: Computer Modeling in Engineering and Sciences, 67
(3). pp. 265-294. ISSN 1526-1492
bundle structures
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
Strunin, D. V. (2006) Similarity without diffusion: shear turbulent layer damped by buoyancy. Journal of Engineering Mathematics, 54 (3). pp. 211-224. ISSN 0022-0833
Burgers equation
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 11 - unsteady incompressible viscous flows. CMES: Computer
Modeling in Engineering and Sciences , 83 (3). pp. 311-351. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I. (2006) A new high-order time-kernel BIEM for the Burgers equation. CMES: Computer Modeling in Engineering and Sciences, 16 (3). pp. 177-186. ISSN
Mai-Duy, Nam and Tran-Cong, Thanh and Tanner, R. I. (2006) A high-order time-kernel BIEM for the Burgers equation. In: International Conference on Boundary Element Techniques VII, 4-6 September 2006,
Paris, France.
Burgers' equation
Roberts, A. J. (2001) Holistic discretisation ensures fidelity to Burger's equation. Applied Numerical Mathematics, 37 (3). pp. 371-396. ISSN 0168-9274
bush fire protection
Sharifian, Ahmad and Buttsworth, David R. (2007) Computational simulation of the wind-force on metal meshes. In: 16th Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast,
Hashempour, Javad and Sharifian, Ahmad (2013) Optimizing the coupling of a firebrand generator to a horizontal wind tunnel. In: 2nd International Conference on Energy and Environmental Protection
(ICEEP 2013), 19-21 Apr 2013, Guilin, China.
bushfire mitigation
Hashempour, Javad and Sharifian, Ahmad (2012) Potentials of metal mesh to contain bushfires. In: 2012 Qld Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
bushfire protection
Sharifian, Ahmad and Buttsworth, David R. (2007) Minimum safe standoff distance for protection from bushfire radiation by commercial metal meshes. In: 8th Australasian Heat and Mass Transfer
Conference, 26-29 Jul 2005, Curtin University of Technology, Perth, Western Australia.
Sharifian, Ahmad and Buttsworth, David R. (2009) Direct radiation from wildfires through square woven screens. In: ASME 2008: Summer Heat Transfer Conference, 10-14 Aug 2008, Jacksonville, FL. USA.
C2-continuous solution
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems. CMES:
Computer Modeling in Engineering and Sciences, 72 (4). pp. 299-334. ISSN 1526-1492
cable equation
Langlands, T. A. M. and Henry, B. I. and Wearne, S. L. (2011) Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions. SIAM Journal on Applied
Mathematics, 71 (4). pp. 1168-1203. ISSN 0036-1399
Shiau, Jim and Smith, Catherine (2013) Developing numerical models for the design of cantilever sheet pile wall. In: 1st Australasia and South-East Asia Structural Engineering and Construction
Conference (ASEA-SEC-1), 28 Nov-2 Dec 2012, Perth, Australia.
Sharifian, Ahmad and Hashempour, Javad (2012) Dilution of toxic gases and smoke emissions from residential chimneys using a low-cost cap. In: 18th Australasian Fluid Mechanics Conference (AFMC 2012),
3-7 Dec 2012, Launceston, Australia.
capillary effect
Stepanyants, Yury (2005) Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons. Proceedings of the Russian Academy of Engineering Sciences Series: Applied
Mathematics and Mechanics, 14. pp. 33-40.
capillary tube
Tangalajuk Siang, Jeri and Sharifian, Ahmad (2013) Reducing the mass of the refrigerant in the capillary tube of a propane air-conditioner. In: 14th Asian Congress of Fluid Mechanics (14 ACFM), 15-19
Oct 2013, Hanoi-Halong, Vietnam.
Buttsworth, David and Jacobs, P. and Morgan, R. G. and Jenniskens, Peter (2012) Near ultraviolet emission spectroscopy of the Hayabusa re-entry. In: 50th AIAA Aerospace Sciences Meeting Including the
New Horizons Forum and Aerospace Exposition (AIAA 2012): Advancing the Science of Flight Technology, 9-12 Jan 2012, Nashville, TN. United States.
carbon footprint
Kist, Alexander A. (2011) Modelling of staged routing for reduced carbon footprints of large server clusters. International Journal of Communication Networks and Distributed Systems, 6 (1). pp.
28-44. ISSN 1754-3916
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
carbon nanotubes
Tran, Canh-Dung (2013) Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications. In: Nanotube superfiber materials: changing engineering design. Elsevier, Oxford,
United Kingdom, pp. 211-242. ISBN 978-1-4557-7863-8
Randeniya, Lakshman K. and Bendavid, Avi and Martin, Philip J. and Tran, Canh-Dung (2010) Composite yarns of multi-walled carbon nanotubes with metallic electrical conductivity. Small, 6 (16). pp.
1806-1811. ISSN 1613-6810
Tran, Canh-Dung and Smith, Shaun M. and Higgerson, G. and Huynh, Chi and Kviz, Ladge and Maudev, George and Lucas, Stuart and Bui, Anh (2010) Spinning CNT based composite yarns using a dry spinning
process. In: 2010 International Conference on Nanoscience and Nanotechnology (ICONN 2010), 22- 26 Feb 2010, Sydney, Australia.
carrier aggregation
Liu, Fei and Xiang, Wei and Zhang, Yueying and Zheng, Kan and Zhao, Hui (2012) A novel QoE-based carrier scheduling scheme in LTE-advanced networks with multi-service. In: 2012 IEEE Vehicular
Technology Conference (VCT 2012-Fall), 3-6 Sept 2012, Quebec City, QC, Canada.
carrier frequency offset
Salim, Omar Hazim and Nasir, Ali and Mehrpouyan, Hani and Xiang, Wei (2013) Phase noise and carrier frequency offset in OFDM systems: joint estimation and hybrid Cramer-Rao lower bound. In: 14th IEEE
International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2013), 16-19 Jun 2013, Darmstadt, Germany.
carrier grade networks
Kist, Alexander A. and Harris, Richard J. (2003) Dynamic resource allocation in 3GPP SIP overlay networks. In: 2003 Joint Conference of the 4th International Conference on Information, Communications
and Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
Cartesian grid
An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T. (2013) ADI method based on C^2-continuous two-node integrated-RBF elements for viscous flows. Applied Mathematical Modelling, 37
(7). pp. 5184-5203. ISSN 0307-904X
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients. CMES: Computer
Modeling in Engineering and Sciences, 89 (4). pp. 303-359. ISSN 1526-1492
Ho-Minh, D. and Mai-Duy, N. and Tran-Cong, T. (2012) Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach. Australian Journal of Mechanical Engineering , 9 (2). pp. 101-112.
ISSN 1448-4846
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2012) A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables. CMES:
Computer Modeling in Engineering and Sciences, 84 (6). pp. 528-557. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis. CMES:
Computer Modeling in Engineering and Sciences, 83 (5). pp. 459-498. ISSN 1526-1492
Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless
& Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.
Mai-Duy, N. and Tran-Cong, T. (2011) A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems. International Journal for Numerical Methods in Fluids, 67 (12). pp.
1973-1992. ISSN 0271-2091
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2011) Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian
grids. Computers and Fluids , 44 (1). pp. 32-42. ISSN 0045-7930
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems. CMES:
Computer Modeling in Engineering and Sciences, 72 (4). pp. 299-334. ISSN 1526-1492
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2011) Discretisation of the velocity-pressure formulation with integrated radial-basis-function networks. Structural Longevity, 6 (2).
pp. 77-91. ISSN 1944-611X
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows. CMES: Computer Modeling in Engineering and
Sciences, 80 (2). pp. 141-177. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems. In: ACAM 6: 6th Australasian Congress
on Applied Mechanics , 12-15 Dec 2010, Perth, Western Australia.
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems. Numerical Methods for Partial
Differential Equations, 26 (6). pp. 1443-1462. ISSN 0749-159X
Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2010) A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.
International Journal for Numerical Methods in Engineering, 82 (4). pp. 435-463. ISSN 0029-5981
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) Galerkin/collocation methods based on 1D-integrated-RBFNs for viscoelastic flows. CMES: Computer Modeling in Engineering and Sciences, 70 (3).
pp. 217-251. ISSN 1526-1492
An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of Newtonian-fluid flows with C2-continuous two-node integrated-RBF elements. Structural Longevity, 4 (1). pp. 39-45. ISSN 1944-611X
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A cartesian-grid integrated-RBF method for viscoelastic flows. In: 9th World Congress on Computational Mechanics and 4th Asian-Pacific
Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2008) An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems. In: 8th World Congress on
Computational Mechanics (WCCM8) and ECCOMAS 2008, 30 June - 4 July 2008, Venice, Italy.
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains. Numerical Methods for Partial Differential
Equations, 23 (5). pp. 1192-1210. ISSN 0749-159X
Mai-Duy, N. and Tanner, R. I. (2007) A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. International Journal of Numerical Methods for Heat and Fluid Flow, 17
(2). pp. 165-186. ISSN 0961-5539
Cartesian grid method
Mai-Duy, Nam and Le-Cao, Khoa and Tran-Cong, Thanh (2008) A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli.
International Journal for Numerical Methods in Fluids, 57 (12). pp. 1709-1730. ISSN 0271-2091
Le-Cao, Khoa and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Radial-basis-function calculations of buoyancy-driven flow in concentric and eccentric annuli. In: 16th Australasian Fluid Mechanics
Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
Cartesian grids
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 1 - natural convection flows in concentric and eccentric
annuli. CMES: Computer Modeling in Engineering and Sciences, 83 (3). pp. 275-310. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method. Computers and
Structures, 89 (1-2). pp. 1-13. ISSN 0045-7949
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Moving least square - one dimensional integrated radial basis function networks for time dependent problems. In: 33rd
International Conference on Boundary Elements and other Mesh Reduction Methods, 28-30 Jun 2011, New Forest, UK.
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A Cartesian-grid integrated-RBF Galerkin technique. In: Recent studies in meshless and other novel computational methods. Tech Science Press,
Duluth, GA. USA, pp. 87-102. ISBN 0-9824205-4-4
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A simple and effective preconditioner for integrated-RBF-based Cartesian-grid schemes. In: 2010 International Conference on Computational and Experimental
Engineering & Sciences 2010, 28 Mar - 1 Apr 2010, Las Vegas, USA.
Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2009) An effective integrated-RBFN Cartesian-grid discretization for the stream function-vorticity temperature formulation in nonrectangular domains.
Numerical Heat Transfer, Part B: Fundamentals, 55 (6). pp. 480-502. ISSN 1040-7790
Cattaneo Vernotte law
Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2002) Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models. Computational Mechanics, 29
(1). pp. 16-26. ISSN 0178-7675
causal structure
Lozanovski, C. and Wylleman, L. (2011) Complex windmill transformation producing new purely magnetic fluids. Classical and Quantum Gravity, 28 (7). 075015-075031. ISSN 0264-9381
cellular network
Wang, Yafeng and Wei, Guoxing and Xiang, Wei (2011) Approximate inter-cell interference modeling for cellular network. Journal of China Universities of Posts and Telecommunications, 18 (3). pp.
75-79. ISSN 1005-8885
cellular networks
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2010) Performance of user cooperation and clustering scheme in cellular networks. In: 2010 IEEE International Conference on
Communications: Communications: Accelerating Growth and Development (ICC 2010), 23-27 May 2010, Capetown, South Africa.
centre manifold
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2007) Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model. Discrete and Continuous Dynamical Systems Series
A, 2007 (Specia). pp. 419-428. ISSN 1078-0947
Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768
centre manifold approach
Roberts, A. J. (2003) A holistic finite difference approach models linear dynamics consistently. Mathematics of Computation, 72 (241). pp. 247-262. ISSN 0025-5718
centre manifold technique
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2006) The dynamics of the vertical structure of turbulence in flood flows. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 48 (CTAC-2). C573-C590. ISSN 1446-8735
centre manifold theory
Roberts, A. J. (2003) Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics. In: Nonlinear dynamics from lasers to butterflies: selected lectures from the 15th
Canberra International Physics Summer School. Lecture Notes in Complex Systems (1). World Scientific, pp. 257-313. ISBN 9789812791252
centre manifolds
Strunin, D. V. and Mohammed, F. J. (2012) Numerical analysis of an averaged model of turbulent transport near a roughness layer. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 53. C142-C154. ISSN 1446-8735
Roberts, A. J. and Strunin, Dmitry V. (2004) Two-zone model of shear dispersion in a channel using centre manifolds. Quarterly Journal of Mechanics and Applied Mathematics, 57 (3). pp. 363-378. ISSN
centrifuge technology
Shiau, Jim S. and Pather, Selvan and Ayers, Ron (2006) Developing physical models for geotechnical teaching and research. In: 6th International Conference on Physical Modelling in Geotechnics, 4-6
Aug 2006, Hong Kong.
Al-Falahi, Amir and Yusoff, M. Z. and Shuaib, N. H. and Yusaf, T. (2009) Flow instability in shock tube due to shock wave-boundary layer-contact surface interactions, a numerical study. European
Journal of Scientific Research, 30 (1). pp. 164-176. ISSN 1450-216X
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2008) Numerical simulation of inviscid transient flows in shock tube and its validations. In: ICFM 2008: 5th International Conference on Fluid
Mechanics, 12-14 Sep 2008, Heidelberg, Germany.
Ng, K. C. and Yusoff, M. Z. and Yusaf, T. F. (2007) Numerical simulation of 3D transonic flow in a compressor rotor. International Journal of Modelling and Simulation, 27 (1). pp. 74-79. ISSN
Mossad, Ruth (2006) Numerical simulation to optimize the design of double glazed doors for closed refrigerated vertical display cabinets. In: 13th International Heat Transfer Conference IHTC-13,
13-18 Aug 2006, Sydney, Australia.
Zakaria, S. and Yusaf, T. and Yusoff, M. Z. (2006) Flow and transient heat transfer in a high speed free piston tunnel: CFD simulations on turbulent and laminar flow conditions. In: 2nd International
Conference on Thermal Engineering Theory and Applications (ICTEA '06), 3-6 Jan 2006, Al Ain, United Arab Emirates.
Buttsworth, David R. and Jacobs, Peter A. and Jones, Terry V. (2002) Simulation of Oxford University gun tunnel performance using a quasi-one-dimensional model. Shock Waves, 11 (5). pp. 377-383. ISSN
CFD Engine Mixer
Yusaf, Talal and Yusoff, Mohammed Zamri (2000) Development of a 3D CFD model to investigate the effect of the mixing quality on the CNG-diesel engine performance. In: The International Conference and
Exhibition and Natural Gas Vehicles, 17-19 Oct 2000, Yokohama, Japan.
Ng, K. C. and Yusoff, M. Z. and Yusaf, T. F. (2007) Numerical simulation of 3D transonic flow in a compressor rotor. International Journal of Modelling and Simulation, 27 (1). pp. 74-79. ISSN
Strunin, Dmitry V. and Roberts, Anthony J. (2009) Low-dimensional boundary-layer model of turbulent dispersion in a channel. In: WCE 2009: World Congress of Engineering , 1-3 Jul 2009, London, United
channel allocation
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Goodput and channel allocation in opportunistic spectrum access networks. In: PIMRC 2009: 20th IEEE International Symposium on
Personal, Indoor and Mobile Radio Communications, 13-16 Sep 2009, Tokyo, Japan.
channel capacity
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
Xiang, Wei and Pietrobon, Steven S. (2003) On the capacity and normalisation of ISI channels. In: 2003 IEEE International Conference on Communications (ICC2003), 11-15 May 2003, Anchorage, Alaska,
channel characterization
Ziri-Castro, Karla and Scanlon, William and Evans, Noel (2004) Indoor radio channel characterization and modeling for a 5.2-GHz bodyworn receiver. IEEE Antennas and Wireless Propagation Letters, 3
(1). pp. 219-222. ISSN 1536-1225
channel coding
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Performance analysis for coded cooperative multiple-relay in distributed turbo channels. In: IEEE 22nd International Symposium on
Personal Indoor and Mobile Radio Communications (PIMRC 2011), 11-14 Sep 2011, Toronto, Canada.
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Iterative decoding of JPEG coded images with channel coding. In: 10th IEEE International Conference on Telecommunications, Feb
2003, Papeete, Tahiti.
channel distortion
Zhou, Yuan and Hou, Chunping and Xiang, Wei and Wu, Feng (2011) Channel distortion modeling for multi-view video transmission over packet-switched networks. IEEE Transactions on Circuits and Systems
for Video Technology, 21 (11). pp. 1679-1692. ISSN 1051-8215
channel reservation
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Throughput and proportional fairness in cognitive radio networks. In: ATC 2009: 2nd International Conference on Advanced
Technologies for Communications, 12-14 Oct 2009, Hai Phong, Vietnam.
Roberts, A. J. and Strunin, Dmitry V. (2004) Two-zone model of shear dispersion in a channel using centre manifolds. Quarterly Journal of Mechanics and Applied Mathematics, 57 (3). pp. 363-378. ISSN
Tangalajuk Siang, Jeri and Sharifian, Ahmad (2013) Reducing the mass of the refrigerant in the capillary tube of a propane air-conditioner. In: 14th Asian Congress of Fluid Mechanics (14 ACFM), 15-19
Oct 2013, Hanoi-Halong, Vietnam.
Stepanyants, Y. A. and Strunin, D. V. (2011) Dynamics of two charged particles in viscous fluid at small Reynolds numbers. In: 2011 International Conference on Mathematics and Computational Methods
Applied to Nuclear Science and Enginnering (MC 2011), 8-12 May 2011, Rio de Janeiro, Brazil.
Chebyshev polynomials
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2009) A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical
Modelling, 33 (1). pp. 284-299. ISSN 0307-904X
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations. In: Leading-edge applied
mathematical modeling research. Nova Science Publishers, Inc., New York, United States, pp. 215-250. ISBN 1-60021-977-2
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A point-collocation method based on integrated Chebyshev polynomials for elliptic differential equations in irregular domains. In: 8th World Congress on
Computational Mechanics (WCCM8) and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.
chemically peculiar
Bond, J. C. and Tinney, C. G. and Butler, R. P. and Jones, H. A. and Marcy, G. W. and Penny, A. J. and Carter, B. D. (2006) The abundance distribution of stars with planets. Monthly Notices of the
Royal Astronomical Society, 370 (1). pp. 163-173. ISSN 0035-8711
Wandel, Andrew P. and Lindstedt, R. Peter (2013) Hybrid multiple mapping conditioning modeling of local extinction. Proceedings of the Combustion Institute, 34 (1). pp. 1365-1372. ISSN 1540-7489
Langlands, T. A. M. and Henry, B. I. (2010) Fractional chemotaxis diffusion equations. Physical Review E: Statistical Nonlinear and Soft Matter Physics, 81 (5). pp. 1-12. ISSN 1539-3755
Sharifian, Ahmad and Hashempour, Javad (2012) Dilution of toxic gases and smoke emissions from residential chimneys using a low-cost cap. In: 18th Australasian Fluid Mechanics Conference (AFMC 2012),
3-7 Dec 2012, Launceston, Australia.
Al-Atresh, Safia and Sharifian, Ahmad and Kueger, Bradley (2012) Using a split chimney for dilution of exhaust pollution: a CFD approach. In: 2012 International Conference on Fluid Dynamics and
Thermodynamics Technologies (FDTT 2012), 17-18 March 2012, Singapore.
Butler, R. P. and Wright, J. T. and Marcy, G. W. and Fischer, D. A. and Vogt, S. S. and Tinney, C. G. and Jones, H. R. A. and Carter, B. D. and Johnson, J. A. and McCarthy, C. and Penny, A. J. (2006)
Catalog of nearby exoplanets. The Astrophysical Journal, 646 (1). pp. 505-522. ISSN 0004-637X
CI engine
Najafi, Gholamhassan and Yusaf, Talal (2009) Experimental investigation of using methanol-diesel blended fuels in diesel engine. In: 4th International Conference on Thermal Engineering Theory and
Applications, 12-14 Jan 2009, Abu Dhabi, UAE.
circular cylinder
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 11 - unsteady incompressible viscous flows. CMES: Computer
Modeling in Engineering and Sciences , 83 (3). pp. 311-351. ISSN 1526-1492
classification accuracy
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
classification method
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) A robust ensemble classification method analysis. In: 2009 International Conference on Bioinformatics and Computational Biology ,
13-16 Jul 2009, Las Vegas, NV. United States.
clean up
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
Lozanovski, Con and Haeusler, Carole and Tobin, Patrick (2011) Incorporating student response systems in mathematics classes. In: 8th Southern Hemisphere Conference on Teaching and Learning of
Undergraduate Mathematics and Statistics: The Long Abiding Path of Knowledge, 27 Nov-2 Dec 2011, Rotorua, New Zealand.
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Donald, Alexis and Ribbe, Joachim and Stone, Roger and Meinke, Holger and Harris, Graham and Power, Brendan and Wheeler, Matthew (2003) The influence of the Madden Julian Oscillation on Queensland's
rainfall. In: 15th Australian New Zealand Climate Forum, 19-21 Mar 2003, Palmerston, New Zealand.
Ribbe, Joachim (2001) Intermediate water mass production controlled by southern hemisphere winds. Geophysical Research Letters, 28 (3). pp. 535-538. ISSN 0094-8276
climate change
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2008) An interpretation of Australian rainfall projections. Geophysical Research Letters, 35 (2). L2072. ISSN 0094-8276
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
Cai, Wenju and Cowan, Tim and Dix, Martin and Rotstayn, Leon and Ribbe, Joachim and Shi, Ge and Wijffels, Susan (2007) Anthropogenic aerosol forcing and the structure of temperature trends in the
southern Indian Ocean. Geophysical Research Letters, 34 (14). L14611. ISSN 0094-8276
You, John and Herold, Nicholas and Muller, Dietmar and Sdrolias, Maria and Ribbe, Joachim (2007) Impact of vegetation on the Miocene Climate optimum. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Cottrill, Andrew and Ribbe, Joachim (2007) Queensland rainfall variability in IPCC AR4 model runs. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8
February 2007, Adelaide, Australia.
You, John and Muller, Dietmar and Sdrolias, Maria and Herold, Nicholas and Ribbe, Joachim (2007) Sensitivity of middle Miocene climate and regional monsoon to palaeo-altimetry. In: 14th National
Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
Cai, W. and Shi, G. and Cowan, T. and Bi, D. and Ribbe, J. (2005) The response of the southern annular mode, the east Australian current, and the southern mid-latitude ocean circulation to global
warming. Geophysical Research Letters, 32 (23). pp. 1-4. ISSN 0094-8276
Ribbe, Joachim (2004) The southern supplier. Nature, 427. pp. 23-24. ISSN 0028-0836
climate dynamics
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
climate modelling
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
You, John and Herold, Nicholas and Muller, Dietmar and Sdrolias, Maria and Ribbe, Joachim (2007) Impact of vegetation on the Miocene Climate optimum. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
You, John and Muller, Dietmar and Sdrolias, Maria and Herold, Nicholas and Ribbe, Joachim (2007) Sensitivity of middle Miocene climate and regional monsoon to palaeo-altimetry. In: 14th National
Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
climate models
Cai, Wenju and Cowan, Tim and Dix, Martin and Rotstayn, Leon and Ribbe, Joachim and Shi, Ge and Wijffels, Susan (2007) Anthropogenic aerosol forcing and the structure of temperature trends in the
southern Indian Ocean. Geophysical Research Letters, 34 (14). L14611. ISSN 0094-8276
Faqih, Akhmad and Ribbe, Joachim and Meinke, Holger (2007) 20th century rainfall variability and the role of large scale climate events within Indo-Pacific region from IPCC AR4 models, reanalysis and
observations. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Cottrill, Andrew and Ribbe, Joachim (2007) Queensland rainfall variability in IPCC AR4 model runs. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8
February 2007, Adelaide, Australia.
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
climate variability
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Cottrill, Andrew and Ribbe, Joachim (2008) Queensland rainfall decline. In: 15th National Conference of the Australian Meteorological and Oceanographic Society: Atmospheric and Oceanic Extremes, 29
Jan - 1 Feb 2008, Geelong, Victoria.
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
Faqih, Akhmad and Ribbe, Joachim and Meinke, Holger (2007) 20th century rainfall variability and the role of large scale climate events within Indo-Pacific region from IPCC AR4 models, reanalysis and
observations. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Cottrill, Andrew and Ribbe, Joachim (2007) Queensland rainfall variability in IPCC AR4 model runs. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8
February 2007, Adelaide, Australia.
Donald, Alexis and Meinke, Holger and Power, Brendan and Maia, Aline de H. N. and Wheeler, Matthew and Stone, Roger C. and Ribbe, Joachim and White, Neil (2006) Near-global impact of the
Madden-Julian Oscillation on rainfall. Geophysical Research Letters, 33 (9). L09704. ISSN 0094-8276
Cai, W. and Shi, G. and Cowan, T. and Bi, D. and Ribbe, J. (2005) The response of the southern annular mode, the east Australian current, and the southern mid-latitude ocean circulation to global
warming. Geophysical Research Letters, 32 (23). pp. 1-4. ISSN 0094-8276
Murphy, Bradley F. and Ribbe, Joachim (2004) Variability of southeast Queensland rainfall and climate indices. International Journal of Climatology, 24 (6). pp. 703-721. ISSN 0899-8418
Donald, Alexis and Ribbe, Joachim and Stone, Roger and Meinke, Holger and Harris, Graham and Power, Brendan and Wheeler, Matthew (2003) The influence of the Madden Julian Oscillation on Queensland's
rainfall. In: 15th Australian New Zealand Climate Forum, 19-21 Mar 2003, Palmerston, New Zealand.
Cai, W. and Shi, G. and Cowan, T. and Bi, D. and Ribbe, J. (2005) The response of the southern annular mode, the east Australian current, and the southern mid-latitude ocean circulation to global
warming. Geophysical Research Letters, 32 (23). pp. 1-4. ISSN 0094-8276
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2010) An FPGA-based fast two-symbol processing architecture for JPEG 2000 arithmetic coding. In: ICASSP 2010: 35th International Conference on
Acoustics, Speech, and Signal Processing, 14-19 Mar 2010, Dallas, TX. USA.
cloud water
Buttsworth, D. R. and Davison, C. and MacLeod, J. D. and Strapp, J. W. (2007) Evaporator design for an isokinetic total water content probe in a naturally aspirating configuration. In: 16th
Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2010) Performance of user cooperation and clustering scheme in cellular networks. In: 2010 IEEE International Conference on
Communications: Communications: Accelerating Growth and Development (ICC 2010), 23-27 May 2010, Capetown, South Africa.
Young, W. R. and Roberts, A. J. and Stuhne, Gordan (2001) Reproductive pair correlations and the clustering of organisms. Nature, 412 (6844). pp. 328-331. ISSN 0028-0836
Hairuddin, A. Aziz and Yusaf, Talal and Wandel, Andrew P. (2013) Implementation of CMC in a 0-D single-zone model of a diesel HCCI engine. In: 7th Australian Combustion Symposium (ACS 2013), 6-8 Nov
2013, Perth, Australia .
Clarke, Jason and Wandel, Andrew P. and Mastorakos, E. (2010) Analysis of data to develop models for spray combustion. In: 2010 Southern Region Engineering Conference (SREC 2010), 11-12 Nov 2010,
Toowoomba, Australia.
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
Najafi, Bahman and Pirouzpanah, Vahab and Najafi, Gholamhassan and Yusaf, Talal and Ghobadian, Barat (2007) Experimental investigation of performance and emission parameters of a small diesel engine
using CNG and biodiesel. In: 13th Small Engine Technology Conference 2007, 30 Oct - 01 Nov 2007, Toki Messe, Niigata, Japan.
CNT fiber
Tran, Canh-Dung (2013) Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications. In: Nanotube superfiber materials: changing engineering design. Elsevier, Oxford,
United Kingdom, pp. 211-242. ISBN 978-1-4557-7863-8
CNT forest
Tran, Canh-Dung (2013) Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications. In: Nanotube superfiber materials: changing engineering design. Elsevier, Oxford,
United Kingdom, pp. 211-242. ISBN 978-1-4557-7863-8
CNT polymer composite yarns
Tran, Canh-Dung and Smith, Shaun M. and Higgerson, G. and Bui, Anh and Randeniya, Lakshman K. and Tran-Cong, Thanh (2010) Spinning CNT based composite yarns using a dry spinning process. In: 2010
International Conference on Nanoscience and Nanotechnology (ICONN 2010), 22-26 Feb 2010, Sydney, Australia.
CNT polymer/metal composite
Tran, Canh-Dung (2013) Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications. In: Nanotube superfiber materials: changing engineering design. Elsevier, Oxford,
United Kingdom, pp. 211-242. ISBN 978-1-4557-7863-8
CNT web
Tran, Canh-Dung and Smith, Shaun M. and Higgerson, G. and Bui, Anh and Randeniya, Lakshman K. and Tran-Cong, Thanh (2010) Spinning CNT based composite yarns using a dry spinning process. In: 2010
International Conference on Nanoscience and Nanotechnology (ICONN 2010), 22-26 Feb 2010, Sydney, Australia.
CNT yarn
Tran, Canh-Dung (2013) Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications. In: Nanotube superfiber materials: changing engineering design. Elsevier, Oxford,
United Kingdom, pp. 211-242. ISBN 978-1-4557-7863-8
Tran, Canh-Dung and Tran-Cong, Thanh and Le-Cao, K. and Ho-Minh, D. (2012) Processing the CNTs' interaction in web using an electro-static field based process. In: 2012 International Conference on
Nanoscience and Nanotechnology (ICONN 2012), 5-9 Feb 2012, Perth, Australia .
coastal bay
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
coastal circulation
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
coastal management
Ribbe, Joachim and Wolff, Jorg-Olaf and Staneva, Joanna and Grawe, Ulf (2008) Assessing water renewal time scales for marine environments from three-dimensional modelling: a case study for Hervey
Bay, Australia. Environmental Modelling and Software, 23 (10-11). pp. 1217-1228. ISSN 1364-8152
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
coastal ocean circulation
Grawe, U. and Ribbe, J. and Wolff, J.-O. and Staneva, J. (2007) Accessing exchange and ventilation time scales from 3-D modelling. In: The Ocean in the Earth System: International Conference and 97th
Annual Meeting of the Geologische Vereinigung e.V., 1-5 Oct 2007, Bremen, Germany.
Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120
coded cooperation
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Performance analysis for coded cooperative multiple-relay in distributed turbo channels. In: IEEE 22nd International Symposium on
Personal Indoor and Mobile Radio Communications (PIMRC 2011), 11-14 Sep 2011, Toronto, Canada.
codimension-2 point
Suslov, Sergey A. (2002) Flow patterns near codimension-2 bifurcation in non-Boussinesq mixed convection. In: Progress in Nonlinear Science, International Conference dedicated to the 100th
Anniversary of A.A. Andronov, 2-6 Jul 2001, Nizhniy Novgorod, Russia.
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
cognitive radio
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Throughput and proportional fairness in cognitive radio networks. In: ATC 2009: 2nd International Conference on Advanced
Technologies for Communications, 12-14 Oct 2009, Hai Phong, Vietnam.
Grawe, U. and Ribbe, J. and Wolff, J.-O. and Staneva, J. (2007) Accessing exchange and ventilation time scales from 3-D modelling. In: The Ocean in the Earth System: International Conference and 97th
Annual Meeting of the Geologische Vereinigung e.V., 1-5 Oct 2007, Bremen, Germany.
Ribbe, Joachim and Wolff, Jorg-Olaf and Staneva, Joanna and Grawe, Ulf (2008) Assessing water renewal time scales for marine environments from three-dimensional modelling: a case study for Hervey
Bay, Australia. Environmental Modelling and Software, 23 (10-11). pp. 1217-1228. ISSN 1364-8152
Smith, Catherine and Shiau, Jim S. (2007) Bearing capacity of footings near slopes. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane, Australia.
coil displacement
Parameswaran, Vinod and Zhou, Hong and Zhang, Zhongwei (2013) Wireless underground sensor network design for irrigation control: simulation of RFID deployment. In: 7th International Conference on
Sensing Technology (ICST 2013), 3-5 Dec 2013, Wellington, New Zealand.
collocation method
Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2010) A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.
International Journal for Numerical Methods in Engineering, 82 (4). pp. 435-463. ISSN 0029-5981
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
Mai-Duy, Nam and Tran-Cong, Thanh (2009) On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems. In: 31st International Conference on Boundary
Elements and Other Mesh Reduction Methods (BEM/MRM 31), 2-4 Sep 2009, New Forest, UK.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations. Communications in Numerical Methods in Engineering, 24
(10). pp. 795-806. ISSN 1069-8299
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2008) An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems. In: 8th World Congress on
Computational Mechanics (WCCM8) and ECCOMAS 2008, 30 June - 4 July 2008, Venice, Italy.
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains. Numerical Methods for Partial Differential
Equations, 23 (5). pp. 1192-1210. ISSN 0749-159X
Mai-Duy, N. and Tanner, R. I. (2007) A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. International Journal of Numerical Methods for Heat and Fluid Flow, 17
(2). pp. 165-186. ISSN 0961-5539
collocation methods
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
collocation point
Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Numerical solution of Fokker-Planck equation using the integral radial basis function networks. In: 10th World Congress on Computational Mechanics
(WCCM 2012), 8-13 July 2012, Sao Paulo, Brazil.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems. Applied Mathematical
Modelling, 32 (12). pp. 2851-2862. ISSN 0307-904X
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Detail guide for CFD on the simulation of biogas combustion in bluff-body mild burner. In: 2nd International Conference of Mechanical
Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Wardana, I. N. G. (2012) Burning characteristics of coconut oil In micro-combustor. In: USQ Combustion Meeting, 26 Nov 2012, Toowoomba, Australia.
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2011) Implementation of conditional moment closure using the Taylor expansion and finite differences. In: 1st International
Conference of Mechanical Engineering Research (ICMER 2011), 5-8 Dec 2011, Kuantan, Malaysia.
combustion gases
Sharifian, Ahmad (2012) The effect of direction of low speed winds on the performance of a split chimney. In: 23rd International Congress of Theoretical and Applied Mechanics (ICTAM 2012), 19-24
Aug2012, Beijing, China.
communication networks
Kist, Alexander A. and Harris, Richard J. (2003) Note on the problem of partially link disjoint paths. In: 2003 Joint Conference of the 4th International Conference on Information, Communications and
Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
communications network
Kist, Alexander A. and Harris, Richard J. (2002) A heuristic to generate all best partially disjoint paths in a communications network. In: 8th International Conference on Communication Systems (ICCS
2002), 25-28 Nov 2002, Singapore.
Wang, Yafeng and Wei, Guo-xing and Yang, Da-cheng and Xiang, Wei (2011) Research on uplink coordinated transmission schemes in LTE-advanced systems. Journal of China Universities of Posts and
Telecommunications, 18 (2). pp. 72-77. ISSN 1005-8885
compact integrated RBF
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow
problems. CMES Computer Modeling in Engineering and Sciences, 96 (1). pp. 49-90. ISSN 1526-1492
compact integrated-RBF stencils
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran, C. -D. and Tran-Cong, T. (2013) A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion
and unsteady fluid flow problems. Engineering Analysis with Boundary Elements , 37 (12). pp. 1653-1667. ISSN 0955-7997
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) A high-order compact integrated-RBF scheme for time-dependent problems. In: 4th International Conference on
Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady
convection-diffusion equations. CMES: Computer Modeling in Engineering and Sciences, 89 (3). pp. 189-220. ISSN 1526-1492
compact local approximations
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2012) Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs. CMES: Computer Modeling in Engineering and
Sciences, 84 (2). pp. 171-203. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) Compact local integrated-RBF approximations for second-order elliptic differential problems. Journal of Computational Physics , 230 (12). pp. 4772-4794. ISSN
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2011) Compact local stencils employed with integrated RBFs for fourth-order differential problems. Structural Longevity, 6 (2). pp. 93-107. ISSN
compact local IRBF approximations
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems. In: 4th
International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
compact local stencil
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2012) A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables. CMES:
Computer Modeling in Engineering and Sciences, 84 (6). pp. 528-557. ISSN 1526-1492
compact local stencils
Mai-Duy, N. and Thai-Quang, N. and Hoang-Trieu, T.-T. and Tran-Cong, T. (2013) A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation. Applied Mathematical Modelling
. ISSN 0307-904X (In Press)
Pham-Sy, N. and Tran, C.-D. and Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2013) Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination
detection based parallel algorithm. CMES Computer Modeling in Engineering and Sciences, 92 (1). pp. 1-31. ISSN 1526-1492
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A finite-volume method based on compact local integrated radial basis function approximations for second-order differential
problems. CMES Computer Modeling in Engineering and Sciences, 91 (6). pp. 485-516. ISSN 1526-1492
Pham-Sy, N. and Hoang-Trieu, T.-T. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Development of parallel algorithm for boundary value problems using compact local integrated RBFN and
domain decomposition. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
complex fluid flows
Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.
complex geometries
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2009) A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical
Modelling, 33 (1). pp. 284-299. ISSN 0307-904X
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations. In: Leading-edge applied
mathematical modeling research. Nova Science Publishers, Inc., New York, United States, pp. 215-250. ISBN 1-60021-977-2
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A point-collocation method based on integrated Chebyshev polynomials for elliptic differential equations in irregular domains. In: 8th World Congress on
Computational Mechanics (WCCM8) and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.
complex Hadamard transforms
Ramesh Kumar, Nandini and Xiang, Wei and Soar, Jeffrey (2011) A novel image compressive sensing method based on complex measurements. In: DICTA 2011: International Conference on Digital Image
Computing: Techniques and Application, 6-8 Dec 2011 , Noosa, Australia.
complex manifolds
Lozanovski, C. and Wylleman, L. (2011) Complex windmill transformation producing new purely magnetic fluids. Classical and Quantum Gravity, 28 (7). 075015-075031. ISSN 0264-9381
Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, Talal (2010) Hydrogen and natural gas comparison in diesel HCCI engines -a review. In: 2010 Southern Region Engineering Conference (SREC2010),
11-12 Nov 2010, Toowoomba, Australia.
component codes
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
composite laminates
Liu, Hong-Yuan and Yan, Wenyi and Mai, Yiu-Wing (2006) Z-pin bridging in composite laminates and some related problems. Australian Journal of Mechanical Engineering, 3 (1). pp. 11-19.
composite yarn
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
Tran, Canh-Dung and Humphries, William and Smith, Shaun M. and Huynh, Chi and Lucas, Stuart (2009) Improving the tensile strength of carbon nanotube spun yarns using a modified spinning process.
