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Tungsten(VI) oxide , also known as tungsten trioxide is a chemical compound of oxygen and the transition metal tungsten , with formula WO 3 . The compound is also called tungstic anhydride , reflecting its relation to tungstic acid H 2 WO 4 . It is a light yellow crystalline solid. [ 1 ]
Tungsten(VI) oxide occurs naturally in the form of hydrates , which include minerals: tungstite WO 3 ·H 2 O, meymacite WO 3 ·2H 2 O and hydrotungstite (of the same composition as meymacite, however sometimes written as H 2 WO 4 ). These minerals are rare to very rare secondary tungsten minerals.
In 1841, a chemist named Robert Oxland gave the first procedures for preparing tungsten trioxide and sodium tungstate . [ 2 ] He was granted patents for his work soon after, and is considered to be the founder of systematic tungsten chemistry. [ 2 ]
The crystal structure of tungsten trioxide is temperature dependent. It is tetragonal at temperatures above 740 °C, orthorhombic from 330 to 740 °C, monoclinic from 17 to 330 °C, triclinic from −50 to 17 °C, and monoclinic again at temperatures below −50 °C. [ 3 ] The most common structure of WO 3 is monoclinic with space group P2 1 /n. [ 2 ]
The pure compound is an electric insulator, but oxygen-deficient varieties, such as WO 2.90 = W 20 O 58 , are dark blue to purple in color and conduct electricity. They can be prepared by combining the trioxide and the dioxide WO 2 at 1000 °C in vacuum. [ 4 ] [ 1 ]
Possible signs of superconductivity with critical temperatures T c = 80–90 K were claimed in sodium-doped and oxygen-deficient WO 3 crystals. If confirmed, these would be the first superconducting materials containing no copper, with T c higher than the boiling point of liquid nitrogen at normal pressure. [ 5 ] [ 4 ]
Tungsten trioxide exists in multiple polymorphs whose structures have been precisely determined using X-ray crystallography and neutron diffraction . Each phase exhibits a distinct arrangement of distorted WO 6 octahedra, which affect its electronic and optical behavior.
Tungsten trioxide (WO₃) is a polymorphic compound whose crystal structure changes depending on temperature. It adopts several forms, including:
The most common ambient phase is monoclinic with space group P2₁/n , featuring distorted WO₆ octahedra linked at their corners. Each polymorph exhibits variations in symmetry, lattice parameters, and atomic positions, making structural determination important for understanding the material’s physical and electronic properties.
This high-temperature phase is observed above 740 °C, but specific crystallographic data are often not tabulated separately in modern studies. It exhibits relatively symmetric WO₆ octahedra.
A less common hexagonal polymorph of WO₃ has been reported and characterized using powder X-ray diffraction. It exhibits higher symmetry and potentially distinct electronic properties.
Tungsten trioxide is obtained as an intermediate in the recovery of tungsten from its minerals. [ 10 ] Tungsten ores can be treated with alkalis to produce soluble tungstates . Alternatively, CaWO 4 , or scheelite , is allowed to react with HCl to produce tungstic acid , which decomposes to WO 3 and water at high temperatures. [ 10 ]
Another common way to synthesize WO 3 is by calcination of ammonium paratungstate (APT) under oxidizing conditions: [ 2 ]
Tungsten trioxide can be reduced with carbon or hydrogen gas yielding the pure metal. [ citation needed ]
Tungsten trioxide is a starting material for the synthesis of tungstates . Barium tungstate BaWO 4 is used as a x-ray screen phosphors . Alkali metal tungstates, such as lithium tungstate Li 2 WO 4 and cesium tungstate Cs 2 WO 4 , give dense solutions that can be used to separate minerals. [ 1 ] Other applications, actual or potential, include:
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Tungsten(VI) oxytetrachloride is the inorganic compound with the formula W O Cl 4 . This diamagnetic solid is used to prepare other complexes of tungsten . The red crystalline compound is soluble in nonpolar solvents but it reacts with alcohols and water and forms adducts with Lewis bases . [ citation needed ] [ clarification needed ]
The solid consists of weakly associated square pyramidal monomers . [ 2 ] The compound is classified as an oxyhalide .
WOCl 4 is prepared from tungsten trioxide or hexachloride : [ 3 ]
It is "difficult to prepare by other means," [ 4 ] but thionyl chloride also oxidizes tungsten(IV) oxide to the oxytetrachloride at 200 °C. [ 5 ]
WOCl 4 is a Lewis acid . It is a precursor to catalysts used for polymerization of alkynes . [ 6 ]
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WORHP ( / w ɔːr p / "warp", an acronym for "We Optimize Really Huge Problems"), also referred to as eNLP (European NLP solver) by ESA , is a mathematical software library for numerically solving large scale continuous nonlinear optimization problems.