Carbon, 47 (11). pp. 2662-2670. ISSN 0008-6223
Compressed natural gas
Yusaf, T. and Baker, P. and Hamawand, I. and Noor, M. M. (2013) Effect of compressed natural gas mixing on the engine performance and emissions. International Journal of Automotive and Mechanical
Engineering, 8. pp. 1416-1429. ISSN 2229-8649
compression effects
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
compression heating
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
compression ignition scramjet
Buttsworth, David R. and Jacobs, Peter A. (2009) Premature ignition in scramjets with intake injection: a preliminary laminar mixing layer simulation. In: Australian Combustion Symposium 2009
(ACS09), 2-4 Dec 2009, Brisbane, Australia.
compression ratio
Hairuddin, A. Aziz and Yusaf, Talal F. and Wandel, Andrew P. (2012) HCCI engine: numerical and experimental approach. In: USQ Combustion Meeting, 26 Sep 2012, Toowoomba, Australia. (Unpublished)
compression waves
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
compressive sensing
Ramesh Kumar, Nandini and Xiang, Wei and Soar, Jeffrey (2011) A novel image compressive sensing method based on complex measurements. In: DICTA 2011: International Conference on Digital Image
Computing: Techniques and Application, 6-8 Dec 2011 , Noosa, Australia.
computation rate
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong (2013) Multi-hop compute-and-forward for generalized two-way relay channels. Transactions on Emerging Telecommunications Technologies. pp. 1-13. (In
Mossad, Ruth and Yang, William and Schwarz, M. Philip (2009) Numerical prediction of air flow in a sharp 90 degree elbow. In: 7th International Conference on Computational Fluid Mechanics in the
Minerals and Process Industries (CFD2009), 9-11 Dec 2009, Melbourne, Australia.
Computational Model
Zhang, Zhongwei and Wang, Zhen (2006) Assessing and assuring trust in e-Commerce systems. In: International Conference on Intelligent Agents, Web Technologies & Internet Commerce (IAWTIC'06), 29 Nov
- 1 Dec 2006, Sydney, Australia.
computational fluid dynamics
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. (2013) Design and development of mild combustion burner. Journal of Mechanical Engineering and Sciences, 5. pp. 662-676. ISSN 2289-4659
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Numerical study of oxygen dilution and temperature distribution of biogas combustion in Bluff-body MILD burner. In: 7th Australian Combustion
Symposium (ACS 2013), 6-8 Nov 2013, Perth, Australia .
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Analysis of recirculation zone and ignition position of non-premixed bluff-body for biogas mild combustion. International Journal of
Automotive and Mechanical Engineering, 8. pp. 1176-1186. ISSN 2229-8649
Yusaf, T. and Baker, P. and Hamawand, I. and Noor, M. M. (2013) Effect of compressed natural gas mixing on the engine performance and emissions. International Journal of Automotive and Mechanical
Engineering, 8. pp. 1416-1429. ISSN 2229-8649
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Detail guide for CFD on the simulation of biogas combustion in bluff-body mild burner. In: 2nd International Conference of Mechanical
Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The analysis of recirculation zone and ignition position of non-premixed bluff-body for biogas mild combustion. In: 2nd International
Conference of Mechanical Engineering Research (ICMER 2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The development of MILD combustion open burner experimental setup. In: 2nd International Conference of Mechanical Engineering Research (ICMER
2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Numerical investigation of influence of air and fuel dilution for open furnace MILD combustion burner. In: 2012 Qld Southern Regional
Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) A preliminary study of control parameters for open furnace mild combustion using CFD. In: 2nd Malaysian Postgraduate Conference (MPC 2012),
7-9 July 2012, Gold Coast, Australia.
computational simulation
Sharifian, Ahmad and Buttsworth, David R. (2007) Computational simulation of the wind-force on metal meshes. In: 16th Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast,
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Mode II delamination toughness of z-pinned laminates. Composites Science and Technology, 64 (13-14). pp. 1937-1945. ISSN 0266-3538
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2003) Numerical study on the mode I delamination toughness of z-pinned laminates. Composites Science and Technology, 63 (10). pp. 1481-1493. ISSN
Wang, Gengkun and Xiang, Wei and Wang, Yafeng (2013) Generalized compute-and-forward schemes for multi-hop two-way relay channels. In: 2013 IEEE 78th Vehicular Technology Conference (VTC Fall), 2-5
Sept 2013, Las Vegas, USA.
computer algebra
Roberts, A. J. (2008) Computer algebra derives discretisations via self-adjoint multiscale modelling. Unpublished. (Unpublished)
Roberts, A. J. (2008) Computer algebra describes flow of turbulent floods via the Smagorinski large eddy closure. Technical Report. University of Southern Queensland, Toowoomba, Australia.
Roberts, A. J. (2007) Computer algebra derives normal forms of stochastic differential equations. Technical Report. University of Southern Queensland, Faculty of Sciences, Department of Maths and
Computing, Toowoomba, Australia. (Unpublished)
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2006) The dynamics of the vertical structure of turbulence in flood flows. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 48 (CTAC-2). C573-C590. ISSN 1446-8735
computer algebra models
Roberts, A. J. (2007) Computer algebra models dynamics on a multigrid across multiple length and time scales. Technical Report. UNSPECIFIED. (Unpublished)
computer architecture
Gao, Rui and Zhou, Hong and Su, Gang (2011) Structure of wireless sensors network based on TinyOS. In: 2011 International Conference on Control, Automation and Systems Engineering (CASE 2011), 30-31
Jul 2011, Singapore.
computer networks
Alajel, Khalid Mohamed and Xiang, Wei (2013) A new hierarchical 16-QAM-based UEP scheme for 3-D video with depth image–based rendering. In: Advanced video communications over wireless networks.
Taylor & Francis (CRC Press), Boca Raton, FL. United States, pp. 355-382. ISBN 978-1-4398-7998-6
Aldraho, Abdelnour and Kist, Alexander A. (2012) Enabling energy efficient and resilient networks using dynamic topologies. In: 2012 Sustainable Internet and ICT for Sustainability (SustainIT 2012),
4-5 Oct 2012, Pisa, Italy.
computer simulation
Buttsworth, David R. and Goozee, Richard J. and Jacobs, Peter A. (2006) Measurement and simulation of the interface in a low-enthalpy shock tunnel. In: 14th International Space Planes and Hypersonic
Systems and Technologies Conference (AIAA/AHI 2006), 6-9 Nov 2006, Canberra, Australia.
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong (2012) Compute-and-forward in generalized multi-way relay channels. IEEE Communications Letters, 16 (12). pp. 2099-2102. ISSN 1089-7798
Al-Atresh, Safia and Sharifian, Ahmad and Kueger, Bradley (2012) Using a split chimney for dilution of exhaust pollution: a CFD approach. In: 2012 International Conference on Fluid Dynamics and
Thermodynamics Technologies (FDTT 2012), 17-18 March 2012, Singapore.
Buttsworth, David R. and Jones, Terry V. (2003) Concentration probe measurements in a Mach 4 nonreacting hydrogen jet. Journal of Fluids Engineering, 125 (4). pp. 628-635. ISSN 0098-2202
concentric annulus
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 1 - natural convection flows in concentric and eccentric
annuli. CMES: Computer Modeling in Engineering and Sciences, 83 (3). pp. 275-310. ISSN 1526-1492
conceptual experimentation
Kist, Alexander A. and Basnet, Badri (2013) Enabling effective and inclusive learning opportunities with software-based remote access laboratories. In: 10th International Conference on Remote
Engineering and Virtual Instrumentation (REV 2013): Moving from Design to Innovation and Impact, 6-8 Feb 2013, Sydney, Australia.
conditional correlations
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
conditional moment closure
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Discretization of three dimensional non-uniform grid: conditional moment closure elliptic equation using finite difference method. In: 3rd
Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2012) Modelling of non-premixed turbulent combustion of hydrogen using conditional moment closure method. IOP Conference
Series: Materials Science and Engineering, 36 (012036). pp. 1-17. ISSN 1757-899X
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2011) Implementation of conditional moment closure using the Taylor expansion and finite differences. In: 1st International
Conference of Mechanical Engineering Research (ICMER 2011), 5-8 Dec 2011, Kuantan, Malaysia.
conditional timescale
Wandel, Andrew P. (2013) Conditional dissipation of scalars in homogeneous turbulence: closure for MMC modelling. Combustion Theory and Modelling , 17 (4). pp. 707-748. ISSN 1364-7830
conductor losses
Wells, Colin G. and Ball, James A. R. (2006) Attenuation of a shielded rectangular dielectric rod waveguide. IEEE Transactions on Microwave Theory and Techniques, 54 (7). pp. 3013-3018. ISSN
confined flow
Deo, Ravinesh C. and Nathan, Graham J. and Mi, Jianchun (2013) Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers. Physics of
Fluids, 25 (1). 015115-1. ISSN 1070-6631
Chan, Auc Fai and Leis, John (2008) Comparison of weighted average and median filters for wireless retransmission timeout estimation. In: ICSPCS 2008: 2nd International Conference on Signal
Processing and Communication Systems, 15-17 Dec 2008, Gold Coast, Australia.
Chan, Auc Fai and Leis, John (2010) Median filtering simulation of bursty traffic. In: ICSPCS 2010: 4th International Conference on Signal Processing and Communication Systems, 13-15 Dec 2010, Gold
Coast, Australia.
congestion control
Zhou, Hong and Gyasi-Agyei, Amoakoh and Zhang, Zhongwei (2006) Performance of STT-Vegas in heterogeneous wired and wireless networks. In: 3rd International Conference on Quality of Service in
Heterogeneous Wired/Wireless Networks (QShine), 7-9 Aug 2006, Waterloo, Canada.
Tran, Canh-Dung and Tran-Cong, Thanh (2004) Element-free simulation of dilute polymeric flows using Brownian configuration fields. Korea-Australia Rheology Journal, 16 (1). pp. 1-15. ISSN 1226-119X
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
contact mechanics
Shiau, Jim S. (2011) A shakedown limit under Hertz contact pressure. In: 2011 International Conference on Advanced Engineering Materials and Technology (AEMT 2011), 29-31 Jul 2011, Sanya, China.
contact surface
Al-Falahi, Amir and Yusoff, M. Z. and Shuaib, N. H. and Yusaf, T. (2009) Flow instability in shock tube due to shock wave-boundary layer-contact surface interactions, a numerical study. European
Journal of Scientific Research, 30 (1). pp. 164-176. ISSN 1450-216X
content instrumentation
Buttsworth, D. R. and Davison, C. and MacLeod, J. D. and Strapp, J. W. (2007) Evaporator design for an isokinetic total water content probe in a naturally aspirating configuration. In: 16th
Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
continental shelf
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
continuum-microscopic method
Tran, C.-D. and Mai-Duy, N. and Le-Cao, K. and Tran-Cong, T. (2012) A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 85 (6). pp. 499-519. ISSN 1526-1492
control volume
Tran, C.-D. and Mai-Duy, N. and Le-Cao, K. and Tran-Cong, T. (2012) A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 85 (6). pp. 499-519. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems. International Journal for Numerical Methods in Fluids, 67 (12). pp.
1973-1992. ISSN 0271-2091
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows. CMES: Computer Modeling in Engineering and
Sciences, 80 (2). pp. 141-177. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems. In: ACAM 6: 6th Australasian Congress
on Applied Mechanics , 12-15 Dec 2010, Perth, Western Australia.
An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of Newtonian-fluid flows with C2-continuous two-node integrated-RBF elements. Structural Longevity, 4 (1). pp. 39-45. ISSN 1944-611X
control volume formulation
Mai-Duy, Nam and Tran-Cong, Thanh (2010) An upwind control-volume method based on integrated RBFs for fluid-flow problems. In: 9th World Congress on Computational Mechanics and 4th Asian-Pacific
Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
control volume method
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients. CMES: Computer
Modeling in Engineering and Sciences, 89 (4). pp. 303-359. ISSN 1526-1492
Mai-Duy, Nam and Tran-Cong, Thanh (2009) On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems. In: 31st International Conference on Boundary
Elements and Other Mesh Reduction Methods (BEM/MRM 31), 2-4 Sep 2009, New Forest, UK.
control volumes
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A control volume technique based on integrated RBFNs for the convection-diffusion equation. Numerical Methods for Partial Differential Equations, 26 (2). 426
-447. ISSN 0749-159X
control-volume discretisation
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems. Numerical Methods for Partial
Differential Equations, 26 (6). pp. 1443-1462. ISSN 0749-159X
control-volume formulation
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems. CMES:
Computer Modeling in Engineering and Sciences, 72 (4). pp. 299-334. ISSN 1526-1492
Sharifulin, Albert and Suslov, Sergey A. (2008) Bifurcations in convection of incompressible fluid in a rotated square cylinder. In: XXII International Congress of Theoretical and Applied Mechanics
ICTAM 2008, 24-29 August 2008, Adelaide, Australia.
Suslov, Sergey A. and Paolucci, Samuel (2002) A Petrov-Galerkin method for flows in cavities: enclosure of aspect ratio 8. International Journal for Numerical Methods in Fluids, 40 (8). pp. 999-1007.
ISSN 0271-2091
Ribbe, Joachim (2001) Intermediate water mass production controlled by southern hemisphere winds. Geophysical Research Letters, 28 (3). pp. 535-538. ISSN 0094-8276
convection-diffusion equation
Mai-Duy, N. and Thai-Quang, N. and Hoang-Trieu, T.-T. and Tran-Cong, T. (2013) A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation. Applied Mathematical Modelling
. ISSN 0307-904X (In Press)
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady
convection-diffusion equations. CMES: Computer Modeling in Engineering and Sciences, 89 (3). pp. 189-220. ISSN 1526-1492
convection-diffusion equations
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A control volume technique based on integrated RBFNs for the convection-diffusion equation. Numerical Methods for Partial Differential Equations, 26 (2). 426
-447. ISSN 0749-159X
convective/absolute instability
Suslov, Sergey A. (2001) Searching convective/absolute instability boundary for flows with fully numerical dispersion relation. Computer Physics Communications, 142 (1-3). pp. 322-325. ISSN 0010-4655
convective/absolute instability transition
Suslov, Sergey A. (2005) Numerical aspects of searching convective/absolute instability transition. Journal of Computational Physics, 212 (1). pp. 188-217. ISSN 0021-9991
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
cooling water
Hamid, H. A. and Yusaf, T. and Yusof, Z. M. (2006) An investigation on the improvement of the operation of Tenom Pangi HPP cooling power system. In: International Conference on Energy and Environment
2006 (ICEE 2006), 28-30 Aug 2006, Kajang, Malaysia.
cooperative communications
Alajel, Khalid Mohamed and Xiang, Wei and Sileh, Ibrahim Khalil (2012) Best relays selection method for error-resilient 3-D video transmission. In: 12th International Symposium on Communications and
Information Technologies (ISCIT 2012), 2-5 Oct 2012, Gold Coast, Australia.
cooperative communication
Ran, Jie and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2011) A novel selection incremental relaying strategy for cooperative networks. In: 2011 IEEE Wireless Communications and Networking
Conference (WCNC 2011) , 28-31 Mar 2011 , Cancun, Mexico.
cooperative MIMO-OFDM
Salim, Omar Hazim and Xiang, Wei and Leis, John (2013) An efficient unequal error protection scheme for 3-D video transmission. In: IEEE Wireless Communication and Networking Conference (WCNC 2013):
Connecting the Future, 7-10 Apr 2013, Shanghai, China.
Salim, Omar Hazim and Xiang, Wei (2012) A novel unequal error protection scheme for 3-D video transmission over cooperative MIMO-OFDM systems. EURASIP Journal on Wireless Communications and
Networking, 2012 (269). ISSN 1687-1499 (In Press)
cooperative networks
Wang, Yafeng and Liang, Min and Xiang, Wei (2011) Semi-distributed relay selection algorithm for multi-user cooperative wireless networks. Journal of Networks, 6 (6). pp. 907-911. ISSN 1796-2056
Ran, Jie and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2011) A novel selection incremental relaying strategy for cooperative networks. In: 2011 IEEE Wireless Communications and Networking
Conference (WCNC 2011) , 28-31 Mar 2011 , Cancun, Mexico.
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
corrugated tube flows
Mai-Duy, Nam and Tanner, Roger I. (2004) Numerical analysis of corrugated tube flow using RBFNs. In: 14th International Congress on Rheology, 22-27 Aug 2004, Seoul, Korea.
Ramesh Kumar, Nandini and Xiang, Wei and Soar, Jeffrey (2011) A novel image compressive sensing method based on complex measurements. In: DICTA 2011: International Conference on Digital Image
Computing: Techniques and Application, 6-8 Dec 2011 , Noosa, Australia.
cost effective
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
coupled Ginzburg-Landau equations
Suslov, Sergey A. (2005) Analysis of coupling between hydrodynamic and thermal instabilities in non-Boussinesq convection. Nonlinear Analysis Theory Methods and Applications, 63 (5-7). e1435-e1443.
ISSN 0362-546X
coupled heat conduction
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2006) A meshless IRBFN-based numerical simulation of adiabatic shear band formation in one dimension. In: 2006 International
Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi Minh City, Vietnam.
coupled systems
Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2001) Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena. Mechanics Research
Communications, 28 (6). pp. 637-651. ISSN 0093-6413
coupled thermomechanical fields
Strunin, D. V. and Melnik, R. V. N. and Roberts, A. J. (2001) Coupled thermomechanical waves in hyperbolic thermoelasticity. Journal of Thermal Stresses, 24 (2). pp. 121-140. ISSN 0149-5739
coupling boundary conditions
Roberts, A. J. and Kevrekidis, I. G. (2007) General tooth boundary conditions for equation free modeling. SIAM Journal on Scientific Computing, 29 (4). pp. 1495-1510. ISSN 1064-8275
course linkage
Wandel, Andrew P. (2010) Linkages between courses: a holistic approach to programmes. In: AaeE 2010: Past, Present, Future - the 'Keys' to Engineering Education Research and Practice, 5-8 Dec 2010,
Sydney, Australia.
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based Galerkin meshless method. CMES: Computer Modeling in Engineering and Sciences, 66 (1). pp. 25-52.
ISSN 1526-1492
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
crack growth
Golshani, Aliakbar and Tran-Cong, Thanh (2008) Simulation of hydraulic fracturing in brittle rocks. In: ISRM International Symposium 2008: 5th Asian Rock Mechanics Symposium, 24-26 Nov 2008, Tehran,
Dahmani, L. and Khennane, A. and Kaci, S. (2009) Modeling and influence of shear retention parameter on the response of reinforced concrete structural elements. Strength of Materials, 41 (4). pp.
423-430. ISSN 0039-2316
Dahmani, L. and Khennane, A. and Kaci, S. (2010) Crack identification in reinforced concrete beams using ANSYS software. Strength of Materials, 42 (2). pp. 232-240. ISSN 0039-2316
creeping flow
Stepanyants, Yury A. and Yeoh, Guan H. (2010) Nanoparticle dynamics in a viscous fluid at small Reynolds numbers. In: 6th Australasian Congress on Applied Mechanics (ACAM 6), 12-15 Dec 2010, Perth,
Western Australia.
critical depth
Stepanyants, Yury (2005) Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons. Proceedings of the Russian Academy of Engineering Sciences Series: Applied
Mathematics and Mechanics, 14. pp. 33-40.
crops biodiesel
Yusaf, T. F. and Al-lwayzy, Saddam H. (2012) The use of microalgae biodiesel in diesel engine: production, extraction and engine performance. In: USQ Combustion Meeting, 21 Nov 2012, Toowoomba,
Australia. (Unpublished)
CS reconstruction
Ramesh Kumar, Nandini and Xiang, Wei and Soar, Jeffrey (2011) A novel image compressive sensing method based on complex measurements. In: DICTA 2011: International Conference on Digital Image
Computing: Techniques and Application, 6-8 Dec 2011 , Noosa, Australia.
CTD observations
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120
curved substrate
Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120
cyclic delay diversity (CDD)
Zheng, Aoyang and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Self-adapting cyclic delay diversity system. In: RSKT 2009: 4th International Conference on Rough Set and Knowledge Technology ,
14-16 Jul 2009, Gold Coast, Australia.
cyclic detection
Wang, Yafeng and Yang, Hao and Yang, Dacheng and Xiang, Wei (2010) Iterative decision feedback equalizer with cyclic detection for DFT-S OFDM system. Computers and Electrical Engineering, 36 (4). pp.
789-801. ISSN 0045-7906
Wang, Yafeng and Yang, Hao and Xiang, Wei (2008) Iterative decision-feedback equalizer with cyclic detection for DFT-S OFDM system. In: 1st International Conference on Signal Processing and
Communication Systems (ICSPCS2007), 17-19 Dec 2007, Gold Coast, Queensland, Australia.
cyclic redundancy check (CRC)
Xiang, Wei and Clemence, Andrew and Leis, John and Wang, Yafeng (2009) Error resilience analysis of wireless image transmission using JPEG, JPEG 2000 and JPWL. In: ICICS 2009: 7th International
Conference on Information, Communications and Signal Processing, 8-10 Dec 2009, Macau, China.
Golshani, Aliakbar and Tran-Cong, Thanh and Buttsworth, David (2008) Impact on a water filled cylinder. In: ACMFMS 2008: Asian Conference on Mechanics of Functional Materials and Structures, 31 Oct-3
Nov 2008, Matsue, Japan.
daily gas load
Zhou, Hong and Su, Gang and Li, Guofang (2011) Forecasting daily gas load with OIHF-Elman neural network. In: 2nd International Conference on Ambient Systems, Networks and Technologies (ANT 2011) ,
19-21 Sep 2011, Niagara Falls, ON. Canada.
dam break
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2009) Modeling turbulent flow from dam break using slow manifolds. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 50. C1033-C1051. ISSN 1446-1811
data analysis
Ng, S. K. and Carter, S. J. B. and Bullen, Frank (2006) A biomimicry approach to automating visual road surveys. In: 22nd ARRB Conference: Research Into Practice, 29 Oct - 02 Nov 2006, Canberra,
data collection
Ng, S. K. and Carter, S. J. B. and Bullen, Frank (2006) A biomimicry approach to automating visual road surveys. In: 22nd ARRB Conference: Research Into Practice, 29 Oct - 02 Nov 2006, Canberra,
data dessemination
Zhou, Hong and Jin, Lu and Zhang, Zhongwei and Ali, Hesham and Wang, Chulho (2007) Applications and performances of extended TTDDs in large-scale wireless sensor networks. In: 3rd International
Conference of Mobile Ad-hoc and Sensor Networks, 12-14 Dec 2007, Beijing, China.
data dissemination
Zhou, Hong and Wu, Huayi (2009) The integration of wireless sensor networks, remote sensing and geographic information systems for autonomous environmental and animal monitoring. In: IADIS
International Conference on Applied Computing 2009 (IADIS 2009), 19-21 Nov 2009, Rome, Italy.
data rates
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Goodput and channel allocation in opportunistic spectrum access networks. In: PIMRC 2009: 20th IEEE International Symposium on
Personal, Indoor and Mobile Radio Communications, 13-16 Sep 2009, Tokyo, Japan.
data sets
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. Technical Report. Joachim Ribbe, Toowoomba, Australia.
data traffic
Norman, Mark and Leis, John (2010) A passive approach to detection of traffic shaping. In: APSIPA 2010: 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference,
14-17 Dec 2010, Biopolis, Singapore.
DC current
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
DC injection
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
Ahfock, A. and Hewitt, A. J. (2006) DC magnetisation of transformers. IET Electric Power Applications, 153 (4). pp. 601-607. ISSN 1350-2352
DC offsets
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
DC power
Ahfock, Tony L. and Bowtell, Leslie (2006) DC offset elimination in a single-phase grid-connected photovoltaic system. In: AUPEC 2006: 16th Australasian Universities Power Engineering Conference,
10-13 Dec 2006, Melbourne, Australia.
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
decadal ocean variability
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
decaying turbulences
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
decision feedback equalizers
Wang, Yafeng and Yang, Hao and Yang, Dacheng and Xiang, Wei (2010) Iterative decision feedback equalizer with cyclic detection for DFT-S OFDM system. Computers and Electrical Engineering, 36 (4). pp.
789-801. ISSN 0045-7906
decode and forward
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
decoding errors
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
deferred correction technique
Mai-Duy, N. and Tran-Cong, T. (2011) A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems. In: ACAM 6: 6th Australasian Congress
on Applied Mechanics , 12-15 Dec 2010, Perth, Western Australia.
deferred-correction technique
Mai-Duy, N. and Tran-Cong, T. (2011) A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems. International Journal for Numerical Methods in Fluids, 67 (12). pp.
1973-1992. ISSN 0271-2091
Mai-Duy, N. and Phan-Thien, N. and Khoo, B. C. (2013) A numerical study of strongly overdamped dissipative particle dynamics (DPD) systems. Journal of Computational Physics , 245. pp. 150-159. ISSN
degree of divergence
Kist, Alexander A. and Harris, Richard J. (2003) Note on the problem of partially link disjoint paths. In: 2003 Joint Conference of the 4th International Conference on Information, Communications and
Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Mode II delamination toughness of z-pinned laminates. Composites Science and Technology, 64 (13-14). pp. 1937-1945. ISSN 0266-3538
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2003) Numerical study on the mode I delamination toughness of z-pinned laminates. Composites Science and Technology, 63 (10). pp. 1481-1493. ISSN
Kist, Alexander A. and Harris, Richard J. (2003) SIP signalling delay in 3GPP. In: Sixth International Symposium on Communications Interworking of IFIP - Interworking 2002, 13-16 Oct 2002, Fremantle,
delay analysis
Zhou, Hong and Zhang, Zhongwei (2009) Adaptive end-to-end QoS provision for real-time multimedia applications in heterogeneous multi-hop wireless networks. In: 5th International ICST Mobile
Multimedia Communications Conference (MobiMedia'09), 7-9 September 2009, London, United Kingdom.
delivery constraints
Norman, Mark and Leis, John (2010) A passive approach to detection of traffic shaping. In: APSIPA 2010: 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference,
14-17 Dec 2010, Biopolis, Singapore.
Langlands, T. A. M. and Henry, B. I. and Wearne, S. L. (2011) Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions. SIAM Journal on Applied
Mathematics, 71 (4). pp. 1168-1203. ISSN 0036-1399
derivative approximation
Mai-Duy, Nam and Tran-Cong, Thanh (2003) Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling, 27 (3). pp. 197-220. ISSN 0307-904X
derivative recovery
Bordas, Stephane and Duflot, Marc and Le, Phong (2008) A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24 (11). pp. 961-971. ISSN 1069-8299
Mai-Duy, Nam (2005) Solving high order ordinary differential equations with radial basis function networks. International Journal for Numerical Methods in Engineering, 62 (6). pp. 824-852. ISSN
design procedure
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
detection algorithm
Norman, Mark and Leis, John (2010) A passive approach to detection of traffic shaping. In: APSIPA 2010: 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference,
14-17 Dec 2010, Biopolis, Singapore.
deterministic delay bound
Zhou, Hong and Zhang, Zhongwei (2011) Examining QoS guarantees for real-time CBR services in broadband wireless access networks. In: Software engineering, artificial intelligence, networking and
parallel/distributed computing 2011. Studies in Computational Intelligence (368). Springer, Berlin, Germany, pp. 25-40. ISBN 978-3-642-22287-0
Zhou, Hong and Zhang, Zhongwei (2010) Differentiated statistical QoS guarantees for real-time CBR services in broadband wireless access networks. In: 6th International Conference on Wireless
Communications, Networking and Mobile Computing (WiCOM 2010), 23-25 Sep 2010, Chengdu, China.
Wang, Yafeng and Yang, Hao and Yang, Dacheng and Xiang, Wei (2010) Iterative decision feedback equalizer with cyclic detection for DFT-S OFDM system. Computers and Electrical Engineering, 36 (4). pp.
789-801. ISSN 0045-7906
Wang, Yafeng and Yang, Hao and Xiang, Wei (2008) Iterative decision-feedback equalizer with cyclic detection for DFT-S OFDM system. In: 1st International Conference on Signal Processing and
Communication Systems (ICSPCS2007), 17-19 Dec 2007, Gold Coast, Queensland, Australia.
DFT-spread-OFDM (DFT-S-OFDM)
Zheng, Aoyang and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Self-adapting cyclic delay diversity system. In: RSKT 2009: 4th International Conference on Rough Set and Knowledge Technology ,
14-16 Jul 2009, Gold Coast, Australia.
DFVLR compressor rotor
Ng, K. C. and Yusoff, M. Z. and Yusaf, T. F. (2007) Numerical simulation of 3D transonic flow in a compressor rotor. International Journal of Modelling and Simulation, 27 (1). pp. 74-79. ISSN
diaphragm pressure
Al-Falahi, Amir and Yusaf, T. and Yusoff, M. Z. (2007) Experimental and CFD study of the effects of design parameters on Reynolds number in a short duration hypersonic test facility. In: EPMESC X:
Enhancement and Promotion of Computational Methods in Engineering and Science X, 21-23 Aug 2006, Sanya, China.
Buttsworth, David R. and Goozee, Richard J. and Jacobs, Peter A. (2006) Measurement and simulation of the interface in a low-enthalpy shock tunnel. In: 14th International Space Planes and Hypersonic
Systems and Technologies Conference (AIAA/AHI 2006), 6-9 Nov 2006, Canberra, Australia.
Alajel, Khalid and Xiang, Wei and Sileh, Ibrahim (2012) Color plus depth 3-D video transmission with hierarchical 16-QAM. In: 6th International Conference on Signal Processing and Communication
Systems (ICSPCS 2012) , 12-14 Dec 2012, Gold Coast, Australia.
Alajel, Khalid Mohamed and Xiang, Wei (2012) Color plus depth 3-D video transmission with heirarchical 16-QAM. In: 3DTV-CON 2012: The True Vision: Capture, Transmission and Display of 3D Video, 15-17
Oct 2012, Zurich, Switzerland.
dielectric waveguides
Wells, Colin G. and Ball, James A. R. (2006) Attenuation of a shielded rectangular dielectric rod waveguide. IEEE Transactions on Microwave Theory and Techniques, 54 (7). pp. 3013-3018. ISSN
Hairuddin, Abdul Aziz and Yusaf, Talal and Wandel, Andrew (2013) Effect of different heat transfer models on a diesel homogeneous charge compression ignition engine. International Journal of
Automotive and Mechanical Engineering, 8. pp. 1305-1317. ISSN 2229-8649
Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, Talal (2010) Hydrogen and natural gas comparison in diesel HCCI engines -a review. In: 2010 Southern Region Engineering Conference (SREC2010),
11-12 Nov 2010, Toowoomba, Australia.
diesel engine
Wardana, I. N. G. (2012) Burning characteristics of coconut oil In micro-combustor. In: USQ Combustion Meeting, 26 Nov 2012, Toowoomba, Australia.
Yusaf, T. F. and Al-lwayzy, Saddam H. (2012) The use of microalgae biodiesel in diesel engine: production, extraction and engine performance. In: USQ Combustion Meeting, 21 Nov 2012, Toowoomba,
Australia. (Unpublished)
Najafi, G. and Ghobadian, B. and Tavakoli, T. and Buttsworth, D. R. and Yusaf, T. F. and Faizollahnejad, M. (2009) Performance and exhaust emissions of a gasoline engine with ethanol blended gasoline
fuels using artificial neural network. Applied Energy, 86 (5). pp. 630-639. ISSN 0306-2619
Ghobadian, B. and Rahimi, H. and Nikbakht, A. M. and Najafi, G. and Yusaf, T. F. (2009) Diesel engine performance and exhaust emission analysis using waste cooking biodiesel fuel with an artificial
neural network. Renewable Energy, 34 (4). pp. 976-982. ISSN 0960-1481
Najafi, Bahman and Pirouzpanah, Vahab and Najafi, Gholamhassan and Yusaf, Talal and Ghobadian, Barat (2007) Experimental investigation of performance and emission parameters of a small diesel engine
using CNG and biodiesel. In: 13th Small Engine Technology Conference 2007, 30 Oct - 01 Nov 2007, Toki Messe, Niigata, Japan.
diesel HCCI
Hairuddin, A. Aziz and Yusaf, Talal and Wandel, Andrew P. (2013) Implementation of CMC in a 0-D single-zone model of a diesel HCCI engine. In: 7th Australian Combustion Symposium (ACS 2013), 6-8 Nov
2013, Perth, Australia .
Rahimi, Hadi and Ghobadian, Barat and Yusaf, Talal and Najafi, Gholamhasan and Khatamifar, Mahdi (2009) Diesterol: an environment-friendly IC engine fuel. Renewable Energy, 34 (1). pp. 335-342. ISSN
Rahimi, Hadi and Ghobadian, Barat and Yusaf, Talal and Najafi, Gholamhasan and Khatamifar, Mahdi (2009) Diesterol: an environment-friendly IC engine fuel. Renewable Energy, 34 (1). pp. 335-342. ISSN
differential algebraic systems
Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2002) Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models. Computational Mechanics, 29
(1). pp. 16-26. ISSN 0178-7675
differential equations
Henry, B. I. and Langlands, T. A. M. and Straka, P. (2010) Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces. Physical Review Letters, 105 (17).
17062-1-170602-4. ISSN 0031-9007
Li, Zhenquan and Roberts, A. J. (2007) Low-dimensional modelling of a generalised Burgers equation. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 203-218. ISSN 0973-1768
differential governing equations
Tran, Canh-Dung and Phillips, David G. and Fraser, W. Barrie (2010) Stationary solution of the ring-spinning balloon in zero air drag using a RBFN based mesh-free method. Journal of the Textile
Institute, 101 (2). pp. 101-110. ISSN 0040-5000
differentially-heated cavity
Suslov, Sergey A. and Paolucci, Samuel (2002) A Petrov-Galerkin method for flows in cavities: enclosure of aspect ratio 8. International Journal for Numerical Methods in Fluids, 40 (8). pp. 999-1007.
ISSN 0271-2091
Li, Zhenquan and Roberts, A. J. (2007) Low-dimensional modelling of a generalised Burgers equation. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 203-218. ISSN 0973-1768
diffusion equation
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
diffusion length
Wandel, Andrew P. (2011) A stochastic micromixing model based on the turbulent diffusion length scale. In: Australian Combustion Symposium 2011 (ACS 2011), 29 Nov-1 Dec 2011, Newcastle, Australia.
digital dc-offset control
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
digital filters
Leis, J. and Martin, P. and Buttsworth, D. (2012) Simplified digital lock-in amplifier algorithm. Electronics Letters, 48 (5). pp. 259-261. ISSN 0013-5194
digital instrumentation
Leis, J. and Martin, P. and Buttsworth, D. (2012) Simplified digital lock-in amplifier algorithm. Electronics Letters, 48 (5). pp. 259-261. ISSN 0013-5194
dilute polymer solution
Tran, Canh-Dung and Phillips, David G. and Tran-Cong, Thanh (2009) Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique. Korea-Australia
Rheology Journal, 21 (1). pp. 1-12. ISSN 1226-119X
Sharifian, Ahmad and Hashempour, Javad (2012) Dilution of toxic gases and smoke emissions from residential chimneys using a low-cost cap. In: 18th Australasian Fluid Mechanics Conference (AFMC 2012),
3-7 Dec 2012, Launceston, Australia.
Al-Atresh, Safia and Sharifian, Ahmad and Kueger, Bradley (2012) Using a split chimney for dilution of exhaust pollution: a CFD approach. In: 2012 International Conference on Fluid Dynamics and
Thermodynamics Technologies (FDTT 2012), 17-18 March 2012, Singapore.
Sharifian, Ahmad (2012) The effect of wind speed on the performance of a split chimney. In: 2012 International Conference on Fluid Dynamics and Thermodynamics Technologies (FDTT 2012), 17-18 March
2012, Singapore.
dimensional analysis
Genet, Martin and Yan, Wenyi and Tran-Cong, Thanh (2009) Investigation of a hydraulic impact: a technology in rock breaking. Archive of Applied Mechanics, 79 (9). pp. 825-841. ISSN 0939-1533
direct current
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
direct forcing
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow
problems. CMES Computer Modeling in Engineering and Sciences, 96 (1). pp. 49-90. ISSN 1526-1492
direct numerical simulations
du Preez, M. and Wandel, Andrew P. (2013) Direct numerical simulations of passive scalars: effect of initial mixture fraction distribution on timescales. In: 7th Australian Combustion Symposium (ACS
2013), 6-8 Nov 2013, Perth, Australia.
Wandel, Andrew P. (2013) Mixture fraction probability density functions in sparse spray flames with spark ignition. In: 7th Australian Combustion Symposium (ACS 2013), 6-8 Nov 2013, Perth, Australia
Wandel, Andrew P. (2013) Conditional dissipation of scalars in homogeneous turbulence: closure for MMC modelling. Combustion Theory and Modelling , 17 (4). pp. 707-748. ISSN 1364-7830
Wandel, Andrew P. and Chakraborty, Nilanjan and Mastorakos, E. (2009) Direct numerical simulations of turbulent flame expansion in fine sprays. Proceedings of the Combustion Institute, 32 (2). pp.
2283-2290. ISSN 1540-7489
direct radiation heat flux
Sharifian, Ahmad and Buttsworth, David (2010) Double-layered metal mesh screens to contain or exclude thermal radiation from bush fires. Journal of Fire Protection Engineering, 20 (4). pp. 291-311.
ISSN 1042-3915
direct-current offsets
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
directed graphs
Kist, Alexander A. and Harris, Richard J. (2002) A heuristic to generate all best partially disjoint paths in a communications network. In: 8th International Conference on Communication Systems (ICCS
2002), 25-28 Nov 2002, Singapore.
Dirichlet boundary condition
Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless
& Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2011) Discretisation of the velocity-pressure formulation with integrated radial-basis-function networks. Structural Longevity, 6 (2).
pp. 77-91. ISSN 1944-611X
Strunin, Dmitry V. and Roberts, Anthony J. (2009) Low-dimensional boundary-layer model of turbulent dispersion in a channel. In: WCE 2009: World Congress of Engineering , 1-3 Jul 2009, London, United
dispersion relation
Clamond, D. and Stepanyants, Y. (2012) Stationary gravity waves with the zero mean vorticity in stratified fluid. Studies in Applied Mathematics, 128 (1). pp. 59-85. ISSN 0022-2526
Stepanyants, Yury (2005) Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons. Proceedings of the Russian Academy of Engineering Sciences Series: Applied
Mathematics and Mechanics, 14. pp. 33-40.
Suslov, Sergey A. (2001) Searching convective/absolute instability boundary for flows with fully numerical dispersion relation. Computer Physics Communications, 142 (1-3). pp. 322-325. ISSN 0010-4655
display cabinets
Mossad, Ruth (2006) Numerical simulation to optimize the design of double glazed doors for closed refrigerated vertical display cabinets. In: 13th International Heat Transfer Conference IHTC-13,
13-18 Aug 2006, Sydney, Australia.
Ostrovsky, Lev and Stepanyants, Yury (2005) Internal solitons in laboratory experiments: Comparison with theoretical models. Chaos, 15 (037111). 037111-1. ISSN 1054-1500
dissipative particle dynamics
Mai-Duy, N. and Phan-Thien, N. and Khoo, B. C. and Tran-Cong, T. (2013) Modelling of solid bodies in dissipative particle dynamics. In: 3rd International Conference on Particle-based Methods
Fundamentals and Applications, Particles, 18-20 Sept 2013, Stuttgart, Germany.
Mai-Duy, N. and Phan-Thien, N. and Khoo, B. C. (2013) A numerical study of strongly overdamped dissipative particle dynamics (DPD) systems. Journal of Computational Physics , 245. pp. 150-159. ISSN
dissipative systems
Strunin, D. V. and Mohammed, M. G. (2012) Parametric space for nonlinearly excited phase equation. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 53. C236-C248.
ISSN 1446-8735
distance education
Brodie, Lyn and Gibbings, Peter (2011) Connecting learners in virtual space: forming learning communities. In: Creating connections in teaching and learning. Research on Teaching and Learning .
Information Age Publishing, Charlotte, NC, United States, pp. 233-248. ISBN 978-1-61735-550-9 (pbk); 978-1-61735-551-6 9 (hbk); 978-1-61735-552-3 (ebook)
Wandel, Andrew P. (2010) Student usage of videos containing worked solutions. In: AaeE 2010: Past, Present, Future - the 'Keys' to Engineering Education Research and Practice, 5-8 Dec 2010, Sydney,
distortion modeling
Zhou, Yuan and Hou, Chunping and Xiang, Wei and Wu, Feng (2011) Channel distortion modeling for multi-view video transmission over packet-switched networks. IEEE Transactions on Circuits and Systems
for Video Technology, 21 (11). pp. 1679-1692. ISSN 1051-8215
Zhou, Yuan and Hou, Chunping and Xiang, Wei (2010) Modeling of transmission distortion for multi-view video in packet lossy networks. In: GLOBECOM 2010: IEEE Global Telecommunications Conference,
6-10 Dec 2010, Miami, FL, USA.
distribute network management
Zhang, Zhongwei and Lai, David (2005) An active approach to multimedia network management. In: 9th WSEAS International Conference on Communications, 11-16 July 2005, Athens, Greece.
distributed network management
Zhang, Zhongwei and Lai, David (2005) Decentralized management of multimedia network using active network technology. WSEAS Transactions on Communications, 4 (7). pp. 325-333. ISSN 1109-2742
distributed termination detection
Pham-Sy, N. and Tran, C.-D. and Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2013) Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination
detection based parallel algorithm. CMES Computer Modeling in Engineering and Sciences, 92 (1). pp. 1-31. ISSN 1526-1492
distributed turbo code
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Performance analysis for coded cooperative multiple-relay in distributed turbo channels. In: IEEE 22nd International Symposium on
Personal Indoor and Mobile Radio Communications (PIMRC 2011), 11-14 Sep 2011, Toronto, Canada.
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) A robust ensemble classification method analysis. In: 2009 International Conference on Bioinformatics and Computational Biology ,
13-16 Jul 2009, Las Vegas, NV. United States.
diversity methods
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
diversity analysis
Long, Hang and Xiang, Wei and Liu, Hongmei and Shen, Shanshan (2012) Diversity analysis of two-way MIMO relaying system based on zero-forcing. In: IEEE International Conference on Communications (ICC
2012): Connect, Communicate, Collaborate, 10-15 Jun 2012, Ottawa, ON. Canada.
Wandel, Andrew P. (2013) Extinction predictors in turbulent sprays. Proceedings of the Combustion Institute, 34 (1). pp. 1625-1632. ISSN 1540-7489
Clarke, Jason and Wandel, Andrew P. and Mastorakos, E. (2010) Analysis of data to develop models for spray combustion. In: 2010 Southern Region Engineering Conference (SREC 2010), 11-12 Nov 2010,
Toowoomba, Australia.
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
domain decomposition
Pham-Sy, N. and Hoang-Trieu, T.-T. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Development of parallel algorithm for boundary value problems using compact local integrated RBFN and
domain decomposition. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 11 - unsteady incompressible viscous flows. CMES: Computer
Modeling in Engineering and Sciences , 83 (3). pp. 311-351. ISSN 1526-1492
Tran, Canh-Dung and Phillips, David G. and Tran-Cong, Thanh (2009) Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique. Korea-Australia
Rheology Journal, 21 (1). pp. 1-12. ISSN 1226-119X
Mai-Duy, Nam and Tran-Cong, Thanh (2009) An integrated-RBF technique based on Galerkin formulation for elliptic differential equations. Engineering Analysis with Boundary Elements, 33 (2). pp.
191-199. ISSN 0955-7997
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations. Communications in Numerical Methods in Engineering, 24
(10). pp. 795-806. ISSN 1069-8299
Mai-Duy, Nam and Tran-Cong, Thanh (2008) On the use of integrated RBFs in Galerkin approximation for elliptic problems. In: BEM/MRM 30: 30th International Conference on Boundary Elements and Other
Mesh Reduction Methods, 7-9 Jul 2008, Maribor, Slovenia.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A multidomain integrated RBF collocation method for elliptic differential equations. In: 8th World Congress on Computational Mechanics (WCCM8), and 5th
European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.
domain decomposition method
Pham-Sy, N. and Tran, C.-D. and Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2013) Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination
detection based parallel algorithm. CMES Computer Modeling in Engineering and Sciences, 92 (1). pp. 1-31. ISSN 1526-1492
domain decompositions
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations. In: Leading-edge applied
mathematical modeling research. Nova Science Publishers, Inc., New York, United States, pp. 215-250. ISBN 1-60021-977-2
domain embedding scheme
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2010) A new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems. In: 9th World Congress on Computational
Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
double boundary conditions
Mai-Duy, Nam and Ho-Minh, D. and Tran-Cong, Thanh (2009) A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations. International Journal
of Computer Mathematics, 86 (10-11). pp. 1746-1759. ISSN 0020-7160
Mai-Duy, Nam and Tran-Cong, Thanh (2008) Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks. In: 8th International Conference on Computational
and Mathematical Methods in Science and Engineering (CMMSE-2008), 13-16 June 2008, Murcia, Spain.
Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I. (2006) A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem. Engineering Analysis with Boundary Elements,
30 (10). pp. 809-817. ISSN 0955-7997
double glazed doors
Mossad, Ruth (2006) Numerical simulation to optimize the design of double glazed doors for closed refrigerated vertical display cabinets. In: 13th International Heat Transfer Conference IHTC-13,
13-18 Aug 2006, Sydney, Australia.
downlink channel
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
drag force
Stepanyants, Y. A. and Strunin, D. V. (2011) Dynamics of two charged particles in viscous fluid at small Reynolds numbers. In: 2011 International Conference on Mathematics and Computational Methods
Applied to Nuclear Science and Enginnering (MC 2011), 8-12 May 2011, Rio de Janeiro, Brazil.
drilling degrees of freedom
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2009) An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis. CMES: Computer Modeling in
Engineering and Sciences, 49 (2). pp. 81-110. ISSN 1526-1492
driven cavity viscous flow
Mai-Duy, Nam and Tran-Cong, Thanh (2005) An efficient indirect RBFN-based method for numerical solution of PDEs. Numerical Methods for Partial Differential Equations, 21 (4). pp. 770-790. ISSN
driver gas contamination
Goozee, R. J. and Jacobs, P. A. and Buttsworth, D. R. (2006) Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. Shock Waves, 15 (3-4). pp. 165-176.
ISSN 0938-1287
droplet evaporations
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
droplet sizes
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
Wandel, Andrew P. and Chakraborty, Nilanjan and Mastorakos, E. (2009) Direct numerical simulations of turbulent flame expansion in fine sprays. Proceedings of the Combustion Institute, 32 (2). pp.
2283-2290. ISSN 1540-7489
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
Cottrill, Andrew and Ribbe, Joachim (2007) Queensland rainfall variability in IPCC AR4 model runs. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8
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dry spinning
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
Tran, Canh-Dung and Humphries, William and Smith, Shaun M. and Huynh, Chi and Lucas, Stuart (2009) Improving the tensile strength of carbon nanotube spun yarns using a modified spinning process.
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dry spinning technique
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dual fuel
Najafi, Bahman and Pirouzpanah, Vahab and Najafi, Gholamhassan and Yusaf, Talal and Ghobadian, Barat (2007) Experimental investigation of performance and emission parameters of a small diesel engine
using CNG and biodiesel. In: 13th Small Engine Technology Conference 2007, 30 Oct - 01 Nov 2007, Toki Messe, Niigata, Japan.
dual-fuel engine
Yusaf, T. and Baker, P. and Hamawand, I. and Noor, M. M. (2013) Effect of compressed natural gas mixing on the engine performance and emissions. International Journal of Automotive and Mechanical
Engineering, 8. pp. 1416-1429. ISSN 2229-8649
dynamic coordination
Wang, Yafeng and Wei, Guo-xing and Yang, Da-cheng and Xiang, Wei (2011) Research on uplink coordinated transmission schemes in LTE-advanced systems. Journal of China Universities of Posts and
Telecommunications, 18 (2). pp. 72-77. ISSN 1005-8885
dynamic dc-offset control
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
dynamic mechanical analyzer
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
Dynamic Password
Lai, David Tai Wai (2010) Supporting secure services on dynamic aggregation of heterogeneous networks. [Thesis (PhD/Research)] (Unpublished)
dynamic performance
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
dynamic resource allocation
Kist, Alexander A. and Harris, Richard J. (2003) Dynamic resource allocation in 3GPP SIP overlay networks. In: 2003 Joint Conference of the 4th International Conference on Information, Communications
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dynamic routing
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Zhang, Zhongwei and Zhou, Hong and Gao, Jason (2009) Scrutinizing performance of ad hoc routing protocols on wireless sensor networks. In: ACIIDS 2009: 1st Asian Conference on Intelligent Information
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Kist, Alexander A. and Harris, Richard J. (2003) Scheme for alternative packet overflow routing (SAPOR). In: 2003 Workshop on High Performance Switching and Routing (HPSR 2003), 24-27 Jun 2003,
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dynamic routing protocols
Zhang, Zhongwei (2009) An intelligent scheme of secure routing for mobile ad hoc networks. In: ICSPCS 2008: 2nd International Conference on Signal Processing and Communication Systems , 15-17 Dec
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dynamic topologies
Kist, Alexander A. and Aldraho, Abdelnour (2011) Dynamic topologies for sustainable and energy efficient traffic routing. Computer Networks, 55 (9). pp. 2271-2288. ISSN 1389-1286
dynamic topology
Aldraho, Abdelnour and Kist, Alexander A. (2010) Enhanced heuristics to reduce power consumption of networks using weight setting. In: 2010 Southern Region Engineering Conference (SREC 2010), 11-12
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dynamical system
Strunin, D. V. (2008) Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet. Bulletin of the Belgian Mathematical Society: Simon Stevin, 15 (5). pp. 935-946. ISSN
dynamical systems
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2007) Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model. Discrete and Continuous Dynamical Systems Series
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Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2006) The dynamics of the vertical structure of turbulence in flood flows. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 48 (CTAC-2). C573-C590. ISSN 1446-8735
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Zhang, Zhongwei and Wang, Zhen (2006) Assessing and assuring trust in e-Commerce systems. In: International Conference on Intelligent Agents, Web Technologies & Internet Commerce (IAWTIC'06), 29 Nov
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Earth atmosphere
McIntyre, T. J. and Khan, R. and Eichmann, T. N. and Upcroft, B. and Buttsworth, D. (2012) Visible and near infrared spectroscopy of Hayabusa re-entry using semi-autonomous tracking. In: 50th AIAA
Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition: Advancing the Science of Flight Technology (AIAA 2012) , 9-12 Jan 2012, Nashville, TN. United States.
earth pressure
Thomas, Caroline and Shiau, Jim S. (2007) Modelling the arching effect in active earth pressure problems. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane,
earth pressures
Shiau, Jim S. and Thomas, Caroline J. and Smith, Catherine A. (2008) A FLAC model for classical earth pressure problems. In: 1st International FLAC/DEM Symposium on Numerical Modeling, 25-27 Aug
2008, Minneapolis, United States.
earth rpessures
Shiau, Jim and Smith, Catherine (2006) Numerical analysis of passive earth pressures with interfaces. In: III European Conference on Computational Mechanics (ECCM 2006), 5-8 June 2006, Lisbon,
East Australia Current
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Cai, W. and Shi, G. and Cowan, T. and Bi, D. and Ribbe, J. (2005) The response of the southern annular mode, the east Australian current, and the southern mid-latitude ocean circulation to global
warming. Geophysical Research Letters, 32 (23). pp. 1-4. ISSN 0094-8276
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2010) An FPGA-based fast two-symbol processing architecture for JPEG 2000 arithmetic coding. In: ICASSP 2010: 35th International Conference on
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eccentric annulus
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annuli. CMES: Computer Modeling in Engineering and Sciences, 83 (3). pp. 275-310. ISSN 1526-1492
echo cancellation
Nguyen-Ky, T. and Leis, J. and Xiang, W. (2010) An improved new error estimation algorithm for optimal filter lengths for stereophonic acoustic echo cancellation. Computers and Electrical
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Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. Technical Report. Joachim Ribbe, Toowoomba, Australia.
Rahimi, Hadi and Ghobadian, Barat and Yusaf, Talal and Najafi, Gholamhasan and Khatamifar, Mahdi (2009) Diesterol: an environment-friendly IC engine fuel. Renewable Energy, 34 (1). pp. 335-342. ISSN
Wen, Peng and Li, Yan (2006) EEG human head modelling based on heterogeneous tissue conductivity. Australasian Physical and Engineering Sciences in Medicine, 29 (3). pp. 235-240. ISSN 0158-9938
effective throughput
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14-17 Dec 2010, Biopolis, Singapore.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Numerical investigation of influence of air and fuel dilution for open furnace MILD combustion burner. In: 2012 Qld Southern Regional
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Eigenvalue tracking
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Ekman layer
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
El Nino
Murphy, Bradley F. and Ribbe, Joachim (2004) Variability of southeast Queensland rainfall and climate indices. International Journal of Climatology, 24 (6). pp. 703-721. ISSN 0899-8418
El Nino Southern Oscillation
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2008) An interpretation of Australian rainfall projections. Geophysical Research Letters, 35 (2). L2072. ISSN 0094-8276
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
elastic plates
Strunin, Dmitry V. (2009) Fluid flow between active elastic plates. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 50. C871-C883. ISSN 1446-1811
Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2010) A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.
International Journal for Numerical Methods in Engineering, 82 (4). pp. 435-463. ISSN 0029-5981
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based Galerkin meshless method. CMES: Computer Modeling in Engineering and Sciences, 66 (1). pp. 25-52.
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Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2008) An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems. In: 8th World Congress on
Computational Mechanics (WCCM8) and ECCOMAS 2008, 30 June - 4 July 2008, Venice, Italy.
elasto-thermo-viscoplastic materials
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2006) A meshless IRBFN-based numerical simulation of adiabatic shear band formation in one dimension. In: 2006 International
Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi Minh City, Vietnam.
Brodie, Lyn and Gibbings, Peter (2011) Connecting learners in virtual space: forming learning communities. In: Creating connections in teaching and learning. Research on Teaching and Learning .
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electric hybrid vehicles
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
electrical conductivity
Randeniya, Lakshman K. and Bendavid, Avi and Martin, Philip J. and Tran, Canh-Dung (2010) Composite yarns of multi-walled carbon nanotubes with metallic electrical conductivity. Small, 6 (16). pp.
1806-1811. ISSN 1613-6810
Ghobadian, Barat and Najafi, Gholamhassan and Rahimi, Hadi and Yusaf, T. F. (2009) Future of renewable energies in Iran. Renewable and Sustainable Energy Reviews, 13 (3). pp. 689-695. ISSN 1364-0321
electro-mechanical problems
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2008) A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures. CMES: Computer Modeling in Engineering and
Sciences, 23 (3). pp. 209-222. ISSN 1526-1492
Nguyen-Van, Hieu and Le, Thong and Mai-Duy, Nam and Tran-Cong, Thanh (2008) Nodal integration finite element techniques for analysis of piezoelectric solids. In: 2008 International Conference on
Computational Solid Mechanics (CSM2008), 27-30 Nov 2008, Ho Chi Minh City, Vietnam.
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2008) A node-based element for analysis of planar piezoelectric structures. CMES: Computer Modeling in Engineering and Sciences, 36 (1). pp.
65-95. ISSN 1526-1492
electro-static field based process
Tran, Canh-Dung and Tran-Cong, Thanh and Le-Cao, K. and Ho-Minh, D. (2012) Processing the CNTs' interaction in web using an electro-static field based process. In: 2012 International Conference on
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electromagnetic waves
Malomed, B. A. and Stepanyants, Y. A. (2010) Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external
potentials. In: ICEAA 2010: International Conference on Electromagnetics in Advanced Applications , 20-24 Sep 2010, Sydney, Australia.
electron concentration
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
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electronic height indicator
Wen, Peng and Kidd, Jason G. (2005) Electronic height indicator for agricultural machines. Australian Journal of Electrical and Electronics Engineering, 2 (1). pp. 13-20. ISSN 1448-837X
electronic nose
Zhao, Weichang and Pinnaduwage, Lal A. and Leis, John W. and Gehl, Anthony C. and Allman, Steve L. and Shepp, Allan and Mahmud, Ken K. (2008) Identification and quantification of components in
ternary vapor mixtures using a microelectromechanical-system-based electronic nose. Journal of Applied Physics, 103 (10). pp. 1-11. ISSN 0021-8979
element-free method
Tran, Canh-Dung and Tran-Cong, Thanh (2004) Element-free simulation of dilute polymeric flows using Brownian configuration fields. Korea-Australia Rheology Journal, 16 (1). pp. 1-15. ISSN 1226-119X
elephant seal
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
elliptic differential equations
Mai-Duy, Nam and Tran-Cong, Thanh (2011) Compact local approximations employed with integrated RBFs for second-order elliptic differential equations. In: 3rd International Symposium on Computational
Mechanics (ISCM III) and 2nd Symposium on Computational Structural Engineering (CSE II), 5-7 Dec 2011, Taipei, Taiwan.
elliptic problems
Mai-Duy, N. and Tran-Cong, T. (2011) Compact local integrated-RBF approximations for second-order elliptic differential problems. Journal of Computational Physics , 230 (12). pp. 4772-4794. ISSN
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A Cartesian-grid integrated-RBF Galerkin technique. In: Recent studies in meshless and other novel computational methods. Tech Science Press,
Duluth, GA. USA, pp. 87-102. ISBN 0-9824205-4-4
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2008) An integral-collocation-based fictitious-domain technique for solving elliptic problems. Communications in Numerical Methods in Engineering,
24 (11). pp. 1291-1314. ISSN 1069-8299
elliptical shapes
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
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ember attack
Hashempour, Javad and Sharifian, Ahmad (2012) Potentials of metal mesh to contain bushfires. In: 2012 Qld Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Sharifian, Ahmad and Buttsworth, David R. (2009) Direct radiation from wildfires through square woven screens. In: ASME 2008: Summer Heat Transfer Conference, 10-14 Aug 2008, Jacksonville, FL. USA.
EMF waveforms
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
emission spectrums
Khan, Razmi and Eichmann, Troy and Buttsworth, David and Upcroft, Ben (2011) Image-based visual servoing for the super-orbital re-entry of Hayabusa spacecraft. In: 2011 Australasian Conference on
Robotics and Automation (ACRA 2011) , 7-9 Dec 2011, Melbourne, Australia.
Bowtell, Les and Kist, Alexander A. and Osbourne, Daniel and Parker, Victoria (2013) Improving clinical practice outcomes for nurses with an interactive emulator. In: 2013 IEEE Global Engineering
Education Conference (EDUCON), 13-15 Mar 2013, Berlin, Germany.
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Outage probability analysis of coded cooperation with multiple relays. In: 2011 IEEE Vehicular Technology Conference: Smarter
Communication for an Intelligent World (VTC 2011-Fall), 5-8 Sept 2011, San Francisco, CA. USA.
encoding techniques
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
end users
Norman, Mark and Leis, John (2010) A passive approach to detection of traffic shaping. In: APSIPA 2010: 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference,
14-17 Dec 2010, Biopolis, Singapore.
end-to-end delay.
Zhang, Zhongwei and Zhou, Hong (2009) Empirical examination of Mobile Ad Hoc Routing Protocols on wireless sensor networks. International Journal of Computer Networks and Communications, 1 (1). pp.
75-87. ISSN 0975-2293
end-to-end SNR
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong and Huang, Tao (2011) Outage analysis of non-regenerative analog network coding for two-way multi-hop networks. IEEE Communications Letters, 15 (6). pp.
662-664. ISSN 1089-7798
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong and Huang, Tao (2011) Outage performance of analog network coding in generalized two-way multi-hop networks. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011) , 28-31 Mar 2011, Cancun, Mexico.
energy consumption
Kist, Alexander A. (2011) Modelling of staged routing for reduced carbon footprints of large server clusters. International Journal of Communication Networks and Distributed Systems, 6 (1). pp.
28-44. ISSN 1754-3916
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
energy efficiency
Aldraho, Abdelnour and Kist, Alexander A. (2012) Enabling energy efficient and resilient networks using dynamic topologies. In: 2012 Sustainable Internet and ICT for Sustainability (SustainIT 2012),
4-5 Oct 2012, Pisa, Italy.
Aldraho, Abdelnour and Kist, Alexander A. and Maxwell, Andrew (2012) Performance investigation of dynamic topologies in MPLS networks. In: International Symposium on Communications and Information
Technologies (ISCIT), 2-5 Oct 2012, Gold Coast, Australia.
Aldraho, Abdelnour and Kist, Alexander A. (2011) Enabling dynamic topologies in communication networks. In: ATNAC 2011: Australian Telecommunication Networks and Applications Conference, 9-11 Nov
2011, Melbourne, Australia.
Kist, Alexander A. (2011) Modelling of staged routing for reduced carbon footprints of large server clusters. International Journal of Communication Networks and Distributed Systems, 6 (1). pp.
28-44. ISSN 1754-3916
energy efficient computing
Kist, Alexander A. (2011) Modelling of staged routing for reduced carbon footprints of large server clusters. International Journal of Communication Networks and Distributed Systems, 6 (1). pp.
28-44. ISSN 1754-3916
energy efficient networking
Kist, Alexander A. and Aldraho, Abdelnour (2011) Dynamic topologies for sustainable and energy efficient traffic routing. Computer Networks, 55 (9). pp. 2271-2288. ISSN 1389-1286
energy efficient computing
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
energy security
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2014) MILD combustion: the future for lean and clean combustion technology. International Review of Mechanical Engineering , 8 (1). pp. 251-257.
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Yusaf, Talal and Noor, M. M. and Wandel, Andrew P. (2013) Mild combustion: the future for lean and clean combustion. In: 2nd International Conference of Mechanical Engineering Research (ICMER 2013):
Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Al-lwayzy, Saddam H. (2012) Alternative fuels from microalgae for diesel engine. In: USQ Combustion Meeting, 10 Oct 2012, Toowoomba, Australia. (Unpublished)
Hairuddin, A. Aziz and Yusaf, Talal F. and Wandel, Andrew P. (2012) HCCI engine: numerical and experimental approach. In: USQ Combustion Meeting, 26 Sep 2012, Toowoomba, Australia. (Unpublished)
engine heat transfer measurements
Buttsworth, David R. (2002) Transient response of an erodable heat flux gauge using finite element analysis. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile
Engineering, 216 (8). pp. 701-716. ISSN 0954-4070
engine life
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
engine operations
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
engine performance
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
Najafi, Gholamhassan and Yusaf, Talal (2009) Experimental investigation of using methanol-diesel blended fuels in diesel engine. In: 4th International Conference on Thermal Engineering Theory and
Applications, 12-14 Jan 2009, Abu Dhabi, UAE.
engine speed
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
Wandel, Andrew P. (2010) Linkages between courses: a holistic approach to programmes. In: AaeE 2010: Past, Present, Future - the 'Keys' to Engineering Education Research and Practice, 5-8 Dec 2010,
Sydney, Australia.
Zhu, SongPing and Strunin, Dmitry V. (2001) Modelling the confinement of spilled oil with floating booms. Applied Mathematical Modelling, 25 (9). pp. 713-729. ISSN 0307-904X
engineering specification
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
ensemble decision tree
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) A robust ensemble classification method analysis. In: 2009 International Conference on Bioinformatics and Computational Biology ,
13-16 Jul 2009, Las Vegas, NV. United States.
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2008) An interpretation of Australian rainfall projections. Geophysical Research Letters, 35 (2). L2072. ISSN 0094-8276
Buttsworth, David R. and Goozee, Richard J. and Jacobs, Peter A. (2006) Measurement and simulation of the interface in a low-enthalpy shock tunnel. In: 14th International Space Planes and Hypersonic
Systems and Technologies Conference (AIAA/AHI 2006), 6-9 Nov 2006, Canberra, Australia.
entrance restriction
Mohammed, H. and Yusaf, T. and Salman, Y. (2006) Experimental investigation of free convection heat transfer with entrance restriction placed at top of a vertical circular tube. In: 8th Biennial ASME
Conference on Engineering Systems Design and Analysis (ESDA 2006), 4-7 Jul 2006, Torino, Italy.
environment management
Zhou, Hong and Wu, Huayi (2009) The integration of wireless sensor networks, remote sensing and geographic information systems for autonomous environmental and animal monitoring. In: IADIS
International Conference on Applied Computing 2009 (IADIS 2009), 19-21 Nov 2009, Rome, Italy.
environment monitoring
Zhou, Hong and Qi, Haixia and Banhazi, Thomas and Low, Tobias (2013) An integrated WSN and mobile robot system for agriculture and environment applications. In: MOBIQUITOUS 2013, 10th International
Conference on Mobile and Ubiquitous Systems: Computing, Networking and Services, 2-4 Dec 2013, Tokyo, Japan.
environmental data
Wang, Gengkun and Xiang, Wei and Chen, Haoyu and Wen, Peng (2011) Wireless sensor home automation networks based upon Sun SPOT. In: ICSSC 2011: IET International Conference on Smart and Sustainable
City (IET ICSSC2011), 6-8 Jul 2011, Shanghai, China.
epoxy material
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
Mai-Duy, N. and Mai-Cao, L. and Tran-Cong, T. (2006) A new meshless RBF-based method for unsteady fluid flow analysis. In: Advances in meshless methods. Tech Science Press, USA, pp. 241-262. ISBN
equivalence ratios
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
ergodic capacity
Long, Hang and Kim, Kyeong Jin and Xiang, Wei and Shen, Shanshan and Zheng, Kan and Wang, Wenbo (2012) Improved wideband precoding with arbitrary subcarrier grouping in MIMO-OFDM systems. ETRI
Journal, 34 (1). pp. 9-16. ISSN 1225-6463
erodable thermocouple
Buttsworth, David R. (2002) Transient response of an erodable heat flux gauge using finite element analysis. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile
Engineering, 216 (8). pp. 701-716. ISSN 0954-4070
Buttsworth, David R. and Stevens, Robert and Stone, C. Richard (2005) Eroding ribbon thermocouples: impulse response and transient heat flux analysis. Measurement Science and Technology, 16 (7). pp.
1487-1494. ISSN 0957-0233
Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768
error correction codes
Sileh, Ibrahim Khalil and Alajel, Khalid Mohamed and Xiang, Wei (2011) Cooperative relay selection based UEP scheme for 3D video transmission over Rayleigh fading channel. In: 2011 International
Conference on Digital Image Computing: Techniques and Application (DICTA 2011), 6-8 Dec 2011, Noosa, Australia .
error estimate
Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768
error estimate algorithm
Nguyen-Ky, T. and Leis, J. and Xiang, W. (2010) An improved new error estimation algorithm for optimal filter lengths for stereophonic acoustic echo cancellation. Computers and Electrical
Engineering, 36 (4). pp. 664-675. ISSN 0045-7906
Nguyen-Ky, Tai and Leis, John W. and Xiang, Wei (2007) An improved error estimation algorithm for stereophonic acoustic echo cancellation systems. In: ICSPCS 2007: 1st International Conference on
Signal Processing and Communication Systems, 17-19 Dec 2007, Gold Coast, Australia.
error protection
Alajel, Khalid Mohamed and Xiang, Wei (2013) A new hierarchical 16-QAM-based UEP scheme for 3-D video with depth image–based rendering. In: Advanced video communications over wireless networks.
Taylor & Francis (CRC Press), Boca Raton, FL. United States, pp. 355-382. ISBN 978-1-4398-7998-6
error resilience
Alajel, Khalid and Xiang, Wei and Sileh, Ibrahim (2012) Color plus depth 3-D video transmission with hierarchical 16-QAM. In: 6th International Conference on Signal Processing and Communication
Systems (ICSPCS 2012) , 12-14 Dec 2012, Gold Coast, Australia.
Alajel, Khalid Mohamed and Xiang, Wei (2012) Color plus depth 3-D video transmission with heirarchical 16-QAM. In: 3DTV-CON 2012: The True Vision: Capture, Transmission and Display of 3D Video, 15-17
Oct 2012, Zurich, Switzerland.
Xiang, Wei and Clemence, Andrew and Leis, John and Wang, Yafeng (2009) Error resilience analysis of wireless image transmission using JPEG, JPEG 2000 and JPWL. In: ICICS 2009: 7th International
Conference on Information, Communications and Signal Processing, 8-10 Dec 2009, Macau, China.
estimation theory
Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768
Ribbe, Joachim and Wolff, Jorg-Olaf and Staneva, Joanna and Grawe, Ulf (2008) Assessing water renewal time scales for marine environments from three-dimensional modelling: a case study for Hervey
Bay, Australia. Environmental Modelling and Software, 23 (10-11). pp. 1217-1228. ISSN 1364-8152
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
estuarine dynamics
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
Euler's numbers
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2008) Numerical simulation of inviscid transient flows in shock tube and its validations. In: ICFM 2008: 5th International Conference on Fluid
Mechanics, 12-14 Sep 2008, Heidelberg, Germany.
Buttsworth, D. R. and Davison, C. and MacLeod, J. D. and Strapp, J. W. (2007) Evaporator design for an isokinetic total water content probe in a naturally aspirating configuration. In: 16th
Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
evolution equation
Stepanyants, Yury (2005) Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons. Proceedings of the Russian Academy of Engineering Sciences Series: Applied
Mathematics and Mechanics, 14. pp. 33-40.
exact solution
Stepanyants, Yury A. and Yeoh, Guan H. (2010) Nanoparticle dynamics in a viscous fluid at small Reynolds numbers. In: 6th Australasian Congress on Applied Mechanics (ACAM 6), 12-15 Dec 2010, Perth,
Western Australia.
exact solutions
Malomed, B. A. and Stepanyants, Y. A. (2010) Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external
potentials. In: ICEAA 2010: International Conference on Electromagnetics in Advanced Applications , 20-24 Sep 2010, Sydney, Australia.
exhaust emission
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
exhaust gas re-circulation (EGR)
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2012) A review of mild combustion and open furnace design consideration. International Journal of Automotive and Mechanical Engineering, 6 (1). pp.
730-754. ISSN 2229-8649
exhaust gas recirculation
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. (2013) Design and development of mild combustion burner. Journal of Mechanical Engineering and Sciences, 5. pp. 662-676. ISSN 2289-4659
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The air fuel ratio study for the mixture of biogas and hydrogen on mild combustion. In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5
Jul 2013, Sydney, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The study of air fuel ratio for open furnace MILD combustion of biogas on bluff-body burner. In: 2012 Qld Southern Regional Engineering
Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The modelling of the effect of air fuel ratio on unburned hydrocarbons for MILD combustion. In: 2nd Malaysian Postgraduate Conference (MPC
2012), 7-9 July 2012, Gold Coast, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) A preliminary study of control parameters for open furnace mild combustion using CFD. In: 2nd Malaysian Postgraduate Conference (MPC 2012),
7-9 July 2012, Gold Coast, Australia.
exhausts gas recirculation
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Numerical investigation of influence of air and fuel dilution for open furnace MILD combustion burner. In: 2012 Qld Southern Regional
Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
expansion tube
Buttsworth, David and Jacobs, Peter and Potter, Daniel and Mudford, Neil and D'Souza, Mary and Eichmann, Troy and Jenniskens, Peter and McIntyre, Tim and Jokic, Michael and Jacobs, Carolyn and
Upcroft, Ben and Khan, Razmi and Porat, Hadas and Neely, Andrew and Lohle, Stefan (2012) Super-orbital re-entry in Australia: laboratory measurement, simulation and flight observation [Keynote
lecture]. In: ISSW28: 28th International Symposium on Shock Waves, 17-22 Jul 2011, Manchester, United Kingdom.
expansion tubes
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
3 Oct 2008, Heraklion, Greece.
experimental data
Phillips, D. G. and Tran, Canh-Dung and Fraser, W. B. and van der Heijden, G. H. M. (2010) Torsional properties of staple fibre plied yarns. Journal of the Textile Institute, 101 (7). pp. 595-612.
ISSN 0040-5000
experimental free convection
Mohammed, H. and Yusaf, T. and Salman, Y. (2006) Experimental investigation of free convection heat transfer with entrance restriction placed at top of a vertical circular tube. In: 8th Biennial ASME
Conference on Engineering Systems Design and Analysis (ESDA 2006), 4-7 Jul 2006, Torino, Italy.
experimental setup
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. (2013) Design and development of mild combustion burner. Journal of Mechanical Engineering and Sciences, 5. pp. 662-676. ISSN 2289-4659
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The development of MILD combustion open burner experimental setup. In: 2nd International Conference of Mechanical Engineering Research (ICMER
2013): Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Buttsworth, David R. and Malpress, Ray (2009) Student views on hardware-based problem solving activities for external and on-campus teams. In: AaeE 2009: Engineering the Curriculum, 6-9 Dec 2009,
Adelaide, Australia.
Chan, Auc Fai and Leis, John (2010) Median filtering simulation of bursty traffic. In: ICSPCS 2010: 4th International Conference on Signal Processing and Communication Systems, 13-15 Dec 2010, Gold
Coast, Australia.
extended finite element method
Bordas, Stephane and Duflot, Marc and Le, Phong (2008) A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24 (11). pp. 961-971. ISSN 1069-8299
extended Hamilton-Jacobi equation
Strunin, D. V. (2008) Two-dimensional particle solution of the extended Hamilton-Jacobi equation. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 50. C282-C291.
ISSN 1446-8735
external systems
Wang, Gengkun and Xiang, Wei and Chen, Haoyu and Wen, Peng (2011) Wireless sensor home automation networks based upon Sun SPOT. In: ICSSC 2011: IET International Conference on Smart and Sustainable
City (IET ICSSC2011), 6-8 Jul 2011, Shanghai, China.