WORHP is a hybrid Fortran and C implementation and can be used from C/ C++ and Fortran programs using different interfaces of varying complexity and flexibility. There are also interfaces for the MATLAB , CasADi and AMPL modelling environments. [ 1 ]
WORHP is designed to solve problems of the form
with sufficiently smooth functions f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } (objective) and g : R n → R m {\displaystyle g:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} (constraints) that may be nonlinear, and need not necessarily be convex. Even problems with large dimensions n {\displaystyle n} and m {\displaystyle m} can be solved efficiently, if the problem is sufficiently sparse.
Cases where objective and constraints cannot be evaluated separately, or where constraints can be evaluated element-wise can be exploited by WORHP to increase the computational efficiency.
WORHP requires the first derivative ( Gradient ) of f {\displaystyle f} and of g {\displaystyle g} ( Jacobian ) and second derivatives ( Hessian matrix ) of the Lagrange function ; in a modelling environment like AMPL, these are provided by automatic differentiation methods, but need to be provided by the caller in other environments. First and second derivatives can be approximated by WORHP using finite differences . To reduce the otherwise prohibitively high number of necessary function evaluations in large scale sparse problems, graph colouring theory is used to group first and second partial derivatives. Second derivatives may also be approximated using variations of the classic BFGS method , including block-diagonal or sparse BFGS matrices.
The NLP level of WORHP is based on SQP , while the quadratic subproblems are solved using an interior point method . This approach was chosen to benefit from the robustness of SQP methods and the reliable runtime complexity of IP methods, since traditional active set methods may be unsuitable for large-scale problems.
Development of WORHP started in 2006 with funding from DLR and was continued under the eNLP label after 2008 with support by ESA / ESTEC together with the Interior-Point solver ipfilter [ 2 ] (whose inclusion in eNLP was discontinued after 2010) to develop a European NLP solver for use in trajectory optimisation, mission analysis and aerospace applications in general. [ 3 ]
The development of WORHP is led by the Steinbeis-Forschungszentrum Optimierung, Steuerung und Regelung and scientists of the Optimization and Optimal Control Group at the University of Bremen , and at the Bundeswehr University of Munich . [ 4 ] The developers stress that WORHP, despite its academic roots, is intended as industrial-grade tool rather than an academic research platform. [ 5 ]
WORHP has been integrated into trajectory analysis tools such as LOTNAV [ 6 ] and ASTOS , and is being used at ESOC and ESTEC . It can be used as optimiser in CasADi (since version 1.5.0beta) [ 7 ] and as local optimiser in SVAGO MDO [ 8 ] tool developed at University of Bremen and Politecnico di Milano on Multidisciplinary design optimization through the ESA PRESTIGE program. [ 9 ]
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The reflected binary code ( RBC ), also known as reflected binary ( RB ) or Gray code after Frank Gray , is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).
For example, the representation of the decimal value "1" in binary would normally be " 001 ", and "2" would be " 010 ". In Gray code, these values are represented as " 001 " and " 011 ". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two.
Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. The use of Gray code in these devices helps simplify logic operations and reduce errors in practice. [ 3 ]
Many devices indicate position by closing and opening switches. If that device uses natural binary codes , positions 3 and 4 are next to each other but all three bits of the binary representation differ:
The problem with natural binary codes is that physical switches are not ideal: it is very unlikely that physical switches will change states exactly in synchrony. In the transition between the two states shown above, all three switches change state. In the brief period while all are changing, the switches will read some spurious position. Even without keybounce , the transition might look like 011 — 001 — 101 — 100 . When the switches appear to be in position 001 , the observer cannot tell if that is the "real" position 1, or a transitional state between two other positions. If the output feeds into a sequential system, possibly via combinational logic , then the sequential system may store a false value.
This problem can be solved by changing only one switch at a time, so there is never any ambiguity of position, resulting in codes assigning to each of a contiguous set of integers , or to each member of a circular list, a word of symbols such that no two code words are identical and each two adjacent code words differ by exactly one symbol. These codes are also known as unit-distance , [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] single-distance , single-step , monostrophic [ 9 ] [ 10 ] [ 7 ] [ 8 ] or syncopic codes , [ 9 ] in reference to the Hamming distance of 1 between adjacent codes.
In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code , or BRGC . Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943. [ 11 ] [ 12 ] [ 13 ] Frank Gray introduced the term reflected binary code in his 1947 patent application, remarking that the code had "as yet no recognized name". [ 14 ] He derived the name from the fact that it "may be built up from the conventional binary code by a sort of reflection process".