Wandel, Andrew P. and Lindstedt, R. Peter (2013) Hybrid multiple mapping conditioning modeling of local extinction. Proceedings of the Combustion Institute, 34 (1). pp. 1365-1372. ISSN 1540-7489
extinction predictor
Wandel, Andrew P. (2013) Extinction predictors in turbulent sprays. Proceedings of the Combustion Institute, 34 (1). pp. 1625-1632. ISSN 1540-7489
facility simulation
Buttsworth, David R. and Jacobs, Peter A. and Jones, Terry V. (2002) Simulation of Oxford University gun tunnel performance using a quasi-one-dimensional model. Shock Waves, 11 (5). pp. 377-383. ISSN
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Outage probability analysis of coded cooperation with multiple relays. In: 2011 IEEE Vehicular Technology Conference: Smarter
Communication for an Intelligent World (VTC 2011-Fall), 5-8 Sept 2011, San Francisco, CA. USA.
Sileh, Ibrahim Khalil and Alajel, Khalid Mohamed and Xiang, Wei (2011) Cooperative relay selection based UEP scheme for 3D video transmission over Rayleigh fading channel. In: 2011 International
Conference on Digital Image Computing: Techniques and Application (DICTA 2011), 6-8 Dec 2011, Noosa, Australia .
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
fading channels
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Performance analysis for coded cooperative multiple-relay in distributed turbo channels. In: IEEE 22nd International Symposium on
Personal Indoor and Mobile Radio Communications (PIMRC 2011), 11-14 Sep 2011, Toronto, Canada.
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
fairness performance
Ma, Zhangchao and Xiang, Wei and Long, Hang and Wang, Wenbo (2011) Proportional fair resource partition for LTE-advanced networks with Type I relay nodes. In: ICC 2011: Source of Innovation: Back to
the Origin, 5-9 Jun 2011 , Kyoto, Japan.
farming systems
Donald, Alexis and Meinke, Holger and Power, Brendan and Maia, Aline de H. N. and Wheeler, Matthew and Stone, Roger C. and Ribbe, Joachim and White, Neil (2006) Near-global impact of the
Madden-Julian Oscillation on rainfall. Geophysical Research Letters, 33 (9). L09704. ISSN 0094-8276
fast response
Buttsworth, David R. and Stevens, Robert and Stone, C. Richard (2005) Eroding ribbon thermocouples: impulse response and transient heat flux analysis. Measurement Science and Technology, 16 (7). pp.
1487-1494. ISSN 0957-0233
fatty acids
Wardana, I. N. G. (2012) Burning characteristics of coconut oil In micro-combustor. In: USQ Combustion Meeting, 26 Nov 2012, Toowoomba, Australia.
feed forward neural networks
Tran, Canh-Dung and Phillips, David G. (2007) Predicting torque of worsted singles yarn using an efficient radial basis function network-based method. Journal of The Textile Institute, 98 (5). pp.
387-396. ISSN 0040-5000
Roberts, Tony (2008) The style files: teach explicit skills with feedback. Gazette of the Australian Mathematical Society, 35 (3). pp. 156-157. ISSN 0311-0729
feedback systems
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
Ghabraie, Behrooz and Ren, Gang and Ghabraie, Kazem and Xie, Yi Min (2013) A study on truss bolt mechanism in controlling stability of underground excavation and cutter roof failure. Geotechnical and
Geological Engineering, 31 (2). pp. 667-682. ISSN 0960-3182
Ghabraie, Behrooz and Ren, Gang and Ghabraie, Kazem (2013) Effects of thickness of roof layers on optimum design of truss bolt system using finite element modeling techniques. Electronic Journal of
Geotechnical Engineering, 13 (A). pp. 147-158.
Suslov, Sergey A. and Bozhko, Alexandra A. and Putin, Gennady F. (2008) Thermo-magneto-convective instabilities in a vertical layer of ferro-magnetic fluid. In: XXXVI International Conference
Advanced Problems in Mechanics, 6-10 Jul 2008, Repino, Russia.
Bozhko, Alexandra A. and Suslov, Sergey A. and Putin, Gennady F. (2008) Magneto-hydrodynamic interaction in a vertical slot filled with ferrofluid. In: 7th PAMIR International Conference on
Fundamental and Applied MHD, 8-12 Sept 2008, Presqu´île de Giens - France.
ferromagnetic fluid
Suslov, Sergey A. (2008) Thermo-magnetic convection in a vertical layer of ferromagnetic fluid. Physics of Fluids, 20 (8). 084101-084118. ISSN 1070-6631
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
Kittipoomwong, Prakorn and See, Howard and Mai-Duy, Nam (2010) Dynamic simulation of non-spherical particulate suspensions. Rheologica Acta, 49 (6). pp. 597-606. ISSN 0035-4511
fibre diameter
Phillips, D. G. and Tran, Canh-Dung and Fraser, W. B. and van der Heijden, G. H. M. (2010) Torsional properties of staple fibre plied yarns. Journal of the Textile Institute, 101 (7). pp. 595-612.
ISSN 0040-5000
fibre optic
Sharifian, S. Ahmad and Buttsworth, David R. (2007) Evaluation of glued-diaphragm fibre optic pressure sensors in a shock tube. Shock Waves, 16 (3). pp. 189-197. ISSN 0938-1287
fibre optic pressure transducer
Sharifian, Ahmad and Watson, Stuart and Buttsworth, David R. and Barton, James (2007) Modelling the static thermal sensitivity of diaphragm-based fibre optic pressure sensors. In: 8th Australasian
Heat and Mass Transfer Conference, 26-29 July 2005, Curtin University of Technology, Perth, Western Australia.
fictitious domains
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2009) A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical
Modelling, 33 (1). pp. 284-299. ISSN 0307-904X
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2008) An integral-collocation-based fictitious-domain technique for solving elliptic problems. Communications in Numerical Methods in Engineering,
24 (11). pp. 1291-1314. ISSN 1069-8299
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A RBF-based fictitious-domain technique for Dirichlet boundary value problems in multiply-connected domains. In: 3rd Asian-Pacific Congress on Computational
Mechanics (APCOM'07) and EPMESC XI, 3-6 Dec 2007, Kyoto, Japan.
field of views
Khan, Razmi and Eichmann, Troy and Buttsworth, David and Upcroft, Ben (2011) Image-based visual servoing for the super-orbital re-entry of Hayabusa spacecraft. In: 2011 Australasian Conference on
Robotics and Automation (ACRA 2011) , 7-9 Dec 2011, Melbourne, Australia.
filter length
Nguyen-Ky, T. and Leis, J. and Xiang, W. (2010) An improved new error estimation algorithm for optimal filter lengths for stereophonic acoustic echo cancellation. Computers and Electrical
Engineering, 36 (4). pp. 664-675. ISSN 0045-7906
fine structures
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
finite difference
Thomas, Caroline and Shiau, Jim S. (2007) Modelling the arching effect in active earth pressure problems. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane,
finite difference method
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Discretization of three dimensional non-uniform grid: conditional moment closure elliptic equation using finite difference method. In: 3rd
Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
finite difference models
Roberts, A. J. (2003) A holistic finite difference approach models linear dynamics consistently. Mathematics of Computation, 72 (241). pp. 247-262. ISSN 0025-5718
finite difference time domain (FDTD)
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
finite different method
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2011) Implementation of conditional moment closure using the Taylor expansion and finite differences. In: 1st International
Conference of Mechanical Engineering Research (ICMER 2011), 5-8 Dec 2011, Kuantan, Malaysia.
finite domain solution
Langlands, T. A. M. and Henry, B. I. and Wearne, S. L. (2011) Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions. SIAM Journal on Applied
Mathematics, 71 (4). pp. 1168-1203. ISSN 0036-1399
finite element method
Ghabraie, B. and Ren, G. and Xie, Y. M. and Ghabraie, K. (2012) Study of truss bolt system for highly stressed rock mass using finite element modelling techniques. In: 11th Australia New Zealand
Conference on Geomechanics: Ground Engineering in a Changing World, 15-18 July 2012, Melbourne, Australia.
finite element simulation
Genet, Martin and Yan, Wenyi and Tran-Cong, Thanh (2009) Investigation of a hydraulic impact: a technology in rock breaking. Archive of Applied Mechanics, 79 (9). pp. 825-841. ISSN 0939-1533
finite element technique
Shiau, Jim S. (2011) A shakedown limit under Hertz contact pressure. In: 2011 International Conference on Advanced Engineering Materials and Technology (AEMT 2011), 29-31 Jul 2011, Sanya, China.
finite elements
Shiau, J. S. and Merifield, R. S. and Lyamin, A. V. and Sloan, S. W. (2011) Undrained stability of footings on slopes. International Journal of Geomechanics, 11 (5). pp. 381-390. ISSN 1532-3641
Shiau, Jim S. and Augarde, Charles E. and Lyamin, Andrei V. and Sloan, Scott W. (2008) Finite element limit analysis of passive earth resistance in cohesionless soils. Soils and Foundations, 48 (6).
pp. 843-850. ISSN 0038-0806
finite point method
Tran, Canh-Dung and Tran-Cong, Thanh (2004) Element-free simulation of dilute polymeric flows using Brownian configuration fields. Korea-Australia Rheology Journal, 16 (1). pp. 1-15. ISSN 1226-119X
finite volume method
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A finite-volume method based on compact local integrated radial basis function approximations for second-order differential
problems. CMES Computer Modeling in Engineering and Sciences, 91 (6). pp. 485-516. ISSN 1526-1492
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems. In: 4th
International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
finite-difference time-domain (FDTD)
Ziri-Castro, Karla and Scanlon, William and Evans, Noel (2004) Indoor radio channel characterization and modeling for a 5.2-GHz bodyworn receiver. IEEE Antennas and Wireless Propagation Letters, 3
(1). pp. 219-222. ISSN 1536-1225
Hashempour, Javad and Sharifian, Ahmad (2013) Optimizing the coupling of a firebrand generator to a horizontal wind tunnel. In: 2nd International Conference on Energy and Environmental Protection
(ICEEP 2013), 19-21 Apr 2013, Guilin, China.
first order system
Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2010) A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.
International Journal for Numerical Methods in Engineering, 82 (4). pp. 435-463. ISSN 0029-5981
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
first-order shear deformation theory
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2009) An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis. CMES: Computer Modeling in
Engineering and Sciences, 49 (2). pp. 81-110. ISSN 1526-1492
Nguyen-Van, H. and Mai-Duy, N. and Tran-Cong, T. (2008) Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element. Journal of
Sound and Vibration, 313 (1-2). pp. 205-223. ISSN 0022-460X
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2007) A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates. CMC: Computers, Materials
and Continua, 6 (3). pp. 159-176. ISSN 1546-2218
Shiau, Jim and Al Abri, Mohammed (2011) A study on the failure mechanisms of horizontal plate anchors in clay. In: ICAGE 2011: International Conference on Advances in Geotechnical Engineering, 7-9
Nov 2011, Perth, Western Australia.
Shiau, J. S. and Hobson, M. A. (2011) Modeling uplift of plate anchor. In: Continuum and Distinct Element Numerical Modeling in Geomechanics, 14-16 Feb 2011, Melbourne, Australia.
Shiau, J. S. and Watson, J. F. (2008) 3D bearing capacity of shallow foundations located near deep excavation sites. In: 2008 International Conference on Deep Excavation: Challenges Risk Management
of Underground Construction (ICDE 2008), 10-12 Nov 2008, Singapore.
Shiau, Jim S. and Thomas, Caroline J. and Smith, Catherine A. (2008) A FLAC model for classical earth pressure problems. In: 1st International FLAC/DEM Symposium on Numerical Modeling, 25-27 Aug
2008, Minneapolis, United States.
Shiau, Jim S. and Watson, Joshua F. and Smith, C. A. (2008) Foundation located near slope: a FLAC study. In: 1st International FLAC/DEM Symposium on Numerical Modeling, 25-27 Aug 2008, Minneapolis,
Smith, Catherine and Shiau, Jim S. (2007) Bearing capacity of footings near slopes. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2012) A review of mild combustion and open furnace design consideration. International Journal of Automotive and Mechanical Engineering, 6 (1). pp.
730-754. ISSN 2229-8649
flat shell
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2009) An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis. CMES: Computer Modeling in
Engineering and Sciences, 49 (2). pp. 81-110. ISSN 1526-1492
flight speed
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
flow based networking
Kist, Alexander A. and Lloyd-Smith, Bill (2008) Internet pooling: routing for load distribution in access networks. In: ATNAC 2007: Next Generation Networks: Enabling Closer International
Cooperation, 2-5 Dec 2007, Christchurch, New Zealand.
Kist, Alexander A. (2005) A flow blocking model for IP overflow traffic. In: 11th Asia-Pacific Conference on Communications, 3-5 Oct 2005, Perth, Australia.
flow blockage
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
flow characteristic
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
flow condition
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
flow density
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
3 Oct 2008, Heraklion, Greece.
flow problems
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
flow-aware networking
Kist, Alexander A. (2007) Erlang B as a performance model for IP flows. In: ICON 2007: 15th IEEE International Conference on Networks, 19-21 Nov 2007, Adelaide, Australia.
flow-based networking
Kist, Alexander A. and Lloyd-Smith, Bill and Harris, Richard J. (2005) A simple IP flow blocking model. In: 19th International Teletraffic Congress (ITC19), 29 August - 2 Sept. 2005, Beijing, China.
Buttsworth, David R. and Jones, Terry V. (2004) Transient temperature probe measurements in a Mach 4 nitrogen jet. Experiments in Fluids, 37 (1). pp. 137-145. ISSN 0723-4864
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
Jin, Lu and Zhang, Zhongwei and Zhou, Hong (2006) Performance comparison of the AODV, SAODV and FLSL routing protocols in mobile ad hoc networks. In: 5th Workshop on the Internet, Telecommunications
and Signal Processing (WITSP2006), 11-13 Dec 2006, Hobart, Australia.
Fluent (software)
Mossad, Ruth and Yang, William and Schwarz, M. Philip (2009) Numerical prediction of air flow in a sharp 90 degree elbow. In: 7th International Conference on Computational Fluid Mechanics in the
Minerals and Process Industries (CFD2009), 9-11 Dec 2009, Melbourne, Australia.
fluent tunnel wave
Al-Falahi, Amir and Yusaf, T. and Yusoff, M. Z. (2007) Experimental and CFD study of the effects of design parameters on Reynolds number in a short duration hypersonic test facility. In: EPMESC X:
Enhancement and Promotion of Computational Methods in Engineering and Science X, 21-23 Aug 2006, Sanya, China.
Mai-Duy, N. and Mai-Cao, L. and Tran-Cong, T. (2006) A new meshless RBF-based method for unsteady fluid flow analysis. In: Advances in meshless methods. Tech Science Press, USA, pp. 241-262. ISBN
fluid dynamics
Deo, Ravinesh C. and Nathan, Graham J. and Mi, Jianchun (2013) Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers. Physics of
Fluids, 25 (1). 015115-1. ISSN 1070-6631
Strunin, Dmitry V. (2011) A model of turbulent dispersion through roughness layer using centre manifolds. In: 6th AIAA Theoretical Fluid Mechanics Conference, 27-30 Jun 2011, Honolulu, HI. United
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2008) Numerical simulation of inviscid transient flows in shock tube and its validations. In: ICFM 2008: 5th International Conference on Fluid
Mechanics, 12-14 Sep 2008, Heidelberg, Germany.
fluid flow
Strunin, Dmitry V. (2009) Fluid flow between active elastic plates. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 50. C871-C883. ISSN 1446-1811
fluid flow problems
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2010) A new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems. In: 9th World Congress on Computational
Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Mai-Duy, Nam and Mai-Cao, Lan and Tran-Cong, Thanh (2007) Computation of transient viscous flows using indirect radial basis function networks. CMES: Computer Modeling in Engineering and Sciences, 18
(1). pp. 59-78. ISSN 1526-1492
fluid mechanics
Roberts, A. J. (2003) Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics. In: Nonlinear dynamics from lasers to butterflies: selected lectures from the 15th
Canberra International Physics Summer School. Lecture Notes in Complex Systems (1). World Scientific, pp. 257-313. ISBN 9789812791252
fluid rotation
Ostrovsky, Lev and Stepanyants, Yury (2005) Internal solitons in laboratory experiments: Comparison with theoretical models. Chaos, 15 (037111). 037111-1. ISSN 1054-1500
fluid-structure interaction
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis. CMES:
Computer Modeling in Engineering and Sciences, 83 (5). pp. 459-498. ISSN 1526-1492
Ribbe, Joachim and Wolff, Jorg-Olaf and Staneva, Joanna and Grawe, Ulf (2008) Assessing water renewal time scales for marine environments from three-dimensional modelling: a case study for Hervey
Bay, Australia. Environmental Modelling and Software, 23 (10-11). pp. 1217-1228. ISSN 1364-8152
focused-ion-beam system
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
fokker-planck equation
Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.
Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Numerical solution of Fokker-Planck equation using the integral radial basis function networks. In: 10th World Congress on Computational Mechanics
(WCCM 2012), 8-13 July 2012, Sao Paulo, Brazil.
Fokker-Plank equation
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
Shiau, J. S. and Merifield, R. S. and Lyamin, A. V. and Sloan, S. W. (2011) Undrained stability of footings on slopes. International Journal of Geomechanics, 11 (5). pp. 381-390. ISSN 1532-3641
Shiau, Jim S. and Watson, Joshua F. and Smith, C. A. (2008) Foundation located near slope: a FLAC study. In: 1st International FLAC/DEM Symposium on Numerical Modeling, 25-27 Aug 2008, Minneapolis,
Shiau, Jim S. and Watson, Joshua Francis and Arnold, Matthew David (2008) Numerical study of a shallow foundation located near 45 degree slopes. In: ASEM 2008: 4th International Conference on
Advances in Structural Engineering and Mechanics , 26-28 May 2008, Jeju, Korea.
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
Tran, Canh-Dung (2013) Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications. In: Nanotube superfiber materials: changing engineering design. Elsevier, Oxford,
United Kingdom, pp. 211-242. ISBN 978-1-4557-7863-8
forced termination probability
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Goodput and channel allocation in opportunistic spectrum access networks. In: PIMRC 2009: 20th IEEE International Symposium on
Personal, Indoor and Mobile Radio Communications, 13-16 Sep 2009, Tokyo, Japan.
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Throughput and proportional fairness in cognitive radio networks. In: ATC 2009: 2nd International Conference on Advanced
Technologies for Communications, 12-14 Oct 2009, Hai Phong, Vietnam.
Zhou, Hong and Su, Gang and Li, Guofang (2011) Forecasting daily gas load with OIHF-Elman neural network. In: 2nd International Conference on Ambient Systems, Networks and Technologies (ANT 2011) ,
19-21 Sep 2011, Niagara Falls, ON. Canada.
Donald, Alexis and Meinke, Holger and Power, Brendan and Maia, Aline de H. N. and Wheeler, Matthew and Stone, Roger C. and Ribbe, Joachim and White, Neil (2006) Near-global impact of the
Madden-Julian Oscillation on rainfall. Geophysical Research Letters, 33 (9). L09704. ISSN 0094-8276
Donald, Alexis and Ribbe, Joachim and Stone, Roger and Meinke, Holger and Harris, Graham and Power, Brendan and Wheeler, Matthew (2003) The influence of the Madden Julian Oscillation on Queensland's
rainfall. In: 15th Australian New Zealand Climate Forum, 19-21 Mar 2003, Palmerston, New Zealand.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Discretization of three dimensional non-uniform grid: conditional moment closure elliptic equation using finite difference method. In: 3rd
Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2012) Modelling of non-premixed turbulent combustion of hydrogen using conditional moment closure method. IOP Conference
Series: Materials Science and Engineering, 36 (012036). pp. 1-17. ISSN 1757-899X
Smith, Catherine and Shiau, Jim S. (2007) Bearing capacity of footings near slopes. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane, Australia.
Fourier law
Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2002) Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models. Computational Mechanics, 29
(1). pp. 16-26. ISSN 0178-7675
Fourier transform infrared spectrometry
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2012) Two-symbol FPGA architecture for fast arithmetic encoding in JPEG 2000. Journal of Signal Processing Systems, 69 (2). pp. 213-224. ISSN
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2010) An FPGA-based fast two-symbol processing architecture for JPEG 2000 arithmetic coding. In: ICASSP 2010: 35th International Conference on
Acoustics, Speech, and Signal Processing, 14-19 Mar 2010, Dallas, TX. USA.
fractal dimension
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
fractal landscape
Tremblay, Yann and Roberts, Antony J. and Costa, Daniel P. (2007) Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Journal of Experimental Biology,
210. pp. 935-945. ISSN 0022-0949
fractional calculus
Langlands, T. A. M. and Henry, B. I. (2010) Fractional chemotaxis diffusion equations. Physical Review E: Statistical Nonlinear and Soft Matter Physics, 81 (5). pp. 1-12. ISSN 1539-3755
Henry, B. I. and Langlands, Trevor and Straka, P. (2010) An introduction to fractional diffusion. In: Proceedings of the 22nd Canberra International Physics Summer School, 8-19 Dec 2008, Canberra,
fractional derivative
Langlands, T. A. M. and Henry, B. I. and Wearne, S. L. (2011) Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions. SIAM Journal on Applied
Mathematics, 71 (4). pp. 1168-1203. ISSN 0036-1399
fractional Fokker-Planck equation
Henry, B. I. and Langlands, T. A. M. and Straka, P. (2010) Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces. Physical Review Letters, 105 (17).
17062-1-170602-4. ISSN 0031-9007
fracture (delamination) toughness
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Mode II delamination toughness of z-pinned laminates. Composites Science and Technology, 64 (13-14). pp. 1937-1945. ISSN 0266-3538
fracture toughness
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2003) Numerical study on the mode I delamination toughness of z-pinned laminates. Composites Science and Technology, 63 (10). pp. 1481-1493. ISSN
free jets
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
free piston
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
free piston compression
Buttsworth, David R. (2002) Heat transfer during transient compression: measurements and simulations. Shock Waves, 12 (1). pp. 87-91. ISSN 0938-1287
free turbulent jet
Strunin, D. V. (2007) Universal regimes of a free turbulent jet. In: 16th Australasian Fluid Mechanics Conference (AFMC 2007), 2-7 Dec 2007, Gold Coast, Australia.
free vibration
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method. Computers and
Structures, 89 (1-2). pp. 1-13. ISSN 0045-7949
Nguyen-Van, H. and Mai-Duy, N. and Tran-Cong, T. (2008) Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element. Journal of
Sound and Vibration, 313 (1-2). pp. 205-223. ISSN 0022-460X
free-flying projectile
Chong, Albert K. and Buttsworth, David and Mudford, Neil and Jokic, Michael and Balage, Sudantha and O'Bryne, Sean (2012) Application of photogrammetry at USQ hypersonic wind tunnel. In: 11th
Australian Space Science Conference (ASSC 2011) , 26-29 Sep 2011, Canberra, Australia.
free-piston compressor
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2009) An experimental evaluation of shock wave strength and peak pressure in a conventional shock tube and a free-piston compressor. In: IMECE 2008:
ASME International Mechanical Engineering Congress and Exposition, 31 Oct-6 Nov 2008, Boston, MA, USA.
free-piston gun-tunnel
Zakaria, S. and Yusaf, T. and Yusoff, M. Z. (2006) Flow and transient heat transfer in a high speed free piston tunnel: CFD simulations on turbulent and laminar flow conditions. In: 2nd International
Conference on Thermal Engineering Theory and Applications (ICTEA '06), 3-6 Jan 2006, Al Ain, United Arab Emirates.
free-piston tunnel
Al-Falahi, Amir and Yusoff, Mohd. Zamri bin and Yusaf, Talal (2008) Development of a short duration hypersonic test facility at Universiti Tenaga Nasional. Institution of Engineers, Malaysia.
Journal, 69 (1). pp. 19-25. ISSN 0126-513X
frequency division multiplexing
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
frequency response
Xiang, Wei and Pietrobon, Steven S. (2003) On the capacity and normalisation of ISI channels. In: 2003 IEEE International Conference on Communications (ICC2003), 11-15 May 2003, Anchorage, Alaska,
friction heat transfer
Yousif, B. F. and El-Tayeb, N. S. M. and Yusaf, Talal (2006) The effects of load and velocity on friction and interface temperature of CGRP sliding against smooth stainless steel. In: 8th Biennial
ASME Conference on Engineering Systems Design and Analysis, 4-7 July 2006, Italy.
front capturing
Mai-Cao, L. and Tran-Cong, T. (2012) A new IRBFN scheme for the numerical simulation of interfacial flows. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold
Coast, Australia.
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Analysis of laminated composite plate/shell structures using a stabilized nodal-integrated quadrilateral element. In: 1st International
Conference on Modern Design, Construction & Maintenance of Structures, 10-11 Dec 2007, Hanoi, Vietnam.
function approximation
Mai-Duy, Nam and Tran-Cong, Thanh (2003) Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling, 27 (3). pp. 197-220. ISSN 0307-904X
functional analysis
Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768
gain improvement
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
Ho-Minh, D. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of fluid flows at high Reynolds/Rayleigh numbers using integrated radial basis functions. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
Galerkin approach
Ho-Minh, D. and Mai-Duy, N. and Tran-Cong, T. (2012) Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach. Australian Journal of Mechanical Engineering , 9 (2). pp. 101-112.
ISSN 1448-4846
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A Cartesian-grid integrated-RBF Galerkin technique. In: Recent studies in meshless and other novel computational methods. Tech Science Press,
Duluth, GA. USA, pp. 87-102. ISBN 0-9824205-4-4
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains. CMES:
Computer Modeling in Engineering and Sciences, 44 (3). pp. 219-248. ISSN 1526-1492
Galerkin formulation
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) Galerkin/collocation methods based on 1D-integrated-RBFNs for viscoelastic flows. CMES: Computer Modeling in Engineering and Sciences, 70 (3).
pp. 217-251. ISSN 1526-1492
Mai-Duy, Nam and Ho-Minh, D. and Tran-Cong, Thanh (2009) A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations. International Journal
of Computer Mathematics, 86 (10-11). pp. 1746-1759. ISSN 0020-7160
Mai-Duy, Nam and Tran-Cong, Thanh (2009) An integrated-RBF technique based on Galerkin formulation for elliptic differential equations. Engineering Analysis with Boundary Elements, 33 (2). pp.
191-199. ISSN 0955-7997
Mai-Duy, Nam and Tran-Cong, Thanh (2008) On the use of integrated RBFs in Galerkin approximation for elliptic problems. In: BEM/MRM 30: 30th International Conference on Boundary Elements and Other
Mesh Reduction Methods, 7-9 Jul 2008, Maribor, Slovenia.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks. In: 8th International Conference on Computational
and Mathematical Methods in Science and Engineering (CMMSE-2008), 13-16 June 2008, Murcia, Spain.
Galerkin method
Mai-Duy, Nam and Tran-Cong, Thanh (2009) On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems. In: 31st International Conference on Boundary
Elements and Other Mesh Reduction Methods (BEM/MRM 31), 2-4 Sep 2009, New Forest, UK.
gap-tooth scheme
Roberts, A. J. and Kevrekidis, I. G. (2007) General tooth boundary conditions for equation free modeling. SIAM Journal on Scientific Computing, 29 (4). pp. 1495-1510. ISSN 1064-8275
gas detection
Leis, John and Buttsworth, David and Martin, Philip (2011) A broadband multisensor approach to gas monitoring. In: 6th Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion,
5-7 Dec 2011, Canberra, Australia.
gas dynamics
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2008) Numerical simulation of inviscid transient flows in shock tube and its validations. In: ICFM 2008: 5th International Conference on Fluid
Mechanics, 12-14 Sep 2008, Heidelberg, Germany.
gas emission
Yusaf, T. and Baker, P. and Hamawand, I. and Noor, M. M. (2013) Effect of compressed natural gas mixing on the engine performance and emissions. International Journal of Automotive and Mechanical
Engineering, 8. pp. 1416-1429. ISSN 2229-8649
Yusaf, T. and Baker, P. and Hamawand, I. and Noor, M. M. (2013) Effect of compressed natural gas mixing on the engine performance and emissions. International Journal of Automotive and Mechanical
Engineering, 8. pp. 1416-1429. ISSN 2229-8649
gaseous flows
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
Rahimi, Hadi and Ghobadian, Barat and Yusaf, Talal and Najafi, Gholamhasan and Khatamifar, Mahdi (2009) Diesterol: an environment-friendly IC engine fuel. Renewable Energy, 34 (1). pp. 335-342. ISSN
gene selection
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
generalised Newtonian flow
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
generalised spatial modulation
Fu, Jinlin and Hou, Chunping and Xiang, Wei and Yan, Lei and Hou, Yonghong (2010) Generalised spatial modulation with multiple active transmit antennas. In: GC 2010: IEEE Globecom Workshops , 5-10
Dec 2010, Miami, FL, USA.
generalized nonlinear phase diffusion equation
Strunin, Dmitry V. (2003) Nonlinear instability in generalized nonlinear phase diffusion equation. Progress of Theoretical Physics. Supplement (150). pp. 444-448. ISSN 0375-9687
genetic algorithm
Xiang, Wei and Zhu, Ce and Siew, Chee Kheong and Xu, Yuanyuan and Liu, Minglei (2009) Forward error correction-based 2-D layered multiple description coding for error-resilient H.264 SVC video
transmission. IEEE Transactions on Circuits and Systems for Video Technology, 19 (12). pp. 1730-1738. ISSN 1051-8215
geographic information systems
Kist, Alexander A. and Basnet, Badri (2013) Enabling effective and inclusive learning opportunities with software-based remote access laboratories. In: 10th International Conference on Remote
Engineering and Virtual Instrumentation (REV 2013): Moving from Design to Innovation and Impact, 6-8 Feb 2013, Sydney, Australia.
Zhou, Hong and Wu, Huayi (2009) The integration of wireless sensor networks, remote sensing and geographic information systems for autonomous environmental and animal monitoring. In: IADIS
International Conference on Applied Computing 2009 (IADIS 2009), 19-21 Nov 2009, Rome, Italy.
geometrical analysis
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
geotechnical earthquake design
Shiau, Jim S. and Lyamin, Andrei V. and Sloan, Scott W. (2006) Application of pseudo-static limit analysis in geotechnical earthquake design. In: 6th European Conference on Numerical Methods in
Geotechnical Engineering, 6-8 Sep 2006, Graz, Austria.
geotechnical research
Shiau, Jim S. and Pather, Selvan and Ayers, Ron (2006) Developing physical models for geotechnical teaching and research. In: 6th International Conference on Physical Modelling in Geotechnics, 4-6
Aug 2006, Hong Kong.
geotechnical stability
Shiau, Jim S. and Lyamin, Andrei V. and Sloan, Scott W. (2006) Application of pseudo-static limit analysis in geotechnical earthquake design. In: 6th European Conference on Numerical Methods in
Geotechnical Engineering, 6-8 Sep 2006, Graz, Austria.
geotechnical teaching
Shiau, Jim S. and Pather, Selvan and Ayers, Ron (2006) Developing physical models for geotechnical teaching and research. In: 6th International Conference on Physical Modelling in Geotechnics, 4-6
Aug 2006, Hong Kong.
Ginzburg-Landau equation
Suslov, Sergey A. (2002) Effect of fluid properties variations on spatio-temporal instability of convection. In: APM 2001: 29th Summer School on 'Advanced Problems in Mechanics, 21-30 Jun 2001, St
Petersburg (Repino), Russia.
Ginzburg-Landau model
Suslov, Sergey A. and Paolucci, Samuel (2004) Stability of non-Boussinesq convection via the complex Ginzburg-Landau model. Fluid Dynamics Research, 35 (3). pp. 159-203. ISSN 0169-5983
Gl/epoxy composites
Hafizi, Z. M. and Epaarachchi, J. and Lau, K. T. (2013) Wave propogation scattering due to defect on thin composite plates. In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney,
glass fibre
Nguyen-Van, Hieu and Khennane, Amar and Tran-Cong, Thanh (2006) Monte-Carlo simulation of the durability of glass fibre reinforced composite under environmental stress corrosion. In: 2006
International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi Minh City, Vietnam.
global approximation
Mai-Duy, Nam and Tran-Cong, Thanh (2003) Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling, 27 (3). pp. 197-220. ISSN 0307-904X
Mai-Duy, Nam and Tran-Cong, Thanh (2001) Numerical solution of differential equations using multiquadric radial basis function networks. Neural Networks, 14 (2). pp. 185-199. ISSN 0893-6080
global climate change
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
Faqih, Akhmad and Ribbe, Joachim and Meinke, Holger (2007) 20th century rainfall variability and the role of large scale climate events within Indo-Pacific region from IPCC AR4 models, reanalysis and
observations. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
global marine environment
Ribbe, Joachim (2004) The southern supplier. Nature, 427. pp. 23-24. ISSN 0028-0836
global warming
Cai, Wenju and Cowan, Tim and Dix, Martin and Rotstayn, Leon and Ribbe, Joachim and Shi, Ge and Wijffels, Susan (2007) Anthropogenic aerosol forcing and the structure of temperature trends in the
southern Indian Ocean. Geophysical Research Letters, 34 (14). L14611. ISSN 0094-8276
You, John and Herold, Nicholas and Muller, Dietmar and Sdrolias, Maria and Ribbe, Joachim (2007) Impact of vegetation on the Miocene Climate optimum. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
You, John and Muller, Dietmar and Sdrolias, Maria and Herold, Nicholas and Ribbe, Joachim (2007) Sensitivity of middle Miocene climate and regional monsoon to palaeo-altimetry. In: 14th National
Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
global wind field
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. Technical Report. Joachim Ribbe, Toowoomba, Australia.
Wardana, I. N. G. (2012) Burning characteristics of coconut oil In micro-combustor. In: USQ Combustion Meeting, 26 Nov 2012, Toowoomba, Australia.
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
good put
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Goodput and channel allocation in opportunistic spectrum access networks. In: PIMRC 2009: 20th IEEE International Symposium on
Personal, Indoor and Mobile Radio Communications, 13-16 Sep 2009, Tokyo, Japan.
governing equations
Phillips, D. G. and Tran, Canh-Dung and Fraser, W. B. and van der Heijden, G. H. M. (2010) Torsional properties of staple fibre plied yarns. Journal of the Textile Institute, 101 (7). pp. 595-612.
ISSN 0040-5000
grade of service
Kist, Alexander A. (2007) Erlang B as a performance model for IP flows. In: ICON 2007: 15th IEEE International Conference on Networks, 19-21 Nov 2007, Adelaide, Australia.
Smith, Catherine and Shiau, Jim S. (2007) Bearing capacity of footings near slopes. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane, Australia.
graph properties
Kist, Alexander A. and Harris, Richard J. (2003) Note on the problem of partially link disjoint paths. In: 2003 Joint Conference of the 4th International Conference on Information, Communications and
Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
gravitation and cosmology
Lozanovski, C. and Wylleman, L. (2011) Complex windmill transformation producing new purely magnetic fluids. Classical and Quantum Gravity, 28 (7). 075015-075031. ISSN 0264-9381
gravity waves
Clamond, D. and Stepanyants, Y. (2012) Stationary gravity waves with the zero mean vorticity in stratified fluid. Studies in Applied Mathematics, 128 (1). pp. 59-85. ISSN 0022-2526
Thomas, Caroline and Shiau, Jim S. (2007) Modelling the arching effect in active earth pressure problems. In: 10th Australia New Zealand Conference on Geomechanics, 21-24 Oct 2007, Brisbane,
Green and Lindsay model
Strunin, Dmitry V. (2001) On characteristic times in generalized thermoelasticity. Journal of Applied Mechanics, 68 (5). pp. 816-817. ISSN 0021-8936
green technology
Amirruddin, A. K. and Noor, M. M. and Kadirgama, K. and Sharma, K. V. (2012) The potential of wind and solar energy in Malaysia east coast: preliminary study at Universiti Malaysia Pahang (UMP). In:
3rd International Conference on Management of Natural Resources, Sustainable Development and Ecological Hazards: Ravage of the Planet III (RAV 2011) , 13-15 Dec 2011, Selangor, Malaysia.
Noor, M. M. and Amiruddin, A. K. and Kadirgama, K. and Sharma, K. V. (2011) The potential of wind and solar energy in Malaysia east coast: preliminary study at Universiti Malaysia Pahang (UMP). In:
3rd International Conference on Energy and Sustainability , 11-13 Apr 2011, Alicante, Spain.
grid connected inverters
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
grid-connected photovoltaic system
Bowtell, L. A. and Ahfock, A. L. (2010) Dynamic analysis of a DC offset controller for grid-connected inverters. In: AUPEC 2010: Power Quality for the 21st Century , 5-8 Dec 2010, Christchurch, New
Bowtell, L. and Ahfock, A. (2010) Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters. IET Renewable Power Generation, 4 (5). pp. 428-437. ISSN
Gross-Pitaevskii equation
Malomed, Boris A. and Stepanyants, Yury A. (2010) The inverse problem for the Gross-Pitaevskii equation. Chaos, 20 (1). ISSN 1054-1500
ground anchor
Shiau, J. S. and Hobson, M. A. (2011) Modeling uplift of plate anchor. In: Continuum and Distinct Element Numerical Modeling in Geomechanics, 14-16 Feb 2011, Melbourne, Australia.
ground control
Ghabraie, Behrooz and Ren, Gang and Ghabraie, Kazem and Xie, Yi Min (2013) A study on truss bolt mechanism in controlling stability of underground excavation and cutter roof failure. Geotechnical and
Geological Engineering, 31 (2). pp. 667-682. ISSN 0960-3182
ground reinforcement
Ghabraie, Behrooz and Ren, Gang and Ghabraie, Kazem (2013) Effects of thickness of roof layers on optimum design of truss bolt system using finite element modeling techniques. Electronic Journal of
Geotechnical Engineering, 13 (A). pp. 147-158.
ground testing
Buttsworth, David R. (2010) Ludwieg tunnel facility with free piston compression heating for supersonic and hypersonic testing. In: 9th Australian Space Science Conference, 28-30 Sept 2009, Sydney,
ground-based tracking
McIntyre, T. J. and Khan, R. and Eichmann, T. N. and Upcroft, B. and Buttsworth, D. (2012) Visible and near infrared spectroscopy of Hayabusa re-entry using semi-autonomous tracking. In: 50th AIAA
Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition: Advancing the Science of Flight Technology (AIAA 2012) , 9-12 Jan 2012, Nashville, TN. United States.
Khan, Razmi and Eichmann, Troy and Buttsworth, David and Upcroft, Ben (2011) Image-based visual servoing for the super-orbital re-entry of Hayabusa spacecraft. In: 2011 Australasian Conference on
Robotics and Automation (ACRA 2011) , 7-9 Dec 2011, Melbourne, Australia.
gun tunnel
Buttsworth, David R. and Jacobs, Peter A. and Jones, Terry V. (2002) Simulation of Oxford University gun tunnel performance using a quasi-one-dimensional model. Shock Waves, 11 (5). pp. 377-383. ISSN
H.264/SVC video transmission
Xiang, Wei and Zhu, Ce and Siew, Chee Kheong and Xu, Yuanyuan and Liu, Minglei (2011) 2-D scalable multiple description coding for robust H.264/SVC video communications. In: Streaming media
architectures, techniques, and applications: recent advances. Information Science Reference (IGI Global), Hershey, PA. United States, pp. 39-57. ISBN 978-1-61692-831-5
Wang, Gengkun and Xiang, Wei and Chen, Haoyu and Wen, Peng (2011) Wireless sensor home automation networks based upon Sun SPOT. In: ICSSC 2011: IET International Conference on Smart and Sustainable
City (IET ICSSC2011), 6-8 Jul 2011, Shanghai, China.
Hall-effect sensor
Wen, Peng and Kidd, Jason G. (2005) Electronic height indicator for agricultural machines. Australian Journal of Electrical and Electronics Engineering, 2 (1). pp. 13-20. ISSN 1448-837X
Kist, Alexander A. (2008) Instant handoffs for wireless infrastructure meshed networks. In: ATNAC 2008: Australasian Telecommunication Networks and Applications Conference , 7-10 Dec 2008, Adelaide,
handportable antennas
Ziri-Castro, Karla and Scanlon, William and Evans, Noel (2004) Indoor radio channel characterization and modeling for a 5.2-GHz bodyworn receiver. IEEE Antennas and Wireless Propagation Letters, 3
(1). pp. 219-222. ISSN 1536-1225
handportable terminals
Ziri-Castro, Karla and Scanlon, William and Evans, Noel (2003) Measured pedestrian movement and bodyworn terminal effects for the indoor channel at 5.2 GHz. European Transactions on
Telecommunications, 14 (6). pp. 529-538. ISSN 1124-318X
Ziri-Castro, Karla and Scanlon, William and Feustle, R. and Evans, Noel (2003) Channel modelling and propagation measurements for a bodyworn 5.2 GHz terminal moving in the indoor environment. In:
12th IEE International Conference on Antennas and Propagation, 31 Mar - 3 April 2003, Exeter, United Kingdom.
Buttsworth, David R. and Malpress, Ray (2009) Student views on hardware-based problem solving activities for external and on-campus teams. In: AaeE 2009: Engineering the Curriculum, 6-9 Dec 2009,
Adelaide, Australia.
Harris-moerder pulse
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
Hairuddin, Abdul Aziz and Yusaf, Talal and Wandel, Andrew (2013) Effect of different heat transfer models on a diesel homogeneous charge compression ignition engine. International Journal of
Automotive and Mechanical Engineering, 8. pp. 1305-1317. ISSN 2229-8649
Hairuddin, A. Aziz and Yusaf, Talal F. and Wandel, Andrew P. (2012) HCCI engine: numerical and experimental approach. In: USQ Combustion Meeting, 26 Sep 2012, Toowoomba, Australia. (Unpublished)
Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, Talal (2010) Hydrogen and natural gas comparison in diesel HCCI engines -a review. In: 2010 Southern Region Engineering Conference (SREC2010),
11-12 Nov 2010, Toowoomba, Australia.
HD 102117
Tinney, C. G. and Butler, R. Paul and Marcy, Geoffrey W. and Jones, Hugh R. A. and Penny, Alan J. and McCarthy, Chris and Carter, Brad D. and Fischer, Debra A. (2005) Three low-mass planets from the
Anglo-Australian planet search. The Astrophysical Journal, 623 (2). pp. 1171-1179. ISSN 0004-637X
HD 117618
Tinney, C. G. and Butler, R. Paul and Marcy, Geoffrey W. and Jones, Hugh R. A. and Penny, Alan J. and McCarthy, Chris and Carter, Brad D. and Fischer, Debra A. (2005) Three low-mass planets from the
Anglo-Australian planet search. The Astrophysical Journal, 623 (2). pp. 1171-1179. ISSN 0004-637X
HD 208487
Tinney, C. G. and Butler, R. Paul and Marcy, Geoffrey W. and Jones, Hugh R. A. and Penny, Alan J. and McCarthy, Chris and Carter, Brad D. and Fischer, Debra A. (2005) Three low-mass planets from the
Anglo-Australian planet search. The Astrophysical Journal, 623 (2). pp. 1171-1179. ISSN 0004-637X
HD 70642
Carter, Brad D. and Butler, R. Paul and Tinney, C. G. and Jones, Hugh R. A. and Marcy, Geoffrey W. and McCarthy, Chris and Fischer, Debra A. and Penny, Alan J. (2003) A planet in a circular orbit
with a 6 year period. Astrophysical Journal Letters , 593 (1). L43-L46. ISSN 2041-8205
Marsden, S. C. and Donati, J.-F. and Semel, M. and Petit, P. and Carter, B. D. (2006) Surface differential rotation and photospheric magnetic field of the young solar-type star HD 171488 (V889 Her).
Monthly Notices of the Royal Astronomical Society, 370 (1). pp. 468-476. ISSN 0035-8711
Tinney, Chris G. and Butler, R. Paul and Marcy, Geoffrey W. and Jones, Hugh R. A. and Laughlin, Gregory and Carter, Brad D. and Bailey, Jeremy and O'Toole, Simon J. (2006) The 2:1 resonant
exoplanetary system orbiting HD 73526. The Astrophysical Journal, 647 (1). pp. 594-599. ISSN 0004-637X
health technologies
Zhou, Hong and Ali, Hesham and Youn, Jon and Zhang, Zhongwei (2010) A hybrid wired and wireless network infrastructure to improve the productivity and quality care of critical medical applications.
In: 2010 IEEE/ICME International Conference on Complex Medical Engineering (CME 2010), 13-15 July 2010, Gold Coast, Australia.
heat and viscous flows
Le-Cao, Khoa (2011) Radial-basis-function calculations of heat and viscous flows in multiply-connected domains. [Thesis (PhD/Research)] (Unpublished)
heat content
Crawford, Jagoda and Stepanyants, Yury (2005) Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps. ANZIAM Journal (Australian & New Zealand
Industrial and Applied Mathematics Journal), 46. C1104-C1125. ISSN 1446-8735
heat flux
Hashempour, Javad and Sharifian, Ahmad (2012) Potentials of metal mesh to contain bushfires. In: 2012 Qld Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Sharifian, Ahmad and Buttsworth, David R. (2009) Direct radiation from wildfires through square woven screens. In: ASME 2008: Summer Heat Transfer Conference, 10-14 Aug 2008, Jacksonville, FL. USA.
heat flux gauge
Buttsworth, David R. (2002) Transient response of an erodable heat flux gauge using finite element analysis. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile
Engineering, 216 (8). pp. 701-716. ISSN 0954-4070
heat shield
Buttsworth, David and Jacobs, P. and Morgan, R. G. and Jenniskens, Peter (2012) Near ultraviolet emission spectroscopy of the Hayabusa re-entry. In: 50th AIAA Aerospace Sciences Meeting Including the
New Horizons Forum and Aerospace Exposition (AIAA 2012): Advancing the Science of Flight Technology, 9-12 Jan 2012, Nashville, TN. United States.
heat shields
McIntyre, T. J. and Khan, R. and Eichmann, T. N. and Upcroft, B. and Buttsworth, D. (2012) Visible and near infrared spectroscopy of Hayabusa re-entry using semi-autonomous tracking. In: 50th AIAA
Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition: Advancing the Science of Flight Technology (AIAA 2012) , 9-12 Jan 2012, Nashville, TN. United States.
Khan, Razmi and Eichmann, Troy and Buttsworth, David and Upcroft, Ben (2011) Image-based visual servoing for the super-orbital re-entry of Hayabusa spacecraft. In: 2011 Australasian Conference on
Robotics and Automation (ACRA 2011) , 7-9 Dec 2011, Melbourne, Australia.
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
heat transfer
Hairuddin, Abdul Aziz and Yusaf, Talal and Wandel, Andrew (2013) Effect of different heat transfer models on a diesel homogeneous charge compression ignition engine. International Journal of
Automotive and Mechanical Engineering, 8. pp. 1305-1317. ISSN 2229-8649
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow
problems. CMES Computer Modeling in Engineering and Sciences, 96 (1). pp. 49-90. ISSN 1526-1492
Eichmann, T. N. and Khan, R. and McIntyre, T. J. and Jacobs, C. and Porat, H. and Buttsworth, D. and Upcroft, B. (2012) Radiometric temperature analysis of the Hayabusa spacecraft re-entry. In: 28th
International Symposium on Shock Waves (ISSW 28), 17-22 Jul 2011, Manchester, United Kingdom.
Sharifian, Ahmad and Buttsworth, David R. (2007) Minimum safe standoff distance for protection from bushfire radiation by commercial metal meshes. In: 8th Australasian Heat and Mass Transfer
Conference, 26-29 Jul 2005, Curtin University of Technology, Perth, Western Australia.
Mohammed, H. and Yusaf, T. (2006) Heat transfer by mixed convection opposing laminar flow from the inside surface of uniformly heated inclined circular tube. In: 8th Biennial ASME Conference on
Engineering Systems Design and Analysis (ESDA 2006), 4-7 Jul 2006, Torino, Italy.
Mai-Duy, Nam and Tran-Cong, Thanh (2003) RBF interpolation of boundary values in the BEM for heat transfer problems. International Journal of Numerical Methods for Heat and Fluid Flow, 13 (5/6). pp.
611-632. ISSN 0961-5539
heat transfer instrumentation
Buttsworth, David R. and Jones, T. V. (1997) Radial conduction effects in transient heat transfer experiments. Aeronautical Journal, 101 (1005). pp. 209-212. ISSN 0001-9240
heat transfer measurement
Wang, Xiaowei and Stone, C. Richard and Buttsworth, David R. and Stevens, Robert and Arita, Yoshi (2006) Finite element analysis of eroding type surface thermocouple with application to engine heat
flux measurement. In: SAE 2006 World Conference and Exhibition, April 2006, Detroit, MI, USA.
heat transfer measurements
Buttsworth, David R. (2002) Heat transfer during transient compression: measurements and simulations. Shock Waves, 12 (1). pp. 87-91. ISSN 0938-1287
heat transfer modelling
Buttsworth, David R. (2002) Heat transfer during transient compression: measurements and simulations. Shock Waves, 12 (1). pp. 87-91. ISSN 0938-1287
heated flow
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
hemicube method
Sharifian, Ahmad and Buttsworth, David (2010) Double-layered metal mesh screens to contain or exclude thermal radiation from bush fires. Journal of Fire Protection Engineering, 20 (4). pp. 291-311.
ISSN 1042-3915
hepatitis C modelling
Zeiler, Irmgard and Langlands, Trevor and Murray, John M. and Ritter, Alison (2010) Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone
maintenance programs. Drug and Alcohol Dependence, 110 (3). pp. 228-233. ISSN 0376-8716
Hertz contact
Shiau, Jim S. (2011) A shakedown limit under Hertz contact pressure. In: 2011 International Conference on Advanced Engineering Materials and Technology (AEMT 2011), 29-31 Jul 2011, Sanya, China.
Hervey Bay
Ribbe, Joachim and Wolff, Jorg-Olaf and Staneva, Joanna and Grawe, Ulf (2008) Assessing water renewal time scales for marine environments from three-dimensional modelling: a case study for Hervey
Bay, Australia. Environmental Modelling and Software, 23 (10-11). pp. 1217-1228. ISSN 1364-8152
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
Grawe, U. and Ribbe, J. and Wolff, J.-O. and Staneva, J. (2007) Accessing exchange and ventilation time scales from 3-D modelling. In: The Ocean in the Earth System: International Conference and 97th
Annual Meeting of the Geologische Vereinigung e.V., 1-5 Oct 2007, Bremen, Germany.
Hervey Bay Water
Ribbe, Joachim (2006) A study into the export of saline water from Hervey Bay, Australia. Estuarine, Coastal and Shelf Science, 66 (3-4). pp. 550-558. ISSN 0272-7714
Kist, Alexander A. and Harris, Richard J. (2002) A heuristic to generate all best partially disjoint paths in a communications network. In: 8th International Conference on Communication Systems (ICCS
2002), 25-28 Nov 2002, Singapore.
heuristic approaches
Kist, Alexander A. and Harris, Richard J. (2003) Note on the problem of partially link disjoint paths. In: 2003 Joint Conference of the 4th International Conference on Information, Communications and
Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
high altitude
Saleh, Khalid and Buttsworth, David and Yusaf, Talal (2010) Development of a small icing wind tunnel for simulating the initial stages of solid phase ice accretion. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
high order
Mai-Duy, Nam (2005) Solving high order ordinary differential equations with radial basis function networks. International Journal for Numerical Methods in Engineering, 62 (6). pp. 824-852. ISSN
high order consistency
Roberts, A. J. and Kevrekidis, I. G. (2007) General tooth boundary conditions for equation free modeling. SIAM Journal on Scientific Computing, 29 (4). pp. 1495-1510. ISSN 1064-8275
high order derivatives
Mai-Duy, N. and Tanner, R. I. (2005) Solving high-order partial differential equations with indirect radial basis function networks. International Journal for Numerical Methods in Engineering, 63
(11). pp. 1636-1654. ISSN 0029-5981
high order upwind scheme
Mai-Duy, Nam and Tran-Cong, Thanh (2010) An upwind control-volume method based on integrated RBFs for fluid-flow problems. In: 9th World Congress on Computational Mechanics and 4th Asian-Pacific
Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
high speed flow experiments
Buttsworth, David R. and Jones, Terry V. (2003) High bandwidth stagnation temperature measurements in a Mach 6 gun tunnel flow. Experimental Thermal and Fluid Science, 27 (2). pp. 177-186. ISSN
high temperature
Buttsworth, David and Jacobs, P. and Morgan, R. G. and Jenniskens, Peter (2012) Near ultraviolet emission spectroscopy of the Hayabusa re-entry. In: 50th AIAA Aerospace Sciences Meeting Including the
New Horizons Forum and Aerospace Exposition (AIAA 2012): Advancing the Science of Flight Technology, 9-12 Jan 2012, Nashville, TN. United States.
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
3 Oct 2008, Heraklion, Greece.
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
high-order approximation
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2012) A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables. CMES:
Computer Modeling in Engineering and Sciences, 84 (6). pp. 528-557. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems. International Journal for Numerical Methods in Fluids, 67 (12). pp.
1973-1992. ISSN 0271-2091
high-order approximations
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran, C. -D. and Tran-Cong, T. (2013) A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion
and unsteady fluid flow problems. Engineering Analysis with Boundary Elements , 37 (12). pp. 1653-1667. ISSN 0955-7997
Mai-Duy, N. and Thai-Quang, N. and Hoang-Trieu, T.-T. and Tran-Cong, T. (2013) A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation. Applied Mathematical Modelling
. ISSN 0307-904X (In Press)
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A finite-volume method based on compact local integrated radial basis function approximations for second-order differential
problems. CMES Computer Modeling in Engineering and Sciences, 91 (6). pp. 485-516. ISSN 1526-1492
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) A high-order compact integrated-RBF scheme for time-dependent problems. In: 4th International Conference on
Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady
convection-diffusion equations. CMES: Computer Modeling in Engineering and Sciences, 89 (3). pp. 189-220. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) Compact local integrated-RBF approximations for second-order elliptic differential problems. Journal of Computational Physics , 230 (12). pp. 4772-4794. ISSN
high-order ODEs
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2012) Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs. CMES: Computer Modeling in Engineering and
Sciences, 84 (2). pp. 171-203. ISSN 1526-1492
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2011) Compact local stencils employed with integrated RBFs for fourth-order differential problems. Structural Longevity, 6 (2). pp. 93-107. ISSN
high-order ordinary differential equations
Mai-Duy, Nam (2006) An effective spectral collocation method for the direct solution of high-order ODEs. Communications in Numerical Methods in Engineering, 22 (6). pp. 627-642. ISSN 1069-8299
high-order partial differential equations
Mai-Duy, N. and Tanner, R. I. (2005) Solving high-order partial differential equations with indirect radial basis function networks. International Journal for Numerical Methods in Engineering, 63
(11). pp. 1636-1654. ISSN 0029-5981
high-order PDEs
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2012) Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs. CMES: Computer Modeling in Engineering and
Sciences, 84 (2). pp. 171-203. ISSN 1526-1492
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2011) Compact local stencils employed with integrated RBFs for fourth-order differential problems. Structural Longevity, 6 (2). pp. 93-107. ISSN
high-speed synchronous data acquisition
Wang, Gengkun and Xiang, Wei and Leis, John and Wang, Yafeng (2010) Design of a wireless portable vibration acquisition and analysis instrument. In: 2010 IEEE International Conference on Wireless
Communications, Networking and Information Security (WCNIS 2010), 25-27 Jun 2010, Beijing, China.
higher education
UNSPECIFIED (2013) Proceedings of the 3rd Malaysian Postgraduate Conference (MPC 2013). In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
Mossad, Ruth and Vella, Anthony and Balusu, Rao (2009) Inertisation of highwall mining to control methane concentrations at the Moura mine. In: 7th International Conference on Computational Fluid
Dynamics in the Minerals and Process Industries (CFD2009), 9-11 Dec 2009, Melbourne, Australia.
holographic interferometry system
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
3 Oct 2008, Heraklion, Greece.
home automation networks
Wang, Gengkun and Xiang, Wei and Chen, Haoyu and Wen, Peng (2011) Wireless sensor home automation networks based upon Sun SPOT. In: ICSSC 2011: IET International Conference on Smart and Sustainable
City (IET ICSSC2011), 6-8 Jul 2011, Shanghai, China.
Hairuddin, A. Aziz and Yusaf, Talal and Wandel, Andrew P. (2013) Implementation of CMC in a 0-D single-zone model of a diesel HCCI engine. In: 7th Australian Combustion Symposium (ACS 2013), 6-8 Nov
2013, Perth, Australia .
horizontal flow
Mossad, Ruth and Aral, Hal (2010) Numerical modeling of flow in a horizontal sand filter. American Journal of Engineering and Applied Sciences, 3 (2). pp. 286-292. ISSN 1941-7020
horizontal plate anchor
Shiau, Jim and Al Abri, Mohammed (2011) A study on the failure mechanisms of horizontal plate anchors in clay. In: ICAGE 2011: International Conference on Advances in Geotechnical Engineering, 7-9
Nov 2011, Perth, Western Australia.
Parameswaran, Vinod and Zhou, Hong and Zhang, Zhongwei (2013) Wireless underground sensor network design for irrigation control: simulation of RFID deployment. In: 7th International Conference on
Sensing Technology (ICST 2013), 3-5 Dec 2013, Wellington, New Zealand.
Parameswaran, Vinod and Zhou, Hong and Zhang, Zhongwei (2012) Irrigation control using wireless underground sensor networks. In: 6th International Conference on Sensing Technology (ICST 2012), 18-21
Dec 2012, Kolkata, India.
Alajel, Khalid and Xiang, Wei and Sileh, Ibrahim (2012) Color plus depth 3-D video transmission with hierarchical 16-QAM. In: 6th International Conference on Signal Processing and Communication
Systems (ICSPCS 2012) , 12-14 Dec 2012, Gold Coast, Australia.
Alajel, Khalid Mohamed and Xiang, Wei (2012) Color plus depth 3-D video transmission with heirarchical 16-QAM. In: 3DTV-CON 2012: The True Vision: Capture, Transmission and Display of 3D Video, 15-17
Oct 2012, Zurich, Switzerland.
Karimkashi, Shervin and Kermani, Mohammad J. and Sharifian, Ahmad and Hashempour, Javad (2012) Numerical computation of pressure drop across an off supplementary firing burner in heat recovery steam
generator. In: 18th Australasian Fluid Mechanics Conference (AFMC 2012), 3-7 Dec 2012, Launceston, Australia.
Huffman codes
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Iterative decoding of JPEG coded images with channel coding. In: 10th IEEE International Conference on Telecommunications, Feb
2003, Papeete, Tahiti.
human head model
Wen, Peng and Li, Yan (2006) EEG human head modelling based on heterogeneous tissue conductivity. Australasian Physical and Engineering Sciences in Medicine, 29 (3). pp. 235-240. ISSN 0158-9938
hybrid binomial Langevin-multiple mapping conditioning model
Wandel, Andrew P. and Lindstedt, R. Peter (2009) Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer. Physics of Fluids, 21 (1). 015103-015116. ISSN 1070-6631
hybrid Cramer-Rao lower bound
Salim, Omar Hazim and Nasir, Ali and Mehrpouyan, Hani and Xiang, Wei (2013) Phase noise and carrier frequency offset in OFDM systems: joint estimation and hybrid Cramer-Rao lower bound. In: 14th IEEE
International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2013), 16-19 Jun 2013, Darmstadt, Germany.
hybrid engine
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
hybrid power
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
hybrid relay protocol
Sileh, Ibrahim Khalil and Xiang, Wei (2012) Distributed space-frequency coding for OFDM-based hybrid relay selection. In: 12th International Symposium on Communications and Information Technologies
(ISCIT 2012), 2-5 Oct 2012, Gold Coast, Australia.
hydraulic engineering
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2008) Numerical simulation of inviscid transient flows in shock tube and its validations. In: ICFM 2008: 5th International Conference on Fluid
Mechanics, 12-14 Sep 2008, Heidelberg, Germany.
hydraulic fracture
Golshani, Aliakbar and Tran-Cong, Thanh (2006) Modelling a borehole subjected to fluid pressure. In: 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006,
Ho Chi Minh City, Vietnam.
hydraulic fracturing
Golshani, Aliakbar and Tran-Cong, Thanh (2009) Energy analysis of hydraulic fracturing. KSCE Journal of Civil Engineering, 13 (4). pp. 219-224. ISSN 1226-7988
Golshani, Aliakbar and Tran-Cong, Thanh (2008) Simulation of hydraulic fracturing in brittle rocks. In: ISRM International Symposium 2008: 5th Asian Rock Mechanics Symposium, 24-26 Nov 2008, Tehran,
Golshani, Aliakbar and Tran-Cong, Thanh (2008) Energy analysis of hydraulic fracturing. In: 12th International Conference of IACMAG, 1-6 Oct 2008, Goa, India.
hydraulic impact
Genet, Martin and Yan, Wenyi and Tran-Cong, Thanh (2009) Investigation of a hydraulic impact: a technology in rock breaking. Archive of Applied Mechanics, 79 (9). pp. 825-841. ISSN 0939-1533
hydrocarbon refrigerants
Tangalajuk Siang, Jeri and Sharifian, Ahmad (2012) Reducing the amount of required propane refrigerant in the condenser of a commercial air-conditioner by increasing the inlet temperature. In:
Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The study of air fuel ratio for open furnace MILD combustion of biogas on bluff-body burner. In: 2012 Qld Southern Regional Engineering
Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
hydrodynamic instability
Suslov, Sergey A. (2008) Thermo-magnetic convection in a vertical layer of ferromagnetic fluid. Physics of Fluids, 20 (8). 084101-084118. ISSN 1070-6631
hydrodynamic instability
Fabrikant, Anatoly and Stepanyants, Yury (1998) Propagation of waves in shear flows. World Scientific, Singapore. ISBN 978-981-02-2052-5
hydrodynamic stability
Tran, Thien Duc and Suslov, Sergey A. (2009) Stability of plane Poiseuille-Couette flows of a piezo-viscous fluid. Journal of Non-Newtonian Fluid Mechanics, 156 (3). pp. 139-149. ISSN 0377-0257
Fabrikant, Anatoly and Stepanyants, Yury (1998) Propagation of waves in shear flows. World Scientific, Singapore. ISBN 978-981-02-2052-5
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The air fuel ratio study for the mixture of biogas and hydrogen on mild combustion. In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5
Jul 2013, Sydney, Australia.
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2012) Modelling of non-premixed turbulent combustion of hydrogen using conditional moment closure method. IOP Conference
Series: Materials Science and Engineering, 36 (012036). pp. 1-17. ISSN 1757-899X
Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, Talal (2010) Hydrogen and natural gas comparison in diesel HCCI engines -a review. In: 2010 Southern Region Engineering Conference (SREC2010),
11-12 Nov 2010, Toowoomba, Australia.
hydrological cycle
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
hyperbolic heat conduction
Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2002) Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models. Computational Mechanics, 29
(1). pp. 16-26. ISSN 0178-7675
Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2002) Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models. Computational Mechanics, 29
(1). pp. 16-26. ISSN 0178-7675
hyperbolic thermoelasticity
Melnik, R. V. N. and Strunin, D. V. and Roberts, A. J. (2005) Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models. Numerical Heat Transfer Part A: Applications, 47
(6). pp. 549-569. ISSN 1040-7782
Strunin, D. V. and Melnik, R. V. N. and Roberts, A. J. (2001) Coupled thermomechanical waves in hyperbolic thermoelasticity. Journal of Thermal Stresses, 24 (2). pp. 121-140. ISSN 0149-5739
Chong, Albert K. and Buttsworth, David and Mudford, Neil and Jokic, Michael and Balage, Sudantha and O'Bryne, Sean (2012) Application of photogrammetry at USQ hypersonic wind tunnel. In: 11th
Australian Space Science Conference (ASSC 2011) , 26-29 Sep 2011, Canberra, Australia.
Buttsworth, David R. (2010) Ludwieg tunnel facility with free piston compression heating for supersonic and hypersonic testing. In: 9th Australian Space Science Conference, 28-30 Sept 2009, Sydney,
hypersonic flow
Widodo, A. S. and Buttsworth, D. R. (2010) Stagnation temperature measurements in the USQ hypersonic wind tunnel. In: 17th Australasian Fluid Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland,
New Zealand.
hypersonic test facility
Al-Falahi, Amir and Yusoff, Mohd. Zamri bin and Yusaf, Talal (2008) Development of a short duration hypersonic test facility at Universiti Tenaga Nasional. Institution of Engineers, Malaysia.
Journal, 69 (1). pp. 19-25. ISSN 0126-513X
hypersonic testing
Al-Falahi, Amir and Yusaf, T. and Yusoff, M. Z. (2007) Experimental and CFD study of the effects of design parameters on Reynolds number in a short duration hypersonic test facility. In: EPMESC X:
Enhancement and Promotion of Computational Methods in Engineering and Science X, 21-23 Aug 2006, Sanya, China.
hypervelocity radiating flows
Morgan, R. G. and McIntyre, T. J. and Jacobs, P. A. and Buttsworth, D. R. and Macrossan, M. N. and Gollan, R. J. and Capra, B. R. and Brandis, A. M. and Potter, D. and Eichmann, T. and Jacobs, C. M.
and McGilvray, M. and van Diem, D. and Scott, M. P. (2006) Impulse facility simulation of hypervelocity radiating flows. In: 2nd International Workshop on Radiation of High Temperature Gases in
Atmospheric Entry, 6-8 Sep 2006, Rome, Italy.
ice accretion
Saleh, Khalid and Buttsworth, David and Yusaf, Talal (2010) Development of a small icing wind tunnel for simulating the initial stages of solid phase ice accretion. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
Saleh, Khalid and Buttsworth, David and Yusaf, Talal (2010) Development of a small icing wind tunnel for simulating the initial stages of solid phase ice accretion. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
Redmond, Petrea and Albion, Peter (2002) In their own words: pre-service teachers’ perceptions of ICT integration. In: 13th International Conference of the Society for Information Technology &
Teacher Education (SITE 2002), 18-23 March 2002, Nashville, Tennessee, USA.
IEEE 802.15.4
Zhang, Zhongwei and Zhou, Hong (2011) A MAC layer protocol supporting the application of WSNs in medicine and healthcare domains. In: 12th ACIS International Conference on Software Engineering,
Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD 2011), 6-8 Jul 2011, Sydney, Australia.
image coding
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Iterative decoding of JPEG coded images with channel coding. In: 10th IEEE International Conference on Telecommunications, Feb
2003, Papeete, Tahiti.
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Joint source-channel decoding of JPEG images using error resilient source codes. In: 2003 IEEE International Symposium on
Information Theory, 29 Jun - 4 Jul 2003, Yokohama, Japan.
image colour analysis
Sileh, Ibrahim Khalil and Alajel, Khalid Mohamed and Xiang, Wei (2011) Cooperative relay selection based UEP scheme for 3D video transmission over Rayleigh fading channel. In: 2011 International
Conference on Digital Image Computing: Techniques and Application (DICTA 2011), 6-8 Dec 2011, Noosa, Australia .
image processing
Ng, S. K. and Carter, S. J. B. and Bullen, Frank (2006) A biomimicry approach to automating visual road surveys. In: 22nd ARRB Conference: Research Into Practice, 29 Oct - 02 Nov 2006, Canberra,
image representation
Ramesh Kumar, Nandini and Xiang, Wei and Soar, Jeffrey (2011) A novel image compressive sensing method based on complex measurements. In: DICTA 2011: International Conference on Digital Image
Computing: Techniques and Application, 6-8 Dec 2011 , Noosa, Australia.
Khan, Razmi and Eichmann, Troy and Buttsworth, David and Upcroft, Ben (2011) Image-based visual servoing for the super-orbital re-entry of Hayabusa spacecraft. In: 2011 Australasian Conference on
Robotics and Automation (ACRA 2011) , 7-9 Dec 2011, Melbourne, Australia.
Marsden, S. C. and Donati, J.-F. and Semel, M. and Petit, P. and Carter, B. D. (2006) Surface differential rotation and photospheric magnetic field of the young solar-type star HD 171488 (V889 Her).
Monthly Notices of the Royal Astronomical Society, 370 (1). pp. 468-476. ISSN 0035-8711
immersed boundary
Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow
problems. CMES Computer Modeling in Engineering and Sciences, 96 (1). pp. 49-90. ISSN 1526-1492
Golshani, Aliakbar and Tran-Cong, Thanh and Buttsworth, David (2008) Impact on a water filled cylinder. In: ACMFMS 2008: Asian Conference on Mechanics of Functional Materials and Structures, 31 Oct-3
Nov 2008, Matsue, Japan.
impact assessment
Ribbe, Joachim and Wolff, Jorg-Olaf and Staneva, Joanna and Grawe, Ulf (2008) Assessing water renewal time scales for marine environments from three-dimensional modelling: a case study for Hervey
Bay, Australia. Environmental Modelling and Software, 23 (10-11). pp. 1217-1228. ISSN 1364-8152
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2007) A numerical study of strain localization in elasto-thermo-viscoplastic materials using radial basis function networks.
Computers, Materials and Continua, 5 (2). pp. 129-150. ISSN 1546-2218
impulse facility
Buttsworth, David R. and Jacobs, Peter A. and Jones, Terry V. (2002) Simulation of Oxford University gun tunnel performance using a quasi-one-dimensional model. Shock Waves, 11 (5). pp. 377-383. ISSN
Ma, Zhangchao and Xiang, Wei and Long, Hang and Wang, Wenbo (2011) Proportional fair resource partition for LTE-advanced networks with Type I relay nodes. In: ICC 2011: Source of Innovation: Back to
the Origin, 5-9 Jun 2011 , Kyoto, Japan.
incoherent addition
Wang, Yafeng and Wei, Guoxing and Xiang, Wei (2011) Approximate inter-cell interference modeling for cellular network. Journal of China Universities of Posts and Telecommunications, 18 (3). pp.
75-79. ISSN 1005-8885
Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2010) A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.
International Journal for Numerical Methods in Engineering, 82 (4). pp. 435-463. ISSN 0029-5981
incompressible fluid
Stepanyants, Yu. A. and Yakubovich, Evsey (2011) Scalar description of three-dimensional vortex flows of incompressible fluid. Doklady Physics, 56 (2). pp. 130-133. ISSN 1028-3358
incremental redundancy
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
Incremental selection amplify-and-forward (ISAF)
Ran, Jie and Wang, Yafeng and Li, Chang and Yang, Dacheng and Xiang, Wei (2010) Joint power allocation and best-relay positioning for incremental selection amplify-and-forward relaying. In: 2010 IEEE
Vehicular Technology Conference (VTC 2010-Fall), 6-9 Sept 2010, Ottawa, Canada.
independent channels
Long, Hang and Kim, Kyeong Jin and Xiang, Wei and Shen, Shanshan and Zheng, Kan and Wang, Wenbo (2012) Improved wideband precoding with arbitrary subcarrier grouping in MIMO-OFDM systems. ETRI
Journal, 34 (1). pp. 9-16. ISSN 1225-6463
Indian Ocean
Cai, Wenju and Cowan, Tim and Dix, Martin and Rotstayn, Leon and Ribbe, Joachim and Shi, Ge and Wijffels, Susan (2007) Anthropogenic aerosol forcing and the structure of temperature trends in the
southern Indian Ocean. Geophysical Research Letters, 34 (14). L14611. ISSN 0094-8276
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2007) Multidecadal variability in the transmission of ENSO signals to the Indian Ocean. Geophysical Research Letters, 34 (9). L09706. ISSN 0094-8276
Indian Ocean dipole
Shi, Ge and Cai, Wenju and Cowan, Tim and Ribbe, Joachim and Rotstayn, Leon and Dix, Martin (2008) Variability and trend of the north west Australia rainfall: observations and coupled climate
modeling. Journal of Climate, 21 (12). pp. 2938-2959. ISSN 0894-8755
Shi, G. and Ribbe, J. and Cai, W. and Cowan, T. (2008) An interpretation of Australian rainfall projections. Geophysical Research Letters, 35 (2). L2072. ISSN 0094-8276
indirect radial basis function network
Mai-Duy, Nam and Tran-Cong, Thanh (2004) An effective RBFN-boundary integral approach for the analysis of natural convection flow. International Journal for Numerical Methods in Fluids, 46 (5). pp.
545-568. ISSN 0271-2091
indirect radial basis function network (IRBFN)
Mai-Duy, N. and Mai-Cao, L. and Tran-Cong, T. (2006) A new meshless RBF-based method for unsteady fluid flow analysis. In: Advances in meshless methods. Tech Science Press, USA, pp. 241-262. ISBN
indirect radial basis function networks
Mai-Duy, N. and Tanner, R. I. (2005) An effective high order interpolation scheme in BIEMs for biharmonic boundary value problems. Engineering Analysis with Boundary Elements, 29 (3). pp. 210-223.
ISSN 0955-7997
indirect radial basis function networks method
Mai-Duy, Nam and Mai-Cao, Lan and Tran-Cong, Thanh (2007) Computation of transient viscous flows using indirect radial basis function networks. CMES: Computer Modeling in Engineering and Sciences, 18
(1). pp. 59-78. ISSN 1526-1492
indirect radial-basis-function networks
Mai-Duy, N. and Tran-Cong, T. (2006) Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis With Boundary Elements, 30
(2). pp. 77-87. ISSN 0955-7997
indirect RBFN
Mai-Duy, Nam (2004) Indirect RBFN method with scattered points for numerical solution of PDEs. CMES: Computer Modeling in Engineering and Sciences, 6 (2). pp. 209-226. ISSN 1526-1492
individual stars
Tuomi, M. and Jones, H. R. A. and Jenkins, J. S. and Tinney, C. G. and Butler, R. P. and Vogt, S. S and Barnes, J. R. and Wittenmyer, R. A. and O'Toole, S. J. and Horner, J. and Bailey, J. and
Carter, B. D. and Wright, D. J. and Salter, G. S. and Pinfield, D. (2013) Signals embedded in the radial velocity noise: Periodic variations in the tau Ceti velocities. Astronomy and Astrophysics,
551 (A79). pp. 1-21. ISSN 0004-6361
Faqih, Akhmad and Ribbe, Joachim and Meinke, Holger (2007) 20th century rainfall variability and the role of large scale climate events within Indo-Pacific region from IPCC AR4 models, reanalysis and
observations. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Roberts, A. J. (2008) The inertial dynamics of thin film flow of non-Newtonian fluids. Physics Letters Section A: General, Atomic and Solid State Physics, 372 (10). pp. 1607-1611. ISSN 0375-9601
Sharifi, Behrooz and Leis, John (2010) Towards three-dimensional fusion of infrared guidance measurements for biopsy procedures: some preliminary results and design considerations. In: ICSPCS 2010:
4th International Conference on Signal Processing and Communication Systems, 13-15 Dec 2010, Gold Coast, Australia.
infrared sensors
Leis, John and Buttsworth, David and Martin, Philip (2011) A broadband multisensor approach to gas monitoring. In: 6th Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion,
5-7 Dec 2011, Canberra, Australia.
inlet design
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2008) Application of topological conservation to model key features of zero-torque multi-ply yarns. Journal of the Textile
Institute, 99 (4). pp. 325-337. ISSN 0040-5000
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2006) Issues in processing unstable twisted fibre assemblies. In: 4th International Industrial Simulation Conference (ISC 2006),
5-7 Jun 2006, Palermo, Italy.