In the standard encoding of the Gray code the least significant bit follows a repetitive pattern of 2 on, 2 off (... 11001100 ...); the next digit a pattern of 4 on, 4 off; the i -th least significant bit a pattern of 2 i on 2 i off. The most significant digit is an exception to this: for an n -bit Gray code, the most significant digit follows the pattern 2 n −1 on, 2 n −1 off, which is the same (cyclic) sequence of values as for the second-most significant digit, but shifted forwards 2 n −2 places. The four-bit version of this is shown below:
For decimal 15 the code rolls over to decimal 0 with only one switch change. This is called the cyclic or adjacency property of the code. [ 15 ]
In modern digital communications , Gray codes play an important role in error correction . For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise .
Despite the fact that Stibitz described this code [ 11 ] [ 12 ] [ 13 ] before Gray, the reflected binary code was later named after Gray by others who used it. Two different 1953 patent applications use "Gray code" as an alternative name for the "reflected binary code"; [ 16 ] [ 17 ] one of those also lists "minimum error code" and "cyclic permutation code" among the names. [ 17 ] A 1954 patent application refers to "the Bell Telephone Gray code". [ 18 ] Other names include "cyclic binary code", [ 12 ] "cyclic progression code", [ 19 ] [ 12 ] "cyclic permuting binary" [ 20 ] or "cyclic permuted binary" (CPB). [ 21 ] [ 22 ]
The Gray code is sometimes misattributed to 19th century electrical device inventor Elisha Gray . [ 13 ] [ 23 ] [ 24 ] [ 25 ]
Reflected binary codes were applied to mathematical puzzles before they became known to engineers.
The binary-reflected Gray code represents the underlying scheme of the classical Chinese rings puzzle , a sequential mechanical puzzle mechanism described by the French Louis Gros in 1872. [ 26 ] [ 13 ]
It can serve as a solution guide for the Towers of Hanoi problem, based on a game by the French Édouard Lucas in 1883. [ 27 ] [ 28 ] [ 29 ] [ 30 ] Similarly, the so-called Towers of Bucharest and Towers of Klagenfurt game configurations yield ternary and pentary Gray codes. [ 31 ]
Martin Gardner wrote a popular account of the Gray code in his August 1972 "Mathematical Games" column in Scientific American . [ 32 ]
The code also forms a Hamiltonian cycle on a hypercube , where each bit is seen as one dimension.
When the French engineer Émile Baudot changed from using a 6-unit (6-bit) code to 5-unit code for his printing telegraph system, in 1875 [ 33 ] or 1876, [ 34 ] [ 35 ] he ordered the alphabetic characters on his print wheel using a reflected binary code, and assigned the codes using only three of the bits to vowels. With vowels and consonants sorted in their alphabetical order, [ 36 ] [ 37 ] [ 38 ] and other symbols appropriately placed, the 5-bit character code has been recognized as a reflected binary code. [ 13 ] This code became known as Baudot code [ 39 ] and, with minor changes, was eventually adopted as International Telegraph Alphabet No. 1 (ITA1, CCITT-1) in 1932. [ 40 ] [ 41 ] [ 38 ]
About the same time, the German-Austrian Otto Schäffler [ de ] [ 42 ] demonstrated another printing telegraph in Vienna using a 5-bit reflected binary code for the same purpose, in 1874. [ 43 ] [ 13 ]
Frank Gray , who became famous for inventing the signaling method that came to be used for compatible color television, invented a method to convert analog signals to reflected binary code groups using vacuum tube -based apparatus. Filed in 1947, the method and apparatus were granted a patent in 1953, [ 14 ] and the name of Gray stuck to the codes. The " PCM tube " apparatus that Gray patented was made by Raymond W. Sears of Bell Labs, working with Gray and William M. Goodall, who credited Gray for the idea of the reflected binary code. [ 44 ]
Gray was most interested in using the codes to minimize errors in converting analog signals to digital; his codes are still used today for this purpose.
Gray codes are used in linear and rotary position encoders ( absolute encoders and quadrature encoders ) in preference to weighted binary encoding. This avoids the possibility that, when multiple bits change in the binary representation of a position, a misread will result from some of the bits changing before others.
For example, some rotary encoders provide a disk which has an electrically conductive Gray code pattern on concentric rings (tracks). Each track has a stationary metal spring contact that provides electrical contact to the conductive code pattern. Together, these contacts produce output signals in the form of a Gray code. Other encoders employ non-contact mechanisms based on optical or magnetic sensors to produce the Gray code output signals.