Sharifian, Ahmad and Watson, Stuart and Buttsworth, David R. and Barton, James (2007) Modelling the static thermal sensitivity of diaphragm-based fibre optic pressure sensors. In: 8th Australasian
Heat and Mass Transfer Conference, 26-29 July 2005, Curtin University of Technology, Perth, Western Australia.
Buttsworth, David R. (2002) Transient response of an erodable heat flux gauge using finite element analysis. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile
Engineering, 216 (8). pp. 701-716. ISSN 0954-4070
intake injection
Buttsworth, David R. and Jacobs, Peter A. (2009) Premature ignition in scramjets with intake injection: a preliminary laminar mixing layer simulation. In: Australian Combustion Symposium 2009
(ACS09), 2-4 Dec 2009, Brisbane, Australia.
integral collocation formulation
Mai-Duy, N. and Tran-Cong, T. (2008) A meshless technique based on integrated radial basis function networks for elliptic partial differential equations. In: 4th International Workshop on Meshfree
Methods for Partial Differential Equations, 17-20 Sep 2007, Bonn, Germany.
integral collocation formulation
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A RBF-based fictitious-domain technique for Dirichlet boundary value problems in multiply-connected domains. In: 3rd Asian-Pacific Congress on Computational
Mechanics (APCOM'07) and EPMESC XI, 3-6 Dec 2007, Kyoto, Japan.
integral collocation formulation
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2009) A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical
Modelling, 33 (1). pp. 284-299. ISSN 0307-904X
Mai-Duy, Nam and Le-Cao, Khoa and Tran-Cong, Thanh (2008) A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli.
International Journal for Numerical Methods in Fluids, 57 (12). pp. 1709-1730. ISSN 0271-2091
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations. In: Leading-edge applied
mathematical modeling research. Nova Science Publishers, Inc., New York, United States, pp. 215-250. ISBN 1-60021-977-2
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A multidomain integrated RBF collocation method for elliptic differential equations. In: 8th World Congress on Computational Mechanics (WCCM8), and 5th
European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A point-collocation method based on integrated Chebyshev polynomials for elliptic differential equations in irregular domains. In: 8th World Congress on
Computational Mechanics (WCCM8) and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.
Mai-Duy, Nam and Tran-Cong, Thanh (2007) Solving partial differential equations with point collocation and one-dimensional integrated interpolation schemes. In: 14th International Conference on
Computational & Experimental Engineering and Sciences, 1-3 Jan 2007, Miami, Florida, USA.
integral formulation
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations. Communications in Numerical Methods in Engineering, 24
(10). pp. 795-806. ISSN 1069-8299
integral length scales
Deo, Ravinesh C. and Nathan, Graham J. and Mi, Jianchun (2013) Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers. Physics of
Fluids, 25 (1). 015115-1. ISSN 1070-6631
integrated basis-functions
Mai-Duy, Nam (2006) An effective spectral collocation method for the direct solution of high-order ODEs. Communications in Numerical Methods in Engineering, 22 (6). pp. 627-642. ISSN 1069-8299
integrated Chebyshev polynomials
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems. Applied Mathematical
Modelling, 32 (12). pp. 2851-2862. ISSN 0307-904X
integrated Chebyshev polynomials
Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2008) An integral-collocation-based fictitious-domain technique for solving elliptic problems. Communications in Numerical Methods in Engineering,
24 (11). pp. 1291-1314. ISSN 1069-8299
Mai-Duy, Nam and Tanner, Roger I. (2007) A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. Journal of Computational and
Applied Mathematics, 201 (1). pp. 30-47. ISSN 0377-0427
integrated radial basis function
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 11 - unsteady incompressible viscous flows. CMES: Computer
Modeling in Engineering and Sciences , 83 (3). pp. 311-351. ISSN 1526-1492
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2012) A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables. CMES:
Computer Modeling in Engineering and Sciences, 84 (6). pp. 528-557. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis. CMES:
Computer Modeling in Engineering and Sciences, 83 (5). pp. 459-498. ISSN 1526-1492
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2011) Discretisation of the velocity-pressure formulation with integrated radial-basis-function networks. Structural Longevity, 6 (2).
pp. 77-91. ISSN 1944-611X
Ngo-Cong, Duc and Mai-Duy, Nam and Karunasena, W. and Tran-Cong, Thanh (2010) Integrated-RBF network method for free vibration analysis of laminated composite plates. In: 9th World Congress on
Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A cartesian-grid integrated-RBF method for viscoelastic flows. In: 9th World Congress on Computational Mechanics and 4th Asian-Pacific
Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2010) A new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems. In: 9th World Congress on Computational
Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Mai-Duy, Nam and Tran-Cong, Thanh (2010) An upwind control-volume method based on integrated RBFs for fluid-flow problems. In: 9th World Congress on Computational Mechanics and 4th Asian-Pacific
Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Mai-Duy, N. and Tanner, R. I. (2007) A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. International Journal of Numerical Methods for Heat and Fluid Flow, 17
(2). pp. 165-186. ISSN 0961-5539
integrated radial basis function network
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems. Numerical Methods for Partial
Differential Equations, 26 (6). pp. 1443-1462. ISSN 0749-159X
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2007) A meshless IRBFN-based numerical simulation of dynamic strain localization in quasi-brittle materials. In: USNCCM9: 9th US
National Congress on Computational Mechanics , 22-26 Jul 2007, San Francisco, CA, United States.
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2006) A meshless IRBFN-based numerical simulation of adiabatic shear band formation in one dimension. In: 2006 International
Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi Minh City, Vietnam.
integrated radial basis function networks
Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.
Tran, C.-D. and An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2011) An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 82 (2). pp. 137-162. ISSN 1526-1492
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A control volume technique based on integrated RBFNs for the convection-diffusion equation. Numerical Methods for Partial Differential Equations, 26 (2). 426
-447. ISSN 0749-159X
Mai-Duy, Nam and Mai-Cao, Lan and Tran-Cong, Thanh (2007) Computation of transient viscous flows using indirect radial basis function networks. CMES: Computer Modeling in Engineering and Sciences, 18
(1). pp. 59-78. ISSN 1526-1492
Le-Cao, Khoa and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Radial-basis-function calculations of buoyancy-driven flow in concentric and eccentric annuli. In: 16th Australasian Fluid Mechanics
Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
integrated radial basis functions
Mai-Duy, N. and Thai-Quang, N. and Hoang-Trieu, T.-T. and Tran-Cong, T. (2013) A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation. Applied Mathematical Modelling
. ISSN 0307-904X (In Press)
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A finite-volume method based on compact local integrated radial basis function approximations for second-order differential
problems. CMES Computer Modeling in Engineering and Sciences, 91 (6). pp. 485-516. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 1 - natural convection flows in concentric and eccentric
annuli. CMES: Computer Modeling in Engineering and Sciences, 83 (3). pp. 275-310. ISSN 1526-1492
Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Numerical solution of Fokker-Planck equation using the integral radial basis function networks. In: 10th World Congress on Computational Mechanics
(WCCM 2012), 8-13 July 2012, Sao Paulo, Brazil.
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients. CMES: Computer
Modeling in Engineering and Sciences, 89 (4). pp. 303-359. ISSN 1526-1492
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2012) Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs. CMES: Computer Modeling in Engineering and
Sciences, 84 (2). pp. 171-203. ISSN 1526-1492
Tran, C.-D. and Mai-Duy, N. and Le-Cao, K. and Tran-Cong, T. (2012) A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 85 (6). pp. 499-519. ISSN 1526-1492
Mai-Duy, N. and Tran-Cong, T. (2011) Compact local integrated-RBF approximations for second-order elliptic differential problems. Journal of Computational Physics , 230 (12). pp. 4772-4794. ISSN
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method. Computers and
Structures, 89 (1-2). pp. 1-13. ISSN 0045-7949
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2011) Compact local stencils employed with integrated RBFs for fourth-order differential problems. Structural Longevity, 6 (2). pp. 93-107. ISSN
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2011) IRBFN-based multiscale solution of a model 1D elliptic equation. In: 33rd International Conference on Boundary Elements and other
Mesh Reduction Methods (BEM/MRM 2011), 28-30 Jun 2011, New Forest, United Kingdom.
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Moving least square - one dimensional integrated radial basis function networks for time dependent problems. In: 33rd
International Conference on Boundary Elements and other Mesh Reduction Methods, 28-30 Jun 2011, New Forest, UK.
Ho-Minh, D. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of fluid flows at high Reynolds/Rayleigh numbers using integrated radial basis functions. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2010) Towards an analysis of shear suspension flows using radial basis functions. CMES: Computer Modeling in Engineering and Sciences, 67
(3). pp. 265-294. ISSN 1526-1492
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A simple and effective preconditioner for integrated-RBF-based Cartesian-grid schemes. In: 2010 International Conference on Computational and Experimental
Engineering & Sciences 2010, 28 Mar - 1 Apr 2010, Las Vegas, USA.
Mai-Duy, Nam and Tran-Cong, Thanh (2009) On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems. In: 31st International Conference on Boundary
Elements and Other Mesh Reduction Methods (BEM/MRM 31), 2-4 Sep 2009, New Forest, UK.
integrated radial-basis-function
Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless
& Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.
integrated radial-basis-function element
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems. CMES:
Computer Modeling in Engineering and Sciences, 72 (4). pp. 299-334. ISSN 1526-1492
integrated radial-basis-function network
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2011) Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian
grids. Computers and Fluids , 44 (1). pp. 32-42. ISSN 0045-7930
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains. Numerical Methods for Partial Differential
Equations, 23 (5). pp. 1192-1210. ISSN 0749-159X
integrated radial-basis-function networks
Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2009) An effective integrated-RBFN Cartesian-grid discretization for the stream function-vorticity temperature formulation in nonrectangular domains.
Numerical Heat Transfer, Part B: Fundamentals, 55 (6). pp. 480-502. ISSN 1040-7790
integrated RBF
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems. In: 4th
International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
Mai-Duy, N. and Tran-Cong, T. (2011) A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems. International Journal for Numerical Methods in Fluids, 67 (12). pp.
1973-1992. ISSN 0271-2091
Mai-Duy, N. and Tran-Cong, T. (2011) A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems. In: ACAM 6: 6th Australasian Congress
on Applied Mechanics , 12-15 Dec 2010, Perth, Western Australia.
integrated RBFN
Ho-Minh, D. and Mai-Duy, N. and Tran-Cong, T. (2012) Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach. Australian Journal of Mechanical Engineering , 9 (2). pp. 101-112.
ISSN 1448-4846
integrated RBFNs
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A Cartesian-grid integrated-RBF Galerkin technique. In: Recent studies in meshless and other novel computational methods. Tech Science Press,
Duluth, GA. USA, pp. 87-102. ISBN 0-9824205-4-4
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions. In: Recent studies in
meshless and other novel computational methods. Tech Science Press, Duluth, GA. United States, pp. 17-33. ISBN 0-9824205-4-4
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
Mai-Duy, Nam and Tran-Cong, Thanh (2009) An integrated-RBF technique based on Galerkin formulation for elliptic differential equations. Engineering Analysis with Boundary Elements, 33 (2). pp.
191-199. ISSN 0955-7997
Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems. CMES: Computer Modeling in Engineering and
Sciences, 51 (3). pp. 213-238. ISSN 1526-1492
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains. CMES:
Computer Modeling in Engineering and Sciences, 44 (3). pp. 219-248. ISSN 1526-1492
integrated RBFs
Pham-Sy, N. and Tran, C.-D. and Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T. (2013) Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination
detection based parallel algorithm. CMES Computer Modeling in Engineering and Sciences, 92 (1). pp. 1-31. ISSN 1526-1492
Pham-Sy, N. and Hoang-Trieu, T.-T. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Development of parallel algorithm for boundary value problems using compact local integrated RBFN and
domain decomposition. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
Mai-Duy, Nam and Tran-Cong, Thanh (2010) Point-wise integrated-RBF-based discretisation of differential equations. In: 2nd International Symposium on Computational Mechanics (ISCM II) in conjunction
with EPMESC 2009, 30 Nov-3 Dec 2009, Hong Kong, Macau.
Mai-Duy, Nam and Ho-Minh, D. and Tran-Cong, Thanh (2009) A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations. International Journal
of Computer Mathematics, 86 (10-11). pp. 1746-1759. ISSN 0020-7160
Mai-Duy, Nam and Tran-Cong, Thanh (2008) On the use of integrated RBFs in Galerkin approximation for elliptic problems. In: BEM/MRM 30: 30th International Conference on Boundary Elements and Other
Mesh Reduction Methods, 7-9 Jul 2008, Maribor, Slovenia.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks. In: 8th International Conference on Computational
and Mathematical Methods in Science and Engineering (CMMSE-2008), 13-16 June 2008, Murcia, Spain.
integrated-radial-basis-function element
An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of Newtonian-fluid flows with C2-continuous two-node integrated-RBF elements. Structural Longevity, 4 (1). pp. 39-45. ISSN 1944-611X
integrated-radial-basis-function elements
An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T. (2013) ADI method based on C^2-continuous two-node integrated-RBF elements for viscous flows. Applied Mathematical Modelling, 37
(7). pp. 5184-5203. ISSN 0307-904X
An-Vo, D.-A. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation. In: 34th
International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2012), 25-27 Jun 2012, Split, Croatia.
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows. CMES: Computer Modeling in Engineering and
Sciences, 80 (2). pp. 141-177. ISSN 1526-1492
Redmond, Petrea and Albion, Peter (2002) In their own words: pre-service teachers’ perceptions of ICT integration. In: 13th International Conference of the Society for Information Technology &
Teacher Education (SITE 2002), 18-23 March 2002, Nashville, Tennessee, USA.
integration constants
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
Intehrated radial basis function network
Mai-Cao, L. and Tran-Cong, T. (2006) A meshless level-set scheme for interfacial flows. In: 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi
Minh City, Vietnam.
intensified cameras
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
3 Oct 2008, Heraklion, Greece.
inter-carrier interference (ICI) reduction
Xiang, Wei and Russell, Julian and Wang, Yafeng (2010) ICI reduction through shaped OFDM in coded MIMO-OFDM systems. International Journal on Advances in Telecommunications, 3 (3&4). pp. 311-323.
ISSN 1942-2601
inter-cell interference
Wang, Yafeng and Wei, Guo-xing and Yang, Da-cheng and Xiang, Wei (2011) Research on uplink coordinated transmission schemes in LTE-advanced systems. Journal of China Universities of Posts and
Telecommunications, 18 (2). pp. 72-77. ISSN 1005-8885
inter-cell interference modeling
Wang, Yafeng and Wei, Guoxing and Xiang, Wei (2011) Approximate inter-cell interference modeling for cellular network. Journal of China Universities of Posts and Telecommunications, 18 (3). pp.
75-79. ISSN 1005-8885
inter-channel interference
Fu, Jinlin and Hou, Chunping and Xiang, Wei and Yan, Lei and Hou, Yonghong (2010) Generalised spatial modulation with multiple active transmit antennas. In: GC 2010: IEEE Globecom Workshops , 5-10
Dec 2010, Miami, FL, USA.
inter-strand pressure
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2008) Application of topological conservation to model key features of zero-torque multi-ply yarns. Journal of the Textile
Institute, 99 (4). pp. 325-337. ISSN 0040-5000
Shiau, Jim and Smith, Catherine (2006) Numerical analysis of passive earth pressures with interfaces. In: III European Conference on Computational Mechanics (ECCM 2006), 5-8 June 2006, Lisbon,
interfaces (materials)
Buttsworth, David R. and Goozee, Richard J. and Jacobs, Peter A. (2006) Measurement and simulation of the interface in a low-enthalpy shock tunnel. In: 14th International Space Planes and Hypersonic
Systems and Technologies Conference (AIAA/AHI 2006), 6-9 Nov 2006, Canberra, Australia.
interfacial debonding
Dai, Shao-Cong and Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Experimental study on z-pin bridging law by pullout test. Composites Science and Technology, 64 (16). pp. 2451-2457. ISSN
interfacial flow
Mai-Cao, L. and Tran-Cong, T. (2012) A new IRBFN scheme for the numerical simulation of interfacial flows. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold
Coast, Australia.
interfacial friction
Dai, Shao-Cong and Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Experimental study on z-pin bridging law by pullout test. Composites Science and Technology, 64 (16). pp. 2451-2457. ISSN
Intergovernmental Panel on Climate Change
Cottrill, Andrew and Ribbe, Joachim (2007) Queensland rainfall variability in IPCC AR4 model runs. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8
February 2007, Adelaide, Australia.
intermediate nodes
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Multicast based dual amplify and forward relay scheme for 2 hop networks. In: LATINCOM 2009: 1st IEEE
Latin-American Conference on Communications, 10-11 Sep 2009, Medellin, Colombia.
intermediate water
Sorensen, Jacob V. T. and Ribbe, Joachim and Shaffer, Gary (2001) Antarctic intermediate water mass formation in ocean general circulation models. Journal of Physical Oceanography, 31 (11). pp.
3295-3311. ISSN 1520-0485
Ribbe, Joachim (2001) Intermediate water mass production controlled by southern hemisphere winds. Geophysical Research Letters, 28 (3). pp. 535-538. ISSN 0094-8276
interMS interference
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
internal ballistics research
Buttsworth, David R. and Stevens, Robert and Stone, C. Richard (2005) Eroding ribbon thermocouples: impulse response and transient heat flux analysis. Measurement Science and Technology, 16 (7). pp.
1487-1494. ISSN 0957-0233
internal combustion engine design
Malpress, Ray and Buttsworth, David R. (2007) A new internal combustion engine configuration: opposed pistons with crank offset. In: 16th Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec
2007, Gold Coast, Australia.
internal combustion engine heat flux
Buttsworth, David R. and Stevens, Robert and Stone, C. Richard (2005) Eroding ribbon thermocouples: impulse response and transient heat flux analysis. Measurement Science and Technology, 16 (7). pp.
1487-1494. ISSN 0957-0233
internal combustion engine simulation
Buttsworth, David R. (2009) Multizone internal combustion engine modelling: initial assessment of a simulation tool developed in Matlab. In: 3rd International Conference on Energy and Environment:
Advancement Towards Global Sustainability (ICEE 2009), 7-8 Dec 2009, Malacca, Malaysia.
internal combustion engines
Wang, Xiaowei and Stone, C. Richard and Buttsworth, David R. and Stevens, Robert and Arita, Yoshi (2006) Finite element analysis of eroding type surface thermocouple with application to engine heat
flux measurement. In: SAE 2006 World Conference and Exhibition, April 2006, Detroit, MI, USA.
internal energy
Golshani, Aliakbar and Tran-Cong, Thanh (2008) Simulation of hydraulic fracturing in brittle rocks. In: ISRM International Symposium 2008: 5th Asian Rock Mechanics Symposium, 24-26 Nov 2008, Tehran,
internal tides
Ribbe, Joachim and Holloway, Peter E. (2001) A model of suspended sediment transport by internal tides. Continental Shelf Research, 21 (4). pp. 395-422. ISSN 0278-4343
internal wave
Ostrovsky, Lev and Stepanyants, Yury (2005) Internal solitons in laboratory experiments: Comparison with theoretical models. Chaos, 15 (037111). 037111-1. ISSN 1054-1500
internal waves
Clamond, D. and Stepanyants, Y. (2012) Stationary gravity waves with the zero mean vorticity in stratified fluid. Studies in Applied Mathematics, 128 (1). pp. 59-85. ISSN 0022-2526
Stepanyants, Yury (2006) On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons. Chaos, Solitons and Fractals, 28 (1). pp. 193-204. ISSN 0960-0779
international space stations
Khan, Razmi and Eichmann, Troy and Buttsworth, David and Upcroft, Ben (2011) Image-based visual servoing for the super-orbital re-entry of Hayabusa spacecraft. In: 2011 Australasian Conference on
Robotics and Automation (ACRA 2011) , 7-9 Dec 2011, Melbourne, Australia.
Kist, Alexander A. and Harris, Richard J. (2004) Cost efficient overflow routing for outbound ISP traffic. In: 9th IEEE Symposium on Computers and Communications (ISCC 2004), 28 Jun - 1 July 2004,
Alexandria, Egypt.
Internet Protocol
Kist, Alexander A. and Lloyd-Smith, Bill and Harris, Richard J. (2005) A simple IP flow blocking model. In: 19th International Teletraffic Congress (ITC19), 29 August - 2 Sept. 2005, Beijing, China.
internet traffic shaping
Norman, Mark and Leis, John (2010) A passive approach to detection of traffic shaping. In: APSIPA 2010: 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference,
14-17 Dec 2010, Biopolis, Singapore.
Shiau, Jim S. and Perumal, Tagarajan and Benjamin, Michael and Pather, Selvan and Ayers, Ron (2006) Developing a track model for testing the road pavement under repeated moving surface loads. In:
22nd ARRB Conference: Research Into Practice, 29 Oct - 02 Nov 2006, Canberra, Australia.
intersymbol interference
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
Xiang, Wei and Pietrobon, Steven S. (2003) On the capacity and normalisation of ISI channels. In: 2003 IEEE International Conference on Communications (ICC2003), 11-15 May 2003, Anchorage, Alaska,
intra-seasonal oscillation
Donald, Alexis and Ribbe, Joachim and Stone, Roger and Meinke, Holger and Harris, Graham and Power, Brendan and Wheeler, Matthew (2003) The influence of the Madden Julian Oscillation on Queensland's
rainfall. In: 15th Australian New Zealand Climate Forum, 19-21 Mar 2003, Palmerston, New Zealand.
intrinsic enrichment
Bordas, Stephane and Duflot, Marc and Le, Phong (2008) A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24 (11). pp. 961-971. ISSN 1069-8299
intrinsic torque
Tran, Canh-Dung and Phillips, David G. (2007) Predicting torque of worsted singles yarn using an efficient radial basis function network-based method. Journal of The Textile Institute, 98 (5). pp.
387-396. ISSN 0040-5000
intrusion detection
Zhang, Zhongwei and Zhou, Hong (2011) A MAC layer protocol supporting the application of WSNs in medicine and healthcare domains. In: 12th ACIS International Conference on Software Engineering,
Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD 2011), 6-8 Jul 2011, Sydney, Australia.
inverse estuary
Grawe, U. and Ribbe, J. and Wolff, J.-O. (2008) The inverse nature of an Australian bay. In: 5th European Geosciences Union General Assembly 2008, 13-18 April 2008, Vienna, Austria. (In Press)
Ribbe, Joachim (2007) Hervey Bay: an inverse subtropical estuary. In: Inaugural Queensland Coastal Conference 2007: Shifting Sands, 17-19 Sept 2007, Bundaberg, Australia.
inverse problem
Malomed, Boris A. and Stepanyants, Yury A. (2010) The inverse problem for the Gross-Pitaevskii equation. Chaos, 20 (1). ISSN 1054-1500
IP multimedia subsystem
Kist, Alexander A. and Harris, Richard J. (2003) Dynamic resource allocation in 3GPP SIP overlay networks. In: 2003 Joint Conference of the 4th International Conference on Information, Communications
and Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
Kist, Alexander A. and Harris, Richard J. (2003) Using virtual SIP links to enable QoS for signalling. In: 11th IEEE International Conference on Networks (ICON 2003), 28 Sept - 1 Oct 2003 , Sydney,
IP Multimedia Subsystem (IMS)
Kist, Alexander A. and Harris, Richard J. (2004) QoS framework for SIP signalling. In: 2004 IASTED International Conference on Communications Systems and Applications (CSA 2004), 8-10 July 2004,
Banff, Canada.
IP networks
Kist, Alexander A. and Harris, Richard J. (2003) Scheme for alternative packet overflow routing (SAPOR). In: 2003 Workshop on High Performance Switching and Routing (HPSR 2003), 24-27 Jun 2003,
Torino, Italy.
Cai, Wenju and Cowan, Tim and Dix, Martin and Rotstayn, Leon and Ribbe, Joachim and Shi, Ge and Wijffels, Susan (2007) Anthropogenic aerosol forcing and the structure of temperature trends in the
southern Indian Ocean. Geophysical Research Letters, 34 (14). L14611. ISSN 0094-8276
Faqih, Akhmad and Ribbe, Joachim and Meinke, Holger (2007) 20th century rainfall variability and the role of large scale climate events within Indo-Pacific region from IPCC AR4 models, reanalysis and
observations. In: 14th National Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Iran power
Ghobadian, Barat and Najafi, Gholamhassan and Rahimi, Hadi and Yusaf, T. F. (2009) Future of renewable energies in Iran. Renewable and Sustainable Energy Reviews, 13 (3). pp. 689-695. ISSN 1364-0321
Mai-Duy, Nam and Tran-Cong, Thanh (2011) Compact local approximations employed with integrated RBFs for second-order elliptic differential equations. In: 3rd International Symposium on Computational
Mechanics (ISCM III) and 2nd Symposium on Computational Structural Engineering (CSE II), 5-7 Dec 2011, Taipei, Taiwan.
Khennane, Amar and Tran-Cong, Thanh (2007) Timoshenko beam-solution in terms of integrated radial basis functions. In: 5th Australasian Congress on Applied Mechanics (ACAM 2007), 10-12 Dec 2007,
Brisbane, Australia.
Mai-Cao, L. and Tran-Cong, T. (2012) A new IRBFN scheme for the numerical simulation of interfacial flows. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold
Coast, Australia.
Mai-Cao, L. and Tran-Cong, T. (2008) A meshless approach to capturing moving interfaces in passive transport problems. CMES: Computer Modeling in Engineering and Sciences, 31 (3). pp. 157-188. ISSN
Le, P. and Mai-Duy, N. and Tran-Cong, T. and Baker, G. (2008) A meshless modeling of dynamic strain localization in quasi-brittle materials using radial basis function networks. CMES: Computer
Modeling in Engineering and Sciences, 25 (1). pp. 43-67. ISSN 1526-1492
IRBFN method
Mai-Cao, L. and Tran-Cong, T. (2005) A meshless IRBFN-based method for transient problems. CMES: Computer Modeling in Engineering and Sciences, 7 (2). pp. 149-171. ISSN 1526-1492
irradiance measurement
Buttsworth, David and Jacobs, P. and Morgan, R. G. and Jenniskens, Peter (2012) Near ultraviolet emission spectroscopy of the Hayabusa re-entry. In: 50th AIAA Aerospace Sciences Meeting Including the
New Horizons Forum and Aerospace Exposition (AIAA 2012): Advancing the Science of Flight Technology, 9-12 Jan 2012, Nashville, TN. United States.
irregular domain
Le-Cao, Khoa and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Radial-basis-function calculations of buoyancy-driven flow in concentric and eccentric annuli. In: 16th Australasian Fluid Mechanics
Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
irregular domain
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems. Numerical Methods for Partial
Differential Equations, 26 (6). pp. 1443-1462. ISSN 0749-159X
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains. Numerical Methods for Partial Differential
Equations, 23 (5). pp. 1192-1210. ISSN 0749-159X
iterative decoding
Xiang, Wei (2006) A power and bandwidth efficient remote wireless video surveillance system using joint source-channel coding. In: 13th Annual Conference on Mechatronics and Machine Vision in
Practice, 5-7 Dec 2006, Toowoomba, Australia.
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Iterative decoding of JPEG coded images with channel coding. In: 10th IEEE International Conference on Telecommunications, Feb
2003, Papeete, Tahiti.
iterative DFE
Wang, Yafeng and Yang, Hao and Yang, Dacheng and Xiang, Wei (2010) Iterative decision feedback equalizer with cyclic detection for DFT-S OFDM system. Computers and Electrical Engineering, 36 (4). pp.
789-801. ISSN 0045-7906
Wang, Yafeng and Yang, Hao and Xiang, Wei (2008) Iterative decision-feedback equalizer with cyclic detection for DFT-S OFDM system. In: 1st International Conference on Signal Processing and
Communication Systems (ICSPCS2007), 17-19 Dec 2007, Gold Coast, Queensland, Australia.
jet mixing and entrainment Kolmogorov scales
Deo, Ravinesh C. and Nathan, Graham J. and Mi, Jianchun (2013) Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers. Physics of
Fluids, 25 (1). 015115-1. ISSN 1070-6631
joint estimation
Salim, Omar Hazim and Nasir, Ali and Mehrpouyan, Hani and Xiang, Wei (2013) Phase noise and carrier frequency offset in OFDM systems: joint estimation and hybrid Cramer-Rao lower bound. In: 14th IEEE
International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2013), 16-19 Jun 2013, Darmstadt, Germany.
joint processing
Wang, Yafeng and Wei, Guo-xing and Yang, Da-cheng and Xiang, Wei (2011) Research on uplink coordinated transmission schemes in LTE-advanced systems. Journal of China Universities of Posts and
Telecommunications, 18 (2). pp. 72-77. ISSN 1005-8885
joint source-channel codec
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Steven (2003) Joint source-channel codec: a more power efficient technology for image transmission. In: 3rd International Symposium on Turbo Codes,
1-5 Sept 2003, Brest, France.
joint source-channel coding
Xiang, Wei (2006) A power and bandwidth efficient remote wireless video surveillance system using joint source-channel coding. In: 13th Annual Conference on Mechatronics and Machine Vision in
Practice, 5-7 Dec 2006, Toowoomba, Australia.
Xiang, Wei and Clemence, Andrew and Leis, John and Wang, Yafeng (2009) Error resilience analysis of wireless image transmission using JPEG, JPEG 2000 and JPWL. In: ICICS 2009: 7th International
Conference on Information, Communications and Signal Processing, 8-10 Dec 2009, Macau, China.
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Joint source-channel decoding of JPEG images using error resilient source codes. In: 2003 IEEE International Symposium on
Information Theory, 29 Jun - 4 Jul 2003, Yokohama, Japan.
JPEG 2000
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2012) Two-symbol FPGA architecture for fast arithmetic encoding in JPEG 2000. Journal of Signal Processing Systems, 69 (2). pp. 213-224. ISSN
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2010) An FPGA-based fast two-symbol processing architecture for JPEG 2000 arithmetic coding. In: ICASSP 2010: 35th International Conference on
Acoustics, Speech, and Signal Processing, 14-19 Mar 2010, Dallas, TX. USA.
Xiang, Wei and Clemence, Andrew and Leis, John and Wang, Yafeng (2009) Error resilience analysis of wireless image transmission using JPEG, JPEG 2000 and JPWL. In: ICICS 2009: 7th International
Conference on Information, Communications and Signal Processing, 8-10 Dec 2009, Macau, China.
JPEG coded image
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Steven (2003) Joint source-channel codec: a more power efficient technology for image transmission. In: 3rd International Symposium on Turbo Codes,
1-5 Sept 2003, Brest, France.
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Joint source-channel decoding of JPEG images using error resilient source codes. In: 2003 IEEE International Symposium on
Information Theory, 29 Jun - 4 Jul 2003, Yokohama, Japan.
Xiang, Wei and Clemence, Andrew and Leis, John and Wang, Yafeng (2009) Error resilience analysis of wireless image transmission using JPEG, JPEG 2000 and JPWL. In: ICICS 2009: 7th International
Conference on Information, Communications and Signal Processing, 8-10 Dec 2009, Macau, China.
k-epsilon model
Strunin, D. V. (2008) Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet. Bulletin of the Belgian Mathematical Society: Simon Stevin, 15 (5). pp. 935-946. ISSN
k-omega turbulence model
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2006) The dynamics of the vertical structure of turbulence in flood flows. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 48 (CTAC-2). C573-C590. ISSN 1446-8735
k-omega turbulent model
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2007) Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model. Discrete and Continuous Dynamical Systems Series
A, 2007 (Specia). pp. 419-428. ISSN 1078-0947
k-shortest path algorithm
Lloyd-Smith, Bill and Kist, Alexander A. and Shrestha, N. and Harris, Richard J. (2004) Shortest paths in stochastic networks. In: 12th IEEE International Conference on Networks (ICON 2004), 16-19
Nov 2004, Singapore.
KdV equation
Obregon, M. A. and Stepanyants, Y. A. (2012) On numerical solution of the Gardner–Ostrovsky equation. Mathematical Modelling of Natural Phenomena, 7 (2). pp. 113-130. ISSN 0973-5348
knowledge transfer
UNSPECIFIED (2013) Proceedings of the 3rd Malaysian Postgraduate Conference (MPC 2013). In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
Korteweg-de Vries equation
Apel, John R. and Ostrovsky, Lev A. and Stepanyants, Yury A. and Lynch, James F. (2007) Internal solitons in the ocean and their effect on underwater sound. Journal of the Acoustical Society of
America, 121 (2). pp. 695-722. ISSN 0001-4966
Korteweg–de Vries equation
Malomed, B. A. and Stepanyants, Y. A. (2010) Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external
potentials. In: ICEAA 2010: International Conference on Electromagnetics in Advanced Applications , 20-24 Sep 2010, Sydney, Australia.
Kruithof method
Eum, Suyong and Harris, Richard J. and Kist, Alexander (2006) Generalized Kruithof approach for traffic matrix estimation. In: 14th IEEE International Conference on Networks (ICON 2006), 13-15 Sep
2006, Singapore.
Kth-bestg approach
Shi, Chenggen and Zhou, Hong and Lu, Jie and Zhang, Guangquan and Zhang, Zhongwei (2007) The Kth-best approach for linear bilevel multifollower programming with partial shared variables among
followers. Applied Mathematics and Computation, 188 (2). pp. 1686-1698. ISSN 0096-3003
Kullback distance
Eum, Suyong and Harris, Richard J. and Kist, Alexander (2006) Generalized Kruithof approach for traffic matrix estimation. In: 14th IEEE International Conference on Networks (ICON 2006), 13-15 Sep
2006, Singapore.
Kuramoto-Sivashinsky equation
Strunin, D. V. and Mohammed, M. G. (2012) Parametric space for nonlinearly excited phase equation. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 53. C236-C248.
ISSN 1446-8735
laboratory experiment
Ostrovsky, Lev and Stepanyants, Yury (2005) Internal solitons in laboratory experiments: Comparison with theoretical models. Chaos, 15 (037111). 037111-1. ISSN 1054-1500
laboratory experiments
Giovanangeli, Jean-Paul and Kharif, Christian and Raj, Nawin and Stepanyants, Yury (2013) Nonlinear spectra of shallow water waves. In: Oceans - San Diego, 2013, 23-26 Sept 2013, San Diego, USA.
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
laminar flow
Mossad, Ruth and Aral, Hal (2010) Numerical modeling of flow in a horizontal sand filter. American Journal of Engineering and Applied Sciences, 3 (2). pp. 286-292. ISSN 1941-7020
laminated composite plate
Mai-Duy, Nam and Khennane, Amar and Tran-Cong, Thanh (2007) Computation of laminated composite plates using integrated radial basis function networks. CMC: Computers, Materials and Continua, 5 (1).
pp. 63-77. ISSN 1546-2218
laminated composite plate and shell
Nguyen-Van, H. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell
element with in-plane rotations. Computers and Structures, 89 (7-8). pp. 612-625. ISSN 0045-7949
laminated composite plates
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method. Computers and
Structures, 89 (1-2). pp. 1-13. ISSN 0045-7949
Ngo-Cong, Duc and Mai-Duy, Nam and Karunasena, W. and Tran-Cong, Thanh (2010) Integrated-RBF network method for free vibration analysis of laminated composite plates. In: 9th World Congress on
Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010), 19-23 July 2010, Sydney, Australia.
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Analysis of laminated composite plate/shell structures using a stabilized nodal-integrated quadrilateral element. In: 1st International
Conference on Modern Design, Construction & Maintenance of Structures, 10-11 Dec 2007, Hanoi, Vietnam.
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2007) A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates. CMC: Computers, Materials
and Continua, 6 (3). pp. 159-176. ISSN 1546-2218
laminated plate/shells
Nguyen-Van, H. and Mai-Duy, N. and Tran-Cong, T. (2008) Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element. Journal of
Sound and Vibration, 313 (1-2). pp. 205-223. ISSN 0022-460X
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2004) Mode II delamination toughness of z-pinned laminates. Composites Science and Technology, 64 (13-14). pp. 1937-1945. ISSN 0266-3538
Yan, Wenyi and Liu, Hong-Yuan and Mai, Yiu-Wing (2003) Numerical study on the mode I delamination toughness of z-pinned laminates. Composites Science and Technology, 63 (10). pp. 1481-1493. ISSN
land mobile radio diversity systems
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
landing site
Buttsworth, David and Jacobs, P. and Morgan, R. G. and Jenniskens, Peter (2012) Near ultraviolet emission spectroscopy of the Hayabusa re-entry. In: 50th AIAA Aerospace Sciences Meeting Including the
New Horizons Forum and Aerospace Exposition (AIAA 2012): Advancing the Science of Flight Technology, 9-12 Jan 2012, Nashville, TN. United States.
Langevin equation
Henry, B. I. and Langlands, T. A. M. and Straka, P. (2010) Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces. Physical Review Letters, 105 (17).
17062-1-170602-4. ISSN 0031-9007
Langevin models
Wandel, Andrew P. and Lindstedt, R. Peter (2013) Hybrid multiple mapping conditioning modeling of local extinction. Proceedings of the Combustion Institute, 34 (1). pp. 1365-1372. ISSN 1540-7489
large-scale systems
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
laser sensor technology
Xiang, Wei and Otto, Colin W. and Wen, Peng (2009) Automated vehicle classification system for AUSTROADS standard based upon laser sensor technology. Australian Journal of Electrical and Electronics
Engineering, 5 (2). pp. 95-106. ISSN 1448-837X
Sharifian, Ahmad (2012) The effect of wind speed on the performance of a split chimney. In: 2012 International Conference on Fluid Dynamics and Thermodynamics Technologies (FDTT 2012), 17-18 March
2012, Singapore.
learning system
Kist, Alexander A. and Gibbings, Peter and Maxwell, Andrew D. and Jolly, Hannah (2013) Supporting remote laboratory activities at an institutional level. International Journal of Online Engineering ,
9 (S5). pp. 38-47.
Leis, John and Buttsworth, David and Martin, Philip (2011) A broadband multisensor approach to gas monitoring. In: 6th Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion,
5-7 Dec 2011, Canberra, Australia.
level set method
Mai-Cao, L. and Tran-Cong, T. (2012) A new IRBFN scheme for the numerical simulation of interfacial flows. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold
Coast, Australia.
Mai-Cao, L. and Tran-Cong, T. (2008) A meshless approach to capturing moving interfaces in passive transport problems. CMES: Computer Modeling in Engineering and Sciences, 31 (3). pp. 157-188. ISSN
level set method (LSM)
Mai-Duy, N. and Mai-Cao, L. and Tran-Cong, T. (2006) A new meshless RBF-based method for unsteady fluid flow analysis. In: Advances in meshless methods. Tech Science Press, USA, pp. 241-262. ISBN
lid-driven cavity flow
Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless
& Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.
lid-driven cavity flow
Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2011) Discretisation of the velocity-pressure formulation with integrated radial-basis-function networks. Structural Longevity, 6 (2).
pp. 77-91. ISSN 1944-611X
light control
Wang, Gengkun and Xiang, Wei and Chen, Haoyu and Wen, Peng (2011) Wireless sensor home automation networks based upon Sun SPOT. In: ICSSC 2011: IET International Conference on Smart and Sustainable
City (IET ICSSC2011), 6-8 Jul 2011, Shanghai, China.
limit analysis
Shiau, J. S. and Merifield, R. S. and Lyamin, A. V. and Sloan, S. W. (2011) Undrained stability of footings on slopes. International Journal of Geomechanics, 11 (5). pp. 381-390. ISSN 1532-3641
Shiau, Jim S. and Augarde, Charles E. and Lyamin, Andrei V. and Sloan, Scott W. (2008) Finite element limit analysis of passive earth resistance in cohesionless soils. Soils and Foundations, 48 (6).
pp. 843-850. ISSN 0038-0806
linear approximation
Clamond, D. and Stepanyants, Y. (2012) Stationary gravity waves with the zero mean vorticity in stratified fluid. Studies in Applied Mathematics, 128 (1). pp. 59-85. ISSN 0022-2526
Linear bilevel programming
Shi, Chenggen and Zhou, Hong and Lu, Jie and Zhang, Guangquan and Zhang, Zhongwei (2007) The Kth-best approach for linear bilevel multifollower programming with partial shared variables among
followers. Applied Mathematics and Computation, 188 (2). pp. 1686-1698. ISSN 0096-3003
Shi, Chenggen and Lu, Jie and Zhang, Guangquan and Zhou, Hong (2006) An extended branch and bound algorithm for linear bilevel programming. Applied Mathematics and Computation, 180 (2). pp. 529-537.
ISSN 0096-3003
linear dynamics
Roberts, A. J. (2003) A holistic finite difference approach models linear dynamics consistently. Mathematics of Computation, 72 (241). pp. 247-262. ISSN 0025-5718
linear precoding vector algorithm
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2008) Application of topological conservation to model key features of zero-torque multi-ply yarns. Journal of the Textile
Institute, 99 (4). pp. 325-337. ISSN 0040-5000
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2006) Issues in processing unstable twisted fibre assemblies. In: 4th International Industrial Simulation Conference (ISC 2006),
5-7 Jun 2006, Palermo, Italy.
link state information
Lloyd-Smith, Bill and Kist, Alexander A. and Shrestha, N. and Harris, Richard J. (2004) Shortest paths in stochastic networks. In: 12th IEEE International Conference on Networks (ICON 2004), 16-19
Nov 2004, Singapore.
load balancing
Kist, Alexander A. (2006) Dynamic routing for multi-homed enterprise gateways. In: ATNAC 2006: Australian Telecommunications Networks and Applications Conference, 4-6 Dec 2006, Melbourne, Australia.
load proportional power consumption
Kist, Alexander A. (2011) Modelling of staged routing for reduced carbon footprints of large server clusters. International Journal of Communication Networks and Distributed Systems, 6 (1). pp.
28-44. ISSN 1754-3916
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
load sharing
Kist, Alexander A. and Harris, Richard J. (2003) SIP Message Overflow Routing Scheme (SMORS). In: ATNAC 2003: Australian Telecommunications Networks and Applications Conference, 8-10 Dec 2003,
Melbourne, Australia.
local approximation
An-Vo, D.-A. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation. In: 34th
International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2012), 25-27 Jun 2012, Split, Croatia.
Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless
& Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems. CMES:
Computer Modeling in Engineering and Sciences, 72 (4). pp. 299-334. ISSN 1526-1492
An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T. (2011) High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows. CMES: Computer Modeling in Engineering and
Sciences, 80 (2). pp. 141-177. ISSN 1526-1492
An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of Newtonian-fluid flows with C2-continuous two-node integrated-RBF elements. Structural Longevity, 4 (1). pp. 39-45. ISSN 1944-611X
local approximations
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions. In: Recent studies in
meshless and other novel computational methods. Tech Science Press, Duluth, GA. United States, pp. 17-33. ISBN 0-9824205-4-4
Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems. CMES: Computer Modeling in Engineering and
Sciences, 51 (3). pp. 213-238. ISSN 1526-1492
local IRBF
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based Galerkin meshless method. CMES: Computer Modeling in Engineering and Sciences, 66 (1). pp. 25-52.
ISSN 1526-1492
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
local RBF approximation
An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T. (2013) ADI method based on C^2-continuous two-node integrated-RBF elements for viscous flows. Applied Mathematical Modelling, 37
(7). pp. 5184-5203. ISSN 0307-904X
local Reynolds number
Deo, Ravinesh C. and Nathan, Graham J. and Mi, Jianchun (2013) Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers. Physics of
Fluids, 25 (1). 015115-1. ISSN 1070-6631
localised stationary solutions
Malomed, Boris A. and Stepanyants, Yury A. (2010) The inverse problem for the Gross-Pitaevskii equation. Chaos, 20 (1). ISSN 1054-1500
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
Nguyen-Van, H. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell
element with in-plane rotations. Computers and Structures, 89 (7-8). pp. 612-625. ISSN 0045-7949
log-likelihood ratios
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
low emission
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
low-cost high-speed camera
Chong, Albert K. and Buttsworth, David and Mudford, Neil and Jokic, Michael and Balage, Sudantha and O'Bryne, Sean (2012) Application of photogrammetry at USQ hypersonic wind tunnel. In: 11th
Australian Space Science Conference (ASSC 2011) , 26-29 Sep 2011, Canberra, Australia.
Jenkins, J. S. and Jones, H. R. A. and Tinney, C. G. and Butler, R. P. and McCarthy, C. and Marcy, G. W. and Pinfield, D. J. and Carter, B. D. and Penny, A. J. (2006) An activity catalogue of
southern stars. Monthly Notices of the Royal Astronomical Society, 372 (1). pp. 163-173. ISSN 0035-8711
low-power electronics
Leis, J. and Martin, P. and Buttsworth, D. (2012) Simplified digital lock-in amplifier algorithm. Electronics Letters, 48 (5). pp. 259-261. ISSN 0013-5194
lower bound
Shiau, Jim S. (2011) A shakedown limit under Hertz contact pressure. In: 2011 International Conference on Advanced Engineering Materials and Technology (AEMT 2011), 29-31 Jul 2011, Sanya, China.
lubricant oil
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
lubrication model
Roberts, A. J. (2006) A normal form of thin fluid film equations solves the transient paradox. Physica D: Nonlinear Phenomena, 223 (1). pp. 69-81. ISSN 0167-2789
Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120
lubrication theory
Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120
Ludwieg tube
Buttsworth, David R. (2010) Ludwieg tunnel facility with free piston compression heating for supersonic and hypersonic testing. In: 9th Australian Space Science Conference, 28-30 Sept 2009, Sydney,
Buttsworth, David R. and Smart, Michael K. (2010) Development of a Ludwieg tube with free piston compression heating for scramjet inlet starting experiments. In: 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010, Orlando, FL. USA.
Al-Falahi, Amir and Yusaf, T. and Yusoff, M. Z. (2007) Experimental and CFD study of the effects of design parameters on Reynolds number in a short duration hypersonic test facility. In: EPMESC X:
Enhancement and Promotion of Computational Methods in Engineering and Science X, 21-23 Aug 2006, Sanya, China.
Mach 4 hydrogen jet
Buttsworth, David R. and Jones, Terry V. (2004) Transient temperature probe measurements in a Mach 4 nitrogen jet. Experiments in Fluids, 37 (1). pp. 137-145. ISSN 0723-4864
Mach 4 nonreacting hydrogen jet
Buttsworth, David R. and Jones, Terry V. (2003) Concentration probe measurements in a Mach 4 nonreacting hydrogen jet. Journal of Fluids Engineering, 125 (4). pp. 628-635. ISSN 0098-2202
Mach 6 carbon dioxide flow
Buttsworth, David R. and Jones, Terry V. (2003) High bandwidth stagnation temperature measurements in a Mach 6 gun tunnel flow. Experimental Thermal and Fluid Science, 27 (2). pp. 177-186. ISSN
Mach number
Al-Falahi, Amir and Yusoff, M. Z. and Yusaf, T. (2008) Numerical simulation of inviscid transient flows in shock tube and its validations. In: ICFM 2008: 5th International Conference on Fluid
Mechanics, 12-14 Sep 2008, Heidelberg, Germany.
Wen, Peng and Kidd, Jason G. (2005) Electronic height indicator for agricultural machines. Australian Journal of Electrical and Electronics Engineering, 2 (1). pp. 13-20. ISSN 1448-837X
macro-micro multi-scale method
Tran, C.-D. and An-Vo, D.-A. and Mai-Duy, N. and Tran-Cong, T. (2011) An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows. CMES: Computer Modeling in
Engineering and Sciences, 82 (2). pp. 137-162. ISSN 1526-1492
macro-micro multi-scale method
Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.
Madden Julian Oscillation
Donald, Alexis and Meinke, Holger and Power, Brendan and Maia, Aline de H. N. and Wheeler, Matthew and Stone, Roger C. and Ribbe, Joachim and White, Neil (2006) Near-global impact of the
Madden-Julian Oscillation on rainfall. Geophysical Research Letters, 33 (9). L09704. ISSN 0094-8276
Donald, Alexis and Ribbe, Joachim and Stone, Roger and Meinke, Holger and Harris, Graham and Power, Brendan and Wheeler, Matthew (2003) The influence of the Madden Julian Oscillation on Queensland's
rainfall. In: 15th Australian New Zealand Climate Forum, 19-21 Mar 2003, Palmerston, New Zealand.
magnetic fields
Marsden, S. C. and Donati, J.-F. and Semel, M. and Petit, P. and Carter, B. D. (2006) Surface differential rotation and photospheric magnetic field of the young solar-type star HD 171488 (V889 Her).
Monthly Notices of the Royal Astronomical Society, 370 (1). pp. 468-476. ISSN 0035-8711
magnetic flux density distribution
Hewitt, Andrew and Ahfock, Tony L. and Suslov, Sergey A. (2005) Magnetic flux density distribution in axial flux machine cores. IET Electric Power Applications, 152 (2). pp. 192-196. ISSN 1350-2352
magnetic induction (MI)
Parameswaran, Vinod and Zhou, Hong and Zhang, Zhongwei (2013) Wireless underground sensor network design for irrigation control: simulation of RFID deployment. In: 7th International Conference on
Sensing Technology (ICST 2013), 3-5 Dec 2013, Wellington, New Zealand.
Magnetic Induction (MI)
Parameswaran, Vinod and Zhou, Hong and Zhang, Zhongwei (2012) Irrigation control using wireless underground sensor networks. In: 6th International Conference on Sensing Technology (ICST 2012), 18-21
Dec 2012, Kolkata, India.
Bozhko, Alexandra A. and Suslov, Sergey A. and Putin, Gennady F. (2008) Magneto-hydrodynamic interaction in a vertical slot filled with ferrofluid. In: 7th PAMIR International Conference on
Fundamental and Applied MHD, 8-12 Sept 2008, Presqu´île de Giens - France.
Suslov, Sergey A. and Bozhko, Alexandra A. and Putin, Gennady F. (2008) Thermo-magneto-convective instabilities in a vertical layer of ferro-magnetic fluid. In: XXXVI International Conference
Advanced Problems in Mechanics, 6-10 Jul 2008, Repino, Russia.
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Noor, M. M. and Rahman, M. M. and Ismail, J., eds. (2012) Proceedings of the 2nd Malaysian Posgraduate Conference (MPC 2012). Education Malaysia, Sydney (EMAS), Gold Coast, Australia.
Amirruddin, A. K. and Noor, M. M. and Kadirgama, K. and Sharma, K. V. (2012) The potential of wind and solar energy in Malaysia east coast: preliminary study at Universiti Malaysia Pahang (UMP). In:
3rd International Conference on Management of Natural Resources, Sustainable Development and Ecological Hazards: Ravage of the Planet III (RAV 2011) , 13-15 Dec 2011, Selangor, Malaysia.
management tool
Suryasaputra, Robert and Kist, Alexander A. and Harris, Richard J. (2005) OptiFlow - a capacity management tool. In: IEEE Tencon (IEEE Region 10 Conference), 21-24 Nov 2005, Melbourne, Australia.
Tran, C.-D. and Lucas, S. and Phillips, D. G. and Randeniya, L. K. and Baughman, R. H. and Tran-Cong, T. (2011) Manufacturing polymer/carbon nanotube composite using a novel direct process.
Nanotechnology, 22 (14). pp. 1453021-1453029. ISSN 0957-4484
marginal increase heuristics
Suryasaputra, R. and Kist, A. A. and Ferra, H. L. and Palmer, R. A. and Dale, M. J. and Harris, R. J. (2006) Comparison of intra-domain traffic engineering methods. In: World Teletraffic Congress
(WTC 2006), 30 April - 3 May 2006, Budapest, Hungary.
Markov chain
Teng, Lanzhi and Wen, Peng (2007) Networked PID control system modeling and simulation using Markov chain. In: 2007 IEEE International Conference on Integration Technology, 20-24 March 2007,
Shenzhen, China.
Tangalajuk Siang, Jeri and Sharifian, Ahmad (2013) Reducing the mass of the refrigerant in the capillary tube of a propane air-conditioner. In: 14th Asian Congress of Fluid Mechanics (14 ACFM), 15-19
Oct 2013, Hanoi-Halong, Vietnam.
mathematical modelling
Zeiler, Irmgard and Langlands, Trevor and Murray, John M. and Ritter, Alison (2010) Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone
maintenance programs. Drug and Alcohol Dependence, 110 (3). pp. 228-233. ISSN 0376-8716
mathematical models
Roberts, A. J. (2001) Holistic discretisation ensures fidelity to Burger's equation. Applied Numerical Mathematics, 37 (3). pp. 371-396. ISSN 0168-9274
mathematical physics
Lozanovski, C. and Wylleman, L. (2011) Complex windmill transformation producing new purely magnetic fluids. Classical and Quantum Gravity, 28 (7). 075015-075031. ISSN 0264-9381
mathematical programming
Shiau, Jim S. (2011) A shakedown limit under Hertz contact pressure. In: 2011 International Conference on Advanced Engineering Materials and Technology (AEMT 2011), 29-31 Jul 2011, Sanya, China.
Wandel, Andrew P. (2010) Linkages between courses: a holistic approach to programmes. In: AaeE 2010: Past, Present, Future - the 'Keys' to Engineering Education Research and Practice, 5-8 Dec 2010,
Sydney, Australia.
Zhu, SongPing and Strunin, Dmitry V. (2001) Modelling the confinement of spilled oil with floating booms. Applied Mathematical Modelling, 25 (9). pp. 713-729. ISSN 0307-904X
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Discretization of three dimensional non-uniform grid: conditional moment closure elliptic equation using finite difference method. In: 3rd
Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
MATLAB simulation
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Multicast based dual amplify and forward relay scheme for 2 hop networks. In: LATINCOM 2009: 1st IEEE
Latin-American Conference on Communications, 10-11 Sep 2009, Medellin, Colombia.
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
Matthias Tomczak
You, Yuzhu and Ribbe, Joachim and Karstensen, Johannes and Church, John (2008) Matthias Tomczak: a distinguished regional oceanographer and water-mass expert. Progress in Oceanography, 77 (4). pp.
269-272. ISSN 0079-6611
You, Yuzhu and Ribbe, Joachim and Karstensen, Johannes and Church, John, eds. (2008) A new view of water masses after WOCE: a special edition [of Progress in Oceanography] for Professor Matthias
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maximum temperature
Yusaf, Talal F. (2009) Diesel engine optimization for electric hybrid vehicles. Journal of Energy Resources Technology, 131 (1). 12203-1-12203-4. ISSN 0195-0738
Leis, John (2013) Simultaneous gain, drift and offset estimation in measurement systems using coherent sampling. In: 7th International Conference on Signal Processing and Communication Systems
(ICSPCS 2013), 16-18 Dec 2013, Gold Coast, Australia.
Leis, J. and Martin, P. and Buttsworth, D. (2012) Simplified digital lock-in amplifier algorithm. Electronics Letters, 48 (5). pp. 259-261. ISSN 0013-5194
Buttsworth, David R. and Jones, Terry V. (2003) Concentration probe measurements in a Mach 4 nonreacting hydrogen jet. Journal of Fluids Engineering, 125 (4). pp. 628-635. ISSN 0098-2202
measurement and analysis
Buttsworth, David and D'Souza, Mary and Potter, Daniel and Eichmann, Troy and Mudford, Neil and McGilvray, Matthew and McIntyre, Timothy J. and Jacobs, Peter and Morgan, Richard (2010) Expansion
tunnel radiation experiments to support Hayabusa re-entry observations. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA 2010), 4-7 Jan 2010,
Orlando, FL, USA.
measurement theory
Buttsworth, David R. and Goozee, Richard J. and Jacobs, Peter A. (2006) Measurement and simulation of the interface in a low-enthalpy shock tunnel. In: 14th International Space Planes and Hypersonic
Systems and Technologies Conference (AIAA/AHI 2006), 6-9 Nov 2006, Canberra, Australia.
Buttsworth, David R. and Jones, Terry V. (2004) Transient temperature probe measurements in a Mach 4 nitrogen jet. Experiments in Fluids, 37 (1). pp. 137-145. ISSN 0723-4864
Zhu, SongPing and Strunin, Dmitry V. (2001) Modelling the confinement of spilled oil with floating booms. Applied Mathematical Modelling, 25 (9). pp. 713-729. ISSN 0307-904X
median filter
Chan, Auc Fai and Leis, John (2008) Comparison of weighted average and median filters for wireless retransmission timeout estimation. In: ICSPCS 2008: 2nd International Conference on Signal
Processing and Communication Systems, 15-17 Dec 2008, Gold Coast, Australia.
medical and Health care
Zhang, Zhongwei and Hu, Xiaohua (2013) ZigBee based wireless sensor networks and their use in medical and health care domain. In: 7th International Conference on Sensing Technology (ICST 2013), 3-5
Dec 2013, Wellington, New Zealand.
medical domains
Zhou, Hong and Ali, Hesham and Youn, Jon and Zhang, Zhongwei (2010) A hybrid wired and wireless network infrastructure to improve the productivity and quality care of critical medical applications.
In: 2010 IEEE/ICME International Conference on Complex Medical Engineering (CME 2010), 13-15 July 2010, Gold Coast, Australia.
medical instruments
Zhou, Hong and Ali, Hesham and Youn, Jon and Zhang, Zhongwei (2010) A hybrid wired and wireless network infrastructure to improve the productivity and quality care of critical medical applications.
In: 2010 IEEE/ICME International Conference on Complex Medical Engineering (CME 2010), 13-15 July 2010, Gold Coast, Australia.
medical profession
Zhou, Hong and Ali, Hesham and Youn, Jon and Zhang, Zhongwei (2010) A hybrid wired and wireless network infrastructure to improve the productivity and quality care of critical medical applications.
In: 2010 IEEE/ICME International Conference on Complex Medical Engineering (CME 2010), 13-15 July 2010, Gold Coast, Australia.
memory-integral drag
Stepanyants, Yury A. and Yeoh, Guan H. (2010) Nanoparticle dynamics in a viscous fluid at small Reynolds numbers. In: 6th Australasian Congress on Applied Mechanics (ACAM 6), 12-15 Dec 2010, Perth,
Western Australia.
Hashempour, Javad and Sharifian, Ahmad (2012) Potentials of metal mesh to contain bushfires. In: 2012 Qld Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
mesh free methods
Khennane, Amar and Tran-Cong, Thanh (2007) Timoshenko beam-solution in terms of integrated radial basis functions. In: 5th Australasian Congress on Applied Mechanics (ACAM 2007), 10-12 Dec 2007,
Brisbane, Australia.
mesh-free method
Mai-Duy, Nam and Tran-Cong, Thanh (2001) Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks. International Journal for Numerical Methods in Fluids, 37
(1). pp. 65-86. ISSN 0271-2091
Mai-Duy, Nam and Tran-Cong, Thanh (2001) Numerical solution of differential equations using multiquadric radial basis function networks. Neural Networks, 14 (2). pp. 185-199. ISSN 0893-6080
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based Galerkin meshless method. CMES: Computer Modeling in Engineering and Sciences, 66 (1). pp. 25-52.
ISSN 1526-1492
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
meshless discretization
Mai-Duy, N. and Tran-Cong, T. (2008) A meshless technique based on integrated radial basis function networks for elliptic partial differential equations. In: 4th International Workshop on Meshfree
Methods for Partial Differential Equations, 17-20 Sep 2007, Bonn, Germany.
meshless level set method
Mai-Cao, L. and Tran-Cong, T. (2006) A meshless level-set scheme for interfacial flows. In: 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi
Minh City, Vietnam.
meshless method
Mai-Cao, L. and Tran-Cong, T. (2012) A new IRBFN scheme for the numerical simulation of interfacial flows. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold
Coast, Australia.
An-Vo, D.-A. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation. In: 34th
International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2012), 25-27 Jun 2012, Split, Croatia.
Tran, Canh-Dung and Phillips, David G. and Tran-Cong, Thanh (2009) Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique. Korea-Australia
Rheology Journal, 21 (1). pp. 1-12. ISSN 1226-119X
Mai-Cao, L. and Tran-Cong, T. (2008) A meshless approach to capturing moving interfaces in passive transport problems. CMES: Computer Modeling in Engineering and Sciences, 31 (3). pp. 157-188. ISSN
Mai-Duy, Nam and Khennane, Amar and Tran-Cong, Thanh (2007) Computation of laminated composite plates using integrated radial basis function networks. CMC: Computers, Materials and Continua, 5 (1).
pp. 63-77. ISSN 1546-2218
Mai-Duy, N. and Tran-Cong, T. (2006) Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis With Boundary Elements, 30
(2). pp. 77-87. ISSN 0955-7997
Mai-Cao, L. and Tran-Cong, T. (2005) A meshless IRBFN-based method for transient problems. CMES: Computer Modeling in Engineering and Sciences, 7 (2). pp. 149-171. ISSN 1526-1492
meshless method for Navier-Stokes equations
Mai-Cao, L. and Tran-Cong, T. (2006) A meshless level-set scheme for interfacial flows. In: 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006, Ho Chi
Minh City, Vietnam.
message loss probabilities
Kist, Alexander A. and Harris, Richard J. (2003) Using virtual SIP links to enable QoS for signalling. In: 11th IEEE International Conference on Networks (ICON 2003), 28 Sept - 1 Oct 2003 , Sydney,
message passing interface (MPI)
Tran, Canh-Dung and Phillips, David G. and Tran-Cong, Thanh (2009) Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique. Korea-Australia
Rheology Journal, 21 (1). pp. 1-12. ISSN 1226-119X
metal mesh
Sharifian, Ahmad and Buttsworth, David R. (2009) Direct radiation from wildfires through square woven screens. In: ASME 2008: Summer Heat Transfer Conference, 10-14 Aug 2008, Jacksonville, FL. USA.
Sharifian, Ahmad and Buttsworth, David R. (2007) Computational simulation of the wind-force on metal meshes. In: 16th Australasian Fluid Mechanics Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast,
metal screens
Hashempour, Javad and Sharifian, Ahmad (2012) Potentials of metal mesh to contain bushfires. In: 2012 Qld Southern Regional Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
methadone treatment
Zeiler, Irmgard and Langlands, Trevor and Murray, John M. and Ritter, Alison (2010) Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone
maintenance programs. Drug and Alcohol Dependence, 110 (3). pp. 228-233. ISSN 0376-8716
Mossad, Ruth and Vella, Anthony and Balusu, Rao (2009) Inertisation of highwall mining to control methane concentrations at the Moura mine. In: 7th International Conference on Computational Fluid
Dynamics in the Minerals and Process Industries (CFD2009), 9-11 Dec 2009, Melbourne, Australia.
Najafi, Gholamhassan and Yusaf, Talal (2009) Experimental investigation of using methanol-diesel blended fuels in diesel engine. In: 4th International Conference on Thermal Engineering Theory and
Applications, 12-14 Jan 2009, Abu Dhabi, UAE.
methanol-diesel blends
Najafi, Gholamhassan and Yusaf, Talal (2009) Experimental investigation of using methanol-diesel blended fuels in diesel engine. In: 4th International Conference on Thermal Engineering Theory and
Applications, 12-14 Jan 2009, Abu Dhabi, UAE.
Al-lwayzy, Saddam H. (2012) Alternative fuels from microalgae for diesel engine. In: USQ Combustion Meeting, 10 Oct 2012, Toowoomba, Australia. (Unpublished)
microalgae biodiesel
Yusaf, T. F. and Al-lwayzy, Saddam H. (2012) The use of microalgae biodiesel in diesel engine: production, extraction and engine performance. In: USQ Combustion Meeting, 21 Nov 2012, Toowoomba,
Australia. (Unpublished)
microarray classification
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
microarray data
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
microarray gene data
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) A robust ensemble classification method analysis. In: 2009 International Conference on Bioinformatics and Computational Biology ,
13-16 Jul 2009, Las Vegas, NV. United States.
microcantilever-based electronic nose
Pinnaduwage, L. A. and Zhao, W. and Gehl, A. C. and Allman, S. L. and Shepp, A. and Mahmud, K. K. and Leis, J. W. (2007) Quantitative analysis of ternary vapor mixtures using a microcantilever-based
electronic nose. Applied Physics Letters, 91 (4). pp. 1-3. ISSN 0003-6951
Wen, Peng and Kidd, Jason G. (2005) Electronic height indicator for agricultural machines. Australian Journal of Electrical and Electronics Engineering, 2 (1). pp. 13-20. ISSN 1448-837X
Golshani, Aliakbar and Okui, Yoshiaki and Oda, Masanobu and Takemura, Takato (2006) A micromechanical model for brittle failure of rock and its relation to crack growth observed in trixial
compression tests of granite. Mechanics of Materials, 38 (4). pp. 287-303. ISSN 0167-6636
micromechanical damage model
Golshani, Aliakbar and Tran-Cong, Thanh (2006) Modelling a borehole subjected to fluid pressure. In: 2006 International Conference on Nonlinear Analysis & Engineering Mechanics Today, 11-14 Dec 2006,
Ho Chi Minh City, Vietnam.
Golshani, Aliakbar and Tran-Cong, Thanh (2009) Energy analysis of hydraulic fracturing. KSCE Journal of Civil Engineering, 13 (4). pp. 219-224. ISSN 1226-7988
Golshani, Aliakbar and Tran-Cong, Thanh (2008) Energy analysis of hydraulic fracturing. In: 12th International Conference of IACMAG, 1-6 Oct 2008, Goa, India.
micromixing model
Wandel, Andrew P. (2011) A stochastic micromixing model based on the turbulent diffusion length scale. In: Australian Combustion Symposium 2011 (ACS 2011), 29 Nov-1 Dec 2011, Newcastle, Australia.
MILD combustion
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2014) MILD combustion: the future for lean and clean combustion technology. International Review of Mechanical Engineering , 8 (1). pp. 251-257.
ISSN 1970-8734
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) The air fuel ratio study for the mixture of biogas and hydrogen on mild combustion. In: 3rd Malaysian Postgraduate Conference (MPC 2013), 4-5
Jul 2013, Sydney, Australia.
Yusaf, Talal and Noor, M. M. and Wandel, Andrew P. (2013) Mild combustion: the future for lean and clean combustion. In: 2nd International Conference of Mechanical Engineering Research (ICMER 2013):
Green Technology for Sustainable Environment, 1-3 Jul 2013, Pahang, Malaysia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2012) A review of mild combustion and open furnace design consideration. International Journal of Automotive and Mechanical Engineering, 6 (1). pp.
730-754. ISSN 2229-8649
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Numerical investigation of influence of air and fuel dilution for open furnace MILD combustion burner. In: 2012 Qld Southern Regional
Engineering Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The study of air fuel ratio for open furnace MILD combustion of biogas on bluff-body burner. In: 2012 Qld Southern Regional Engineering
Conference (SREC 2012), 1 Sep 2012, Toowoomba, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Investigation of Biogas Moderate or Intense Low Oxygen Dilution (MILD) combustion on open furnace bluff-body burner. In: USQ Combustion
Meeting, 29 Aug 2012, Toowoomba, Australia. (Unpublished)
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) Mild combustion: a technical review towards open furnace combustion. In: 2nd Malaysian Postgraduate Conference (MPC 2012), 7-9 July 2012,
Gold Coast, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) The modelling of the effect of air fuel ratio on unburned hydrocarbons for MILD combustion. In: 2nd Malaysian Postgraduate Conference (MPC
2012), 7-9 July 2012, Gold Coast, Australia.
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2012) A preliminary study of control parameters for open furnace mild combustion using CFD. In: 2nd Malaysian Postgraduate Conference (MPC 2012),
7-9 July 2012, Gold Coast, Australia.
Long, Hang and Xiang, Wei and Zhang, Yueying and Wang, Jing and Wu, Bin (2012) Analysis of unitary distributed spatial-temporal precoding in MIMO relay systems. In: 12th IEEE International Conference
on Computer and Information Technology, 27-29 Oct 2012, Chengdu, China.
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
MIMO systems
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
MIMO-OFDM systems
Long, Hang and Kim, Kyeong Jin and Xiang, Wei and Shen, Shanshan and Zheng, Kan and Wang, Wenbo (2012) Improved wideband precoding with arbitrary subcarrier grouping in MIMO-OFDM systems. ETRI
Journal, 34 (1). pp. 9-16. ISSN 1225-6463
Mossad, Ruth and Vella, Anthony and Balusu, Rao (2009) Inertisation of highwall mining to control methane concentrations at the Moura mine. In: 7th International Conference on Computational Fluid
Dynamics in the Minerals and Process Industries (CFD2009), 9-11 Dec 2009, Melbourne, Australia.
You, John and Herold, Nicholas and Muller, Dietmar and Sdrolias, Maria and Ribbe, Joachim (2007) Impact of vegetation on the Miocene Climate optimum. In: 14th National Conference of the Australian
Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
You, John and Muller, Dietmar and Sdrolias, Maria and Herold, Nicholas and Ribbe, Joachim (2007) Sensitivity of middle Miocene climate and regional monsoon to palaeo-altimetry. In: 14th National
Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
Miocene Climate Optimum
You, John and Muller, Dietmar and Sdrolias, Maria and Herold, Nicholas and Ribbe, Joachim (2007) Sensitivity of middle Miocene climate and regional monsoon to palaeo-altimetry. In: 14th National
Conference of the Australian Meteorological and Oceanographic Society, 5-8 Feb 2007, Adelaide, Australia.
mixed convection
Suslov, Sergey A. (2007) Convective and absolute instabilities in non-Boussinesq mixed convection. Theoretical and Computational Fluid Dynamics, 21 (4). pp. 271-290. ISSN 0935-4964
mixed convection opposing laminar flow
Mohammed, H. and Yusaf, T. (2006) Heat transfer by mixed convection opposing laminar flow from the inside surface of uniformly heated inclined circular tube. In: 8th Biennial ASME Conference on
Engineering Systems Design and Analysis (ESDA 2006), 4-7 Jul 2006, Torino, Italy.
mixed formulation
Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2010) A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.
International Journal for Numerical Methods in Engineering, 82 (4). pp. 435-463. ISSN 0029-5981
Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham (2008) An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems. In: 8th World Congress on
Computational Mechanics (WCCM8) and ECCOMAS 2008, 30 June - 4 July 2008, Venice, Italy.
Ribbe, Joachim (2001) Intermediate water mass production controlled by southern hemisphere winds. Geophysical Research Letters, 28 (3). pp. 535-538. ISSN 0094-8276
mixing model
Noor, M. M. and Wandel, Andrew P. and Yusaf, T. F. (2011) A hybrid EMST-modified Curl's model for turbulent combustion modelling. In: 2011 USQ Research Evening, 17 Nov 2011, Toowoomba, Australia.
mixing time
Yusaf, Talal and Buttsworth, David R. (2007) Characterisation of mixing rate due to high power ultrasound. Ultrasonics Sonochemistry, 14 (2). pp. 266-274. ISSN 1350-4177
mixture fraction
Wandel, Andrew P. (2013) Mixture fraction probability density functions in sparse spray flames with spark ignition. In: 7th Australian Combustion Symposium (ACS 2013), 6-8 Nov 2013, Perth, Australia
mixture fractions
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
Wandel, Andrew P. and Lindstedt, R. Peter (2013) Hybrid multiple mapping conditioning modeling of local extinction. Proceedings of the Combustion Institute, 34 (1). pp. 1365-1372. ISSN 1540-7489
mobile ad hoc networks
Zhang, Zhongwei (2011) A novel secure routing protocol for MANETs. In: Mobile ad-hoc networks: protocol design. InTech, Rijeka, Croatia, pp. 455-466. ISBN 978-953-307-402-3
Zhang, Zhongwei (2009) An intelligent scheme of secure routing for mobile ad hoc networks. In: ICSPCS 2008: 2nd International Conference on Signal Processing and Communication Systems , 15-17 Dec
2008, Gold Coast, Australia.
Mobile ad-hoc networks
Jin, Lu and Zhang, Zhongwei and Zhou, Hong (2007) Deliberation and implementation of adaptive fuzzy logic based security level routing protocol for mobile ad hoc network. In: 4th Annual IEEE Consumer
Communications and Networking Conference (CCNC 2007), 11-13 Jan 2007, Harrah's Las Vegas, Nevada USA.
mobile antennas
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Outage probability analysis of coded cooperation with multiple relays. In: 2011 IEEE Vehicular Technology Conference: Smarter
Communication for an Intelligent World (VTC 2011-Fall), 5-8 Sept 2011, San Francisco, CA. USA.
mobile networks
Jin, Lu and Zhang, Zhongwei and Zhou, Hong (2006) Performance comparison of the AODV, SAODV and FLSL routing protocols in mobile ad hoc networks. In: 5th Workshop on the Internet, Telecommunications
and Signal Processing (WITSP2006), 11-13 Dec 2006, Hobart, Australia.
mobile sink
Zhou, Hong and Jin, Lu and Zhang, Zhongwei and Ali, Hesham and Wang, Chulho (2007) Applications and performances of extended TTDDs in large-scale wireless sensor networks. In: 3rd International
Conference of Mobile Ad-hoc and Sensor Networks, 12-14 Dec 2007, Beijing, China.
mobile source
Zhou, Hong and Jin, Lu and Zhang, Zhongwei and Ali, Hesham and Wang, Chulho (2007) Applications and performances of extended TTDDs in large-scale wireless sensor networks. In: 3rd International
Conference of Mobile Ad-hoc and Sensor Networks, 12-14 Dec 2007, Beijing, China.
mobile station
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
Kist, Alexander A. (2008) Instant handoffs for wireless infrastructure meshed networks. In: ATNAC 2008: Australasian Telecommunication Networks and Applications Conference , 7-10 Dec 2008, Adelaide,
mode matching methods
Wells, Colin G. and Ball, James A. R. (2006) Attenuation of a shielded rectangular dielectric rod waveguide. IEEE Transactions on Microwave Theory and Techniques, 54 (7). pp. 3013-3018. ISSN
mode operation
McIntyre, Timothy J. and Eichmann, Troy N. and Mallon, Michael and Potter, Daniel and Brandis, Aaron and Jacobs, Carolyn and Morgan, Richard and Jacobs, Peter and Buttsworth, David R. (2009) The
generation and measurement of high temperature radiating flows in a high enthalpy pulsed facility. In: 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 30 Sep -
3 Oct 2008, Heraklion, Greece.
mode water
Sorensen, Jacob V. T. and Ribbe, Joachim and Shaffer, Gary (2001) Antarctic intermediate water mass formation in ocean general circulation models. Journal of Physical Oceanography, 31 (11). pp.
3295-3311. ISSN 1520-0485
model equation
Ostrovsky, Lev and Stepanyants, Yury (2005) Internal solitons in laboratory experiments: Comparison with theoretical models. Chaos, 15 (037111). 037111-1. ISSN 1054-1500
Dahmani, L. and Khennane, A. and Kaci, S. (2009) Modeling and influence of shear retention parameter on the response of reinforced concrete structural elements. Strength of Materials, 41 (4). pp.
423-430. ISSN 0039-2316
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2009) Modeling turbulent flow from dam break using slow manifolds. ANZIAM Journal (Australian & New Zealand Industrial and Applied
Mathematics Journal), 50. C1033-C1051. ISSN 1446-1811
Zhu, SongPing and Strunin, Dmitry V. (2001) Modelling the confinement of spilled oil with floating booms. Applied Mathematical Modelling, 25 (9). pp. 713-729. ISSN 0307-904X
modelling dynamics
Roberts, A. J. (2007) Computer algebra models dynamics on a multigrid across multiple length and time scales. Technical Report. UNSPECIFIED. (Unpublished)
modified dry spinning process
Tran, Canh-Dung and Smith, Shaun M. and Higgerson, G. and Bui, Anh and Randeniya, Lakshman K. and Tran-Cong, Thanh (2010) Spinning CNT based composite yarns using a dry spinning process. In: 2010
International Conference on Nanoscience and Nanotechnology (ICONN 2010), 22-26 Feb 2010, Sydney, Australia.
molecular dynamics
Mai-Duy, N. and Tran-Cong, T. and Phan-Thien, N. (2011) A numerical technique based on integrated RBFs for the system evolution in molecular dynamics. CMES: Computer Modeling in Engineering and
Sciences, 79 (4). pp. 223-236. ISSN 1526-1492
molecular models
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
motor design
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
moving boundary
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis. CMES:
Computer Modeling in Engineering and Sciences, 83 (5). pp. 459-498. ISSN 1526-1492
moving interfaces
Mai-Cao, L. and Tran-Cong, T. (2008) A meshless approach to capturing moving interfaces in passive transport problems. CMES: Computer Modeling in Engineering and Sciences, 31 (3). pp. 157-188. ISSN
moving IRBF
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based Galerkin meshless method. CMES: Computer Modeling in Engineering and Sciences, 66 (1). pp. 25-52.
ISSN 1526-1492
Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp.
63-109. ISSN 1526-1492
moving least square
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 1 - natural convection flows in concentric and eccentric
annuli. CMES: Computer Modeling in Engineering and Sciences, 83 (3). pp. 275-310. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 11 - unsteady incompressible viscous flows. CMES: Computer
Modeling in Engineering and Sciences , 83 (3). pp. 311-351. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Moving least square - one dimensional integrated radial basis function networks for time dependent problems. In: 33rd
International Conference on Boundary Elements and other Mesh Reduction Methods, 28-30 Jun 2011, New Forest, UK.
moving least-squares approximation
Bordas, Stephane and Duflot, Marc and Le, Phong (2008) A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24 (11). pp. 961-971. ISSN 1069-8299
moving surface loads
Shiau, Jim S. and Perumal, Tagarajan and Benjamin, Michael and Pather, Selvan and Ayers, Ron (2006) Developing a track model for testing the road pavement under repeated moving surface loads. In:
22nd ARRB Conference: Research Into Practice, 29 Oct - 02 Nov 2006, Canberra, Australia.
Shiau, Jim S. (2006) Numerical investigation of shakedown residual stresses under moving surface loads. In: III European Conference on Computational Mechanics (ECCM 2006), 5-8 June 2006, Lisbon,
Suryasaputra, Robert and Kist, Alexander A. and Harris, Richard J. (2005) Verification of MPLS traffic engineering techniques. In: 13th IEEE International Conference on Networks (ICON 2005), 16-18
Nov 2005, Kuala Lumpur, Malaysia.
Kist, Alexander A. and Harris, Richard J. (2003) Scheme for alternative packet overflow routing (SAPOR). In: 2003 Workshop on High Performance Switching and Routing (HPSR 2003), 24-27 Jun 2003,
Torino, Italy.
Ramesh Kumar, Nandini and Xiang, Wei and Wang, Yafeng (2012) Two-symbol FPGA architecture for fast arithmetic encoding in JPEG 2000. Journal of Signal Processing Systems, 69 (2). pp. 213-224. ISSN
Geng, Jian and Wang, Yafeng and Huang, Fan and Xiang, Wei and Yang, Dacheng (2011) Analysis on the impact of antenna gain mismatch on precoding vector. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011), 28-31 Mar 2011, Cancun, Mexico.
Shi, Chenggen and Zhou, Hong and Lu, Jie and Zhang, Guangquan and Zhang, Zhongwei (2007) The Kth-best approach for linear bilevel multifollower programming with partial shared variables among
followers. Applied Mathematics and Computation, 188 (2). pp. 1686-1698. ISSN 0096-3003
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Performance of co-operative relay for multicast multi-hop networks using virtual MIMO. In: IEEE International
Conference on Advanced Infocomm Technology (ICAIT09), 7-9 July 2009, Xi'an, China.
Multi-hop compute-and-forward
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong (2013) Multi-hop compute-and-forward for generalized two-way relay channels. Transactions on Emerging Telecommunications Technologies. pp. 1-13. (In
multi-hop networks
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong and Huang, Tao (2011) Outage analysis of non-regenerative analog network coding for two-way multi-hop networks. IEEE Communications Letters, 15 (6). pp.
662-664. ISSN 1089-7798
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong and Huang, Tao (2011) Outage performance of analog network coding in generalized two-way multi-hop networks. In: 2011 IEEE Wireless Communications and
Networking Conference (WCNC 2011) , 28-31 Mar 2011, Cancun, Mexico.
multi-hop two-way relay channel
Wang, Gengkun and Xiang, Wei and Wang, Yafeng (2013) Generalized compute-and-forward schemes for multi-hop two-way relay channels. In: 2013 IEEE 78th Vehicular Technology Conference (VTC Fall), 2-5
Sept 2013, Las Vegas, USA.
multi-layer circuit boards
Gambetta, D. and Ahfock, A. (2009) Designing printed circuit stators for brushless permanent magnet motors. IET Electric Power Applications, 3 (5). pp. 482-490. ISSN 1751-8660
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2006) Issues in processing unstable twisted fibre assemblies. In: 4th International Industrial Simulation Conference (ISC 2006),
5-7 Jun 2006, Palermo, Italy.
multi-ply yarn
Phillips, D. G. and Tran, Canh-Dung and Fraser, W. B. and van der Heijden, G. H. M. (2010) Torsional properties of staple fibre plied yarns. Journal of the Textile Institute, 101 (7). pp. 595-612.
ISSN 0040-5000
Tran, Canh-Dung and van der Heijden, G. H. M. and Phillips, David G. (2008) Application of topological conservation to model key features of zero-torque multi-ply yarns. Journal of the Textile
Institute, 99 (4). pp. 325-337. ISSN 0040-5000
Zhou, Yuan and Hou, Chunping and Xiang, Wei (2010) Modeling of transmission distortion for multi-view video in packet lossy networks. In: GLOBECOM 2010: IEEE Global Telecommunications Conference,
6-10 Dec 2010, Miami, FL, USA.
multi-view coding
Zhou, Yuan and Hou, Chunping and Xiang, Wei and Wu, Feng (2011) Channel distortion modeling for multi-view video transmission over packet-switched networks. IEEE Transactions on Circuits and Systems
for Video Technology, 21 (11). pp. 1679-1692. ISSN 1051-8215
multi-view video
Zhou, Yuan and Hou, Chunping and Xiang, Wei and Wu, Feng (2011) Channel distortion modeling for multi-view video transmission over packet-switched networks. IEEE Transactions on Circuits and Systems
for Video Technology, 21 (11). pp. 1679-1692. ISSN 1051-8215
multi-way relay channels
Wang, Gengkun and Xiang, Wei and Yuan, Jinhong (2012) Compute-and-forward in generalized multi-way relay channels. IEEE Communications Letters, 16 (12). pp. 2099-2102. ISSN 1089-7798
multicast relay
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Multicast based dual amplify and forward relay scheme for 2 hop networks. In: LATINCOM 2009: 1st IEEE
Latin-American Conference on Communications, 10-11 Sep 2009, Medellin, Colombia.
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Performance of co-operative relay for multicast multi-hop networks using virtual MIMO. In: IEEE International
Conference on Advanced Infocomm Technology (ICAIT09), 7-9 July 2009, Xi'an, China.
multigridspace-time scales
Roberts, A. J. (2007) Computer algebra models dynamics on a multigrid across multiple length and time scales. Technical Report. UNSPECIFIED. (Unpublished)
multihomed internet service providers
Kist, Alexander A. and Harris, Richard J. (2004) Cost efficient overflow routing for outbound ISP traffic. In: 9th IEEE Symposium on Computers and Communications (ISCC 2004), 28 Jun - 1 July 2004,
Alexandria, Egypt.
multihop networks
Adnan, Muhammad and She, Haoqiu and Wang, Yafeng and Yang, Dacheng and Xiang, Wei (2009) Multicast based dual amplify and forward relay scheme for 2 hop networks. In: LATINCOM 2009: 1st IEEE
Latin-American Conference on Communications, 10-11 Sep 2009, Medellin, Colombia.
multilayered composite
Yousif, B. F. and Devadas, Alvin and Yusaf, Talal (2009) Adhesive wear and frictional behaviour of multilayered polyester composite based on betelnut fiber mats under wet contact conditions. Surface
Review and Letters, 16 (3). pp. 407-414. ISSN 0218-625X
multimedia applications
Zhou, Hong and Zhang, Zhongwei (2009) Adaptive end-to-end QoS provision for real-time multimedia applications in heterogeneous multi-hop wireless networks. In: 5th International ICST Mobile
Multimedia Communications Conference (MobiMedia'09), 7-9 September 2009, London, United Kingdom.
multimedia communication
Xiang, Wei and Pietrobon, Steven S. and Barbulescu, Sorin Adrian (2003) Iterative decoding of JPEG coded images with channel coding. In: 10th IEEE International Conference on Telecommunications, Feb
2003, Papeete, Tahiti.
multimedia networking
Zhang, Zhongwei and Lai, David (2005) An active approach to multimedia network management. In: 9th WSEAS International Conference on Communications, 11-16 July 2005, Athens, Greece.
Zhang, Zhongwei and Lai, David (2005) Decentralized management of multimedia network using active network technology. WSEAS Transactions on Communications, 4 (7). pp. 325-333. ISSN 1109-2742
multipath channels
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
multiphase flows
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2010) Towards an analysis of shear suspension flows using radial basis functions. CMES: Computer Modeling in Engineering and Sciences, 67
(3). pp. 265-294. ISSN 1526-1492
multiple antenna
Long, Hang and Xiang, Wei and Liu, Hongmei and Shen, Shanshan (2012) Diversity analysis of two-way MIMO relaying system based on zero-forcing. In: IEEE International Conference on Communications (ICC
2012): Connect, Communicate, Collaborate, 10-15 Jun 2012, Ottawa, ON. Canada.
multiple boundary conditions
Mai-Duy, Nam and Tran-Cong, Thanh (2009) An integrated-RBF technique based on Galerkin formulation for elliptic differential equations. Engineering Analysis with Boundary Elements, 33 (2). pp.
191-199. ISSN 0955-7997
Mai-Duy, Nam and Tran-Cong, Thanh (2008) On the use of integrated RBFs in Galerkin approximation for elliptic problems. In: BEM/MRM 30: 30th International Conference on Boundary Elements and Other
Mesh Reduction Methods, 7-9 Jul 2008, Maribor, Slovenia.
Mai-Duy, Nam and Tran-Cong, Thanh (2008) An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations. In: Leading-edge applied
mathematical modeling research. Nova Science Publishers, Inc., New York, United States, pp. 215-250. ISBN 1-60021-977-2
Mai-Duy, Nam and Tanner, Roger I. (2007) A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. Journal of Computational and
Applied Mathematics, 201 (1). pp. 30-47. ISSN 0377-0427
Mai-Duy, N. and Tanner, R. I. (2007) A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. International Journal of Numerical Methods for Heat and Fluid Flow, 17
(2). pp. 165-186. ISSN 0961-5539
Mai-Duy, Nam (2006) An effective spectral collocation method for the direct solution of high-order ODEs. Communications in Numerical Methods in Engineering, 22 (6). pp. 627-642. ISSN 1069-8299
Mai-Duy, N. and Tran-Cong, T. (2006) Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis With Boundary Elements, 30
(2). pp. 77-87. ISSN 0955-7997
Mai-Duy, N. and Tanner, R. I. (2005) Solving high-order partial differential equations with indirect radial basis function networks. International Journal for Numerical Methods in Engineering, 63
(11). pp. 1636-1654. ISSN 0029-5981
multiple channels
Ahmed, Waqas and Gao, Jason and Zhou, Hong and Faulkner, Michael (2009) Goodput and channel allocation in opportunistic spectrum access networks. In: PIMRC 2009: 20th IEEE International Symposium on
Personal, Indoor and Mobile Radio Communications, 13-16 Sep 2009, Tokyo, Japan.
multiple input
Long, Hang and Xiang, Wei and Liu, Hongmei and Shen, Shanshan (2012) Diversity analysis of two-way MIMO relaying system based on zero-forcing. In: IEEE International Conference on Communications (ICC
2012): Connect, Communicate, Collaborate, 10-15 Jun 2012, Ottawa, ON. Canada.
multiple mapping conditioning
Wandel, Andrew P. (2013) Conditional dissipation of scalars in homogeneous turbulence: closure for MMC modelling. Combustion Theory and Modelling , 17 (4). pp. 707-748. ISSN 1364-7830
multiple mapping conditioning model
Wandel, Andrew P. and Lindstedt, R. Peter (2009) Application of hybrid binomial Langevin-multiple mapping conditioning method to reacting jet flow. In: Australian Combustion Symposium 2009 (ACS09),
2-4 Dec 2009, Brisbane, Australia.
multiple output
Russell, Julian and Xiang, Wei (2009) Pulse shaping in MIMO COFDM over Rayleigh fading channels. In: ICWMC 2009: 5th International Conference on Wireless and Mobile Communications, 23-29 Aug 2009,
Cannes, France.
multiple outputs
Long, Hang and Xiang, Wei and Liu, Hongmei and Shen, Shanshan (2012) Diversity analysis of two-way MIMO relaying system based on zero-forcing. In: IEEE International Conference on Communications (ICC
2012): Connect, Communicate, Collaborate, 10-15 Jun 2012, Ottawa, ON. Canada.
multiple relay nodes
Ma, Zhangchao and Xiang, Wei and Long, Hang and Wang, Wenbo (2011) Proportional fair-based in-cell routing for relay-enhanced cellular networks. In: 2011 IEEE Wireless Communications and Networking
Conference (WCNC 2011) , 28-31 Mar 2011, Cancun, Mexico.
multiple relays
Li, Chang and Wang, Yafeng and Xiang, Wei and Yang, Dacheng (2011) Performance analysis for coded cooperative multiple-relay in distributed turbo channels. In: IEEE 22nd International Symposium on
Personal Indoor and Mobile Radio Communications (PIMRC 2011), 11-14 Sep 2011, Toronto, Canada.
multiple-input and multiple-output (MIMO)
Xiang, Wei and Russell, Julian and Wang, Yafeng (2010) ICI reduction through shaped OFDM in coded MIMO-OFDM systems. International Journal on Advances in Telecommunications, 3 (3&4). pp. 311-323.
ISSN 1942-2601
multiple-input multiple-output (MIMO)
Ziri-Castro, Karla I. and Scanlon, William G. and Evans, Noel E. (2005) Prediction of variation in MIMO channel capacity for the populated indoor environment using a radar cross-section-based
pedestrian model. IEEE Transactions on Wireless Communications, 4 (3). pp. 1186-1194. ISSN 1536-1276
multiply-connected domain
Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2011) Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian
grids. Computers and Fluids , 44 (1). pp. 32-42. ISSN 0045-7930
Mai-Duy, Nam and Le-Cao, Khoa and Tran-Cong, Thanh (2008) A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli.
International Journal for Numerical Methods in Fluids, 57 (12). pp. 1709-1730. ISSN 0271-2091
multiply-connected domains
Le-Cao, Khoa (2011) Radial-basis-function calculations of heat and viscous flows in multiply-connected domains. [Thesis (PhD/Research)] (Unpublished)
Mai-Duy, Nam and Tran-Cong, Thanh (2007) A RBF-based fictitious-domain technique for Dirichlet boundary value problems in multiply-connected domains. In: 3rd Asian-Pacific Congress on Computational
Mechanics (APCOM'07) and EPMESC XI, 3-6 Dec 2007, Kyoto, Japan.
multiquadric function
Mai-Duy, Nam and Tran-Cong, Thanh (2001) Numerical solution of differential equations using multiquadric radial basis function networks. Neural Networks, 14 (2). pp. 185-199. ISSN 0893-6080
multiscale computation
Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.
Roberts, A. J. and Kevrekidis, I. G. (2007) General tooth boundary conditions for equation free modeling. SIAM Journal on Scientific Computing, 29 (4). pp. 1495-1510. ISSN 1064-8275
multiscale elliptic problem
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF computation of multiscale elliptic problems [Keynote paper]. In: 8th ICCES Special Symposium on Meshless & Other Novel
Computational Methods (ICCES MM 2012), 2-6 Sep 2012, Budva, Montenegro.
multiscale elliptic problems
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients. CMES: Computer
Modeling in Engineering and Sciences, 89 (4). pp. 303-359. ISSN 1526-1492
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2011) IRBFN-based multiscale solution of a model 1D elliptic equation. In: 33rd International Conference on Boundary Elements and other
Mesh Reduction Methods (BEM/MRM 2011), 28-30 Jun 2011, New Forest, United Kingdom.
multiscale method
An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients. CMES: Computer
Modeling in Engineering and Sciences, 89 (4). pp. 303-359. ISSN 1526-1492
multiscale modelling
Roberts, A. J. (2008) Computer algebra derives discretisations via self-adjoint multiscale modelling. Unpublished. (Unpublished)
Roberts, A. J. (2008) Normal form transforms separate slow and fast modes in stochastic dynamical systems. Physica A: Statistical Mechanics and Its Applications, 387 (1). pp. 12-38. ISSN 0378-4371
multiservice IP transport networks
Kist, Alexander A. and Harris, Richard J. (2003) Using virtual SIP links to enable QoS for signalling. In: 11th IEEE International Conference on Networks (ICON 2003), 28 Sept - 1 Oct 2003 , Sydney,
multiservices transport network
Kist, Alexander A. and Harris, Richard J. (2003) Dynamic resource allocation in 3GPP SIP overlay networks. In: 2003 Joint Conference of the 4th International Conference on Information, Communications
and Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
Salim, Omar Hazim and Xiang, Wei and Leis, John (2013) An efficient unequal error protection scheme for 3-D video transmission. In: IEEE Wireless Communication and Networking Conference (WCNC 2013):
Connecting the Future, 7-10 Apr 2013, Shanghai, China.
Randeniya, Lakshman K. and Bendavid, Avi and Martin, Philip J. and Tran, Canh-Dung (2010) Composite yarns of multi-walled carbon nanotubes with metallic electrical conductivity. Small, 6 (16). pp.
1806-1811. ISSN 1613-6810
nano-crystalline materials
Randeniya, Lakshman K. and Bendavid, Avi and Martin, Philip J. and Tran, Canh-Dung (2010) Composite yarns of multi-walled carbon nanotubes with metallic electrical conductivity. Small, 6 (16). pp.
1806-1811. ISSN 1613-6810
narrow bands
Long, Hang and Kim, Kyeong Jin and Xiang, Wei and Shen, Shanshan and Zheng, Kan and Wang, Wenbo (2012) Improved wideband precoding with arbitrary subcarrier grouping in MIMO-OFDM systems. ETRI
Journal, 34 (1). pp. 9-16. ISSN 1225-6463
natural convection
Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A finite-volume method based on compact local integrated radial basis function approximations for second-order differential
problems. CMES Computer Modeling in Engineering and Sciences, 91 (6). pp. 485-516. ISSN 1526-1492
Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2012) Local moving least square - one-dimensional IRBFN technique: part 1 - natural convection flows in concentric and eccentric
annuli. CMES: Computer Modeling in Engineering and Sciences, 83 (3). pp. 275-310. ISSN 1526-1492
Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains. CMES:
Computer Modeling in Engineering and Sciences, 44 (3). pp. 219-248. ISSN 1526-1492
Mai-Duy, Nam and Le-Cao, Khoa and Tran-Cong, Thanh (2008) A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli.
International Journal for Numerical Methods in Fluids, 57 (12). pp. 1709-1730. ISSN 0271-2091
Le-Cao, Khoa and Mai-Duy, Nam and Tran-Cong, Thanh (2007) Radial-basis-function calculations of buoyancy-driven flow in concentric and eccentric annuli. In: 16th Australasian Fluid Mechanics
Conference (AFMC 2007), 3-7 Dec 2007, Gold Coast, Australia.
natural convection flow
Mai-Duy, Nam and Tran-Cong, Thanh (2004) An effective RBFN-boundary integral approach for the analysis of natural convection flow. International Journal for Numerical Methods in Fluids, 46 (5). pp.
545-568. ISSN 0271-2091
natural roof arch
Ghabraie, B. and Ren, G. and Xie, Y. M. and Ghabraie, K. (2012) Study of truss bolt system for highly stressed rock mass using finite element modelling techniques. In: 11th Australia New Zealand
Conference on Geomechanics: Ground Engineering in a Changing World, 15-18 July 2012, Melbourne, Australia.
natural vibration
Nguyen-Van, H. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T. (2011) Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell
element with in-plane rotations. Computers and Structures, 89 (7-8). pp. 612-625. ISSN 0045-7949
Navier Stokes equations
Buttsworth, David R. and Goozee, Richard J. and Jacobs, Peter A. (2006) Measurement and simulation of the interface in a low-enthalpy shock tunnel. In: 14th International Space Planes and Hypersonic
Systems and Technologies Conference (AIAA/AHI 2006), 6-9 Nov 2006, Canberra, Australia.
Navier-Stokes equation
Mai-Duy, Nam and Tran-Cong, Thanh (2005) An efficient indirect RBFN-based method for numerical solution of PDEs. Numerical Methods for Partial Differential Equations, 21 (4). pp. 770-790. ISSN
Navier-Stokes equations
An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T. (2013) ADI method based on C^2-continuous two-node integrated-RBF elements for viscous flows. Applied Mathematical Modelling, 37
(7). pp. 5184-5203. ISSN 0307-904X
Ho-Minh, D. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2010) Simulation of fluid flows at high Reynolds/Rayleigh numbers using integrated radial basis functions. In: 17th Australasian Fluid
Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.
Ng, K. C. and Yusoff, M. Z. and Yusaf, T. F. (2007) Numerical simulation of 3D transonic flow in a compressor rotor. International Journal of Modelling and Simulation, 27 (1). pp. 74-79. ISSN
Mai-Duy, Nam and Tran-Cong, Thanh (2001) Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks. International Journal for Numerical Methods in Fluids, 37
(1). pp. 65-86. ISSN 0271-2091
Navier–Stokes equations
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
Shi, Sue and Ribbe, Joachim and Cowan, Tim and Cai, Wenju (2007) A dataset of the wind-driven global ocean circulation for climate research. Technical Report. Joachim Ribbe, Toowoomba, Australia.
near-tip enrichment
Bordas, Stephane and Duflot, Marc and Le, Phong (2008) A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24 (11). pp. 961-971. ISSN 1069-8299
needle guidance
Sharifi, Behrooz and Leis, John (2010) Towards three-dimensional fusion of infrared guidance measurements for biopsy procedures: some preliminary results and design considerations. In: ICSPCS 2010:
4th International Conference on Signal Processing and Communication Systems, 13-15 Dec 2010, Gold Coast, Australia.
negative energy waves
Fabrikant, Anatoly and Stepanyants, Yury (1998) Propagation of waves in shear flows. World Scientific, Singapore. ISBN 978-981-02-2052-5
negative values
Schroll, Peter and Wandel, Andrew P. and Cant, R. Stewart and Mastorakos, E. (2009) Direct numerical simulations of autoignition in turbulent two-phase flows. Proceedings of the Combustion Institute,
32 (2). pp. 2275-2282. ISSN 1540-7489
network condition
Norman, Mark and Leis, John (2010) A passive approach to detection of traffic shaping. In: APSIPA 2010: 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference,
14-17 Dec 2010, Biopolis, Singapore.
network infrastructure
Zhou, Hong and Ali, Hesham and Youn, Jon and Zhang, Zhongwei (2010) A hybrid wired and wireless network infrastructure to improve the productivity and quality care of critical medical applications.
In: 2010 IEEE/ICME International Conference on Complex Medical Engineering (CME 2010), 13-15 July 2010, Gold Coast, Australia.
network management
Zhang, Zhongwei and Lai, David (2005) An active approach to multimedia network management. In: 9th WSEAS International Conference on Communications, 11-16 July 2005, Athens, Greece.
Zhang, Zhongwei and Lai, David (2005) Decentralized management of multimedia network using active network technology. WSEAS Transactions on Communications, 4 (7). pp. 325-333. ISSN 1109-2742
network optimisation
Aldraho, Abdelnour and Kist, Alexander A. (2011) Enabling dynamic topologies in communication networks. In: ATNAC 2011: Australian Telecommunication Networks and Applications Conference, 9-11 Nov
2011, Melbourne, Australia.
Kist, Alexander A. and Aldraho, Abdelnour (2011) Dynamic topologies for sustainable and energy efficient traffic routing. Computer Networks, 55 (9). pp. 2271-2288. ISSN 1389-1286
Kist, Alexander A. and Lloyd-Smith, Bill (2008) Internet pooling: routing for load distribution in access networks. In: ATNAC 2007: Next Generation Networks: Enabling Closer International
Cooperation, 2-5 Dec 2007, Christchurch, New Zealand.
Suryasaputra, Robert and Kist, Alexander A. and Harris, Richard J. (2006) Reconfiguration in multi class of services networks. In: ATNAC 2006: Australian Telecommunications Networks and Applications
Conference, 4-6 Dec 2006, Melbourne, Australia.
network scenario
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
network servers
Kist, Alexander A. (2009) Staged request routing for reduced carbon footprints of large scale server systems. In: ATNAC 2009: Australasian Telecommunication Networks and Applications Conference, 9-11
Nov 2009, Canberra, Australia.
network synthesis
Kist, Alexander A. and Harris, Richard J. (2003) Note on the problem of partially link disjoint paths. In: 2003 Joint Conference of the 4th International Conference on Information, Communications and
Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
network topology
Aldraho, Abdelnour and Kist, Alexander A. and Maxwell, Andrew (2012) Performance investigation of dynamic topologies in MPLS networks. In: International Symposium on Communications and Information
Technologies (ISCIT), 2-5 Oct 2012, Gold Coast, Australia.
Kist, Alexander A. and Harris, Richard J. (2003) Note on the problem of partially link disjoint paths. In: 2003 Joint Conference of the 4th International Conference on Information, Communications and
Signal Processing and the 4th Pacific Rim Conference on Multimedia, 15-18 Dec 2003, Singapore.
network transformation
Kist, Alexander A. and Aldraho, Abdelnour (2011) Dynamic topologies for sustainable and energy efficient traffic routing. Computer Networks, 55 (9). pp. 2271-2288. ISSN 1389-1286
networked control system
Teng, Lanzhi and Wen, Peng (2007) Networked PID control system modeling and simulation using Markov chain. In: 2007 IEEE International Conference on Integration Technology, 20-24 March 2007,
Shenzhen, China.
Neumann boundary condition
Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless
& Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.
Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems. Numerical Methods for Partial
Differential Equations, 26 (6). pp. 1443-1462. ISSN 0749-159X
Neumann boundary conditions
Mai-Duy, Nam and Tran-Cong, Thanh (2009) An integrated-RBF technique based on Galerkin formulation for elliptic differential equations. Engineering Analysis with Boundary Elements, 33 (2). pp.
191-199. ISSN 0955-7997
Mai-Duy, Nam and Tran-Cong, Thanh (2008) On the use of integrated RBFs in Galerkin approximation for elliptic problems. In: BEM/MRM 30: 30th International Conference on Boundary Elements and Other
Mesh Reduction Methods, 7-9 Jul 2008, Maribor, Slovenia.
neural network
Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997
neural networks
Tran, Canh-Dung and Phillips, David G. and Fraser, W. Barrie (2010) Stationary solution of the ring-spinning balloon in zero air drag using a RBFN based mesh-free method. Journal of the Textile
Institute, 101 (2). pp. 101-110. ISSN 0040-5000
Suryasaputra, R. and Kist, A. A. and Ferra, H. L. and Palmer, R. A. and Dale, M. J. and Harris, R. J. (2006) Comparison of intra-domain traffic engineering methods. In: World Teletraffic Congress
(WTC 2006), 30 April - 3 May 2006, Budapest, Hungary.
Tran, Canh-Dung and Tran-Cong, Thanh (2002) Computation of viscoelastic flow using neural networks and stochastic simulation. Korea-Australia Rheology Journal, 14 (4). pp. 161-174. ISSN 1226-119X
new european driving cycle
Malpress, Ray and Buttsworth, David (2010) A comparison between two-position variable compression ratio and continuously variable compression ratio engines using numerical simulation. In: ICEF 2009:
ASME Internal Combustion Engine Division Fall Technical Conference , 27-30 Sep 2009, Lucerne, Switzerland.
new technologies
Zhou, Hong and Ali, Hesham and Youn, Jon and Zhang, Zhongwei (2010) A hybrid wired and wireless network infrastructure to improve the productivity and quality care of critical medical applications.
In: 2010 IEEE/ICME International Conference on Complex Medical Engineering (CME 2010), 13-15 July 2010, Gold Coast, Australia.
Newtonian fluid
Ho-Minh, D. and Mai-Duy, N. and Tran-Cong, T. (2012) Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach. Australian Journal of Mechanical Engineering , 9 (2). pp. 101-112.
ISSN 1448-4846
Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
nickel-iron batteries
Helwig, A. and Ahfock, A. (2011) Sizing nickel iron batteries for RAPS systems. In: 2011 IET Renewable Power Generation Conference (RPG 2011) , 6-8 Sep 2011, Edinburgh, UK.
nitial conditions
Roberts, A. J. (2006) A normal form of thin fluid film equations solves the transient paradox. Physica D: Nonlinear Phenomena, 223 (1). pp. 69-81. ISSN 0167-2789
nitrous oxide
Buttsworth, D. R. (2009) Nitrous oxide decomposition for supersonic combustion experiments in the USQ Ludwieg Tube facility. In: Australian Combustion Symposium 2009 (ACS09), 2-4 Dec 2009, Brisbane,
nodal integration finite element method
Nguyen-Van, Hieu and Le, Thong and Mai-Duy, Nam and Tran-Cong, Thanh (2008) Nodal integration finite element techniques for analysis of piezoelectric solids. In: 2008 International Conference on
Computational Solid Mechanics (CSM2008), 27-30 Nov 2008, Ho Chi Minh City, Vietnam.
node-based smoothed finite element
Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh (2008) A node-based element for analysis of planar piezoelectric structures. CMES: Computer Modeling in Engineering and Sciences, 36 (1). pp.
65-95. ISSN 1526-1492
Leis, John (2013) Simultaneous gain, drift and offset estimation in measurement systems using coherent sampling. In: 7th International Conference on Signal Processing and Communication Systems
(ICSPCS 2013), 16-18 Dec 2013, Gold Coast, Australia.
noise reduction technology
Xiang, Wei and Otto, Colin W. and Wen, Peng (2008) Automated vehicle classification system using advanced noise reduction technology. In: 1st International Conference on Signal Processing and
Communication Systems (ICSPCS 2007), 17-19 Dec 2007, Gold Coast, Australia.
noisy data
Zhang, Zhongwei and Li, Jiuyong and Hu, Hong and Zhou, Hong (2010) On the effectiveness of gene selection for microarray classification methods. In: 2nd Asian Conference on Intelligent Information
and Database Systems (ACIIDS 2010), 24-26 Mar 2010, Hue City, Vietnam.
non-Boussinesq convection
Suslov, Sergey A. (2009) Analysis of instability patterns in non-Boussinesq mixed convection using a direct numerical evaluation of disturbance integrals. Computers and Fluids, 38 (3). pp. 590-601.
ISSN 0045-7930
Suslov, Sergey A. (2007) New spatio-temporal instability scenarios in non-Boussinesq mixed convection. In: 60th Annual Meeting of the Divison of Fluid Dynamics, American Physical Society, 18-20 Nov
2007, Salt Lake City, Utah, USA.
Suslov, Sergey A. (2007) Convective and absolute instabilities in non-Boussinesq mixed convection. Theoretical and Computational Fluid Dynamics, 21 (4). pp. 271-290. ISSN 0935-4964
Suslov, Sergey A. (2005) Analysis of coupling between hydrodynamic and thermal instabilities in non-Boussinesq convection. Nonlinear Analysis Theory Methods and Applications, 63 (5-7). e1435-e1443.
ISSN 0362-546X
Suslov, Sergey A. and Paolucci, Samuel (2004) Stability of non-Boussinesq convection via the complex Ginzburg-Landau model. Fluid Dynamics Research, 35 (3). pp. 159-203. ISSN 0169-5983
Suslov, Sergey A. (2004) Multi-mode spatio-temporal instability in non-Boussinesq convection. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 45(E). pp. 149-162.
ISSN 1446-1811
Suslov, Sergey A. (2004) Spatio-temporal instabilities in mixed convection of air subject to large temperature gradient. In: International Conference: Advanced Problems in Thermal Convection, 24-27
Nov 2003, Perm, Russia.
Suslov, Sergey A. (2002) Effect of fluid properties variations on spatio-temporal instability of convection. In: APM 2001: 29th Summer School on 'Advanced Problems in Mechanics, 21-30 Jun 2001, St
Petersburg (Repino), Russia.
Suslov, Sergey A. (2002) Flow patterns near codimension-2 bifurcation in non-Boussinesq mixed convection. In: Progress in Nonlinear Science, International Conference dedicated to the 100th
Anniversary of A.A. Andronov, 2-6 Jul 2001, Nizhniy Novgorod, Russia.
Obiedat, Esam and Xiang, Wei and Leis, John W. and Cao, Lei (2010) Soft incremental redundancy for distributed turbo product codes. In: CCNC 2010: 7th IEEE Consumer Communications and Networking
Conference, 9-12 Jan 2010, Las Vegas, NV. United States.
non-explosive method
Genet, Martin and Yan, Wenyi and Tran-Cong, Thanh (2009) Investigation of a hydraulic impact: a technology in rock breaking. Archive of Applied Mechanics, 79 (9). pp. 825-841. ISSN 0939-1533
Xiang, Wei and Otto, Colin W. and Wen, Peng (2009) Automated vehicle classification system for AUSTROADS standard based upon laser sensor technology. Australian Journal of Electrical and Electronics
Engineering, 5 (2). pp. 95-106. ISSN 1448-837X
non-Newtonian fluid
Roberts, A. J. (2008) The inertial dynamics of thin film flow of non-Newtonian fluids. Physics Letters Section A: General, Atomic and Solid State Physics, 372 (10). pp. 1607-1611. ISSN 0375-9601
Mai-Duy, N. and Tanner, R. I. (2005) Computing non-Newtonian fluid flow with radial basis function networks. International Journal for Numerical Methods in Fluids, 48 (12). pp. 1309-1336. ISSN
non-newtonian fluid flows
Mai-Duy, Nam and Tran-Cong, Thanh (2009) Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows. Computers and Structures, 87 (11-12). pp. 642-650. ISSN
non-overlapping domain decomposition
Mai-Duy, Nam and Tran-Cong, Thanh (2008) A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems. Applied Mathematical
Modelling, 32 (12). pp. 2851-2862. ISSN 0307-904X
Noor, M. M. and Hairuddin, A. Aziz and Wandel, Andrew P. and Yusaf, T. F. (2012) Modelling of non-premixed turbulent combustion of hydrogen using conditional moment closure method. IOP Conference
Series: Materials Science and Engineering, 36 (012036). pp. 1-17. ISSN 1757-899X
non-rectangular domains
Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2009) An effective integrated-RBFN Cartesian-grid discretization for the stream function-vorticity temperature formulation in nonrectangular domains.
Numerical Heat Transfer, Part B: Fundamentals, 55 (6). pp. 480-502. ISSN 1040-7790
non-uniform grid
Noor, M. M. and Wandel, Andrew P. and Yusaf, Talal (2013) Discretization of three dimensional non-uniform grid: conditional moment closure elliptic equation using finite difference method. In: 3rd
Malaysian Postgraduate Conference (MPC 2013), 4-5 Jul 2013, Sydney, Australia.
nonlinear diffusion
Strunin, Dmitry V. (2007) Attractors in confined source problems for coupled nonlinear diffusion. SIAM Journal on Applied Mathematics, 67 (6). pp. 1654-1674. ISSN 0036-1399
nonlinear dynamics
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