Regardless of the mechanism or precision of a moving encoder, position measurement error can occur at specific positions (at code boundaries) because the code may be changing at the exact moment it is read (sampled). A binary output code could cause significant position measurement errors because it is impossible to make all bits change at exactly the same time. If, at the moment the position is sampled, some bits have changed and others have not, the sampled position will be incorrect. In the case of absolute encoders, the indicated position may be far away from the actual position and, in the case of incremental encoders, this can corrupt position tracking.
In contrast, the Gray code used by position encoders ensures that the codes for any two consecutive positions will differ by only one bit and, consequently, only one bit can change at a time. In this case, the maximum position error will be small, indicating a position adjacent to the actual position.
Due to the Hamming distance properties of Gray codes, they are sometimes used in genetic algorithms . [ 15 ] They are very useful in this field, since mutations in the code allow for mostly incremental changes, but occasionally a single bit-change can cause a big leap and lead to new properties.
Gray codes are also used in labelling the axes of Karnaugh maps since 1953 [ 45 ] [ 46 ] [ 47 ] as well as in Händler circle graphs since 1958, [ 48 ] [ 49 ] [ 50 ] [ 51 ] both graphical methods for logic circuit minimization .
In modern digital communications , 1D- and 2D-Gray codes play an important role in error prevention before applying an error correction . For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise .
Digital logic designers use Gray codes extensively for passing multi-bit count information between synchronous logic that operates at different clock frequencies. The logic is considered operating in different "clock domains". It is fundamental to the design of large chips that operate with many different clocking frequencies.
If a system has to cycle sequentially through all possible combinations of on-off states of some set of controls, and the changes of the controls require non-trivial expense (e.g. time, wear, human work), a Gray code minimizes the number of setting changes to just one change for each combination of states. An example would be testing a piping system for all combinations of settings of its manually operated valves.
A balanced Gray code can be constructed, [ 52 ] that flips every bit equally often. Since bit-flips are evenly distributed, this is optimal in the following way: balanced Gray codes minimize the maximal count of bit-flips for each digit.
George R. Stibitz utilized a reflected binary code in a binary pulse counting device in 1941 already. [ 11 ] [ 12 ] [ 13 ]
A typical use of Gray code counters is building a FIFO (first-in, first-out) data buffer that has read and write ports that exist in different clock domains. The input and output counters inside such a dual-port FIFO are often stored using Gray code to prevent invalid transient states from being captured when the count crosses clock domains. [ 53 ] The updated read and write pointers need to be passed between clock domains when they change, to be able to track FIFO empty and full status in each domain. Each bit of the pointers is sampled non-deterministically for this clock domain transfer. So for each bit, either the old value or the new value is propagated. Therefore, if more than one bit in the multi-bit pointer is changing at the sampling point, a "wrong" binary value (neither new nor old) can be propagated. By guaranteeing only one bit can be changing, Gray codes guarantee that the only possible sampled values are the new or old multi-bit value. Typically Gray codes of power-of-two length are used.
Sometimes digital buses in electronic systems are used to convey quantities that can only increase or decrease by one at a time, for example the output of an event counter which is being passed between clock domains or to a digital-to-analog converter. The advantage of Gray codes in these applications is that differences in the propagation delays of the many wires that represent the bits of the code cannot cause the received value to go through states that are out of the Gray code sequence. This is similar to the advantage of Gray codes in the construction of mechanical encoders, however the source of the Gray code is an electronic counter in this case. The counter itself must count in Gray code, or if the counter runs in binary then the output value from the counter must be reclocked after it has been converted to Gray code, because when a value is converted from binary to Gray code, [ nb 1 ] it is possible that differences in the arrival times of the binary data bits into the binary-to-Gray conversion circuit will mean that the code could go briefly through states that are wildly out of sequence. Adding a clocked register after the circuit that converts the count value to Gray code may introduce a clock cycle of latency, so counting directly in Gray code may be advantageous. [ 54 ]
To produce the next count value in a Gray-code counter, it is necessary to have some combinational logic that will increment the current count value that is stored. One way to increment a Gray code number is to convert it into ordinary binary code, [ 55 ] add one to it with a standard binary adder, and then convert the result back to Gray code. [ 56 ] Other methods of counting in Gray code are discussed in a report by Robert W. Doran , including taking the output from the first latches of the master-slave flip flops in a binary ripple counter. [ 57 ]
As the execution of program code typically causes an instruction memory access pattern of locally consecutive addresses, bus encodings using Gray code addressing instead of binary addressing can reduce the number of state changes of the address bits significantly, thereby reducing the CPU power consumption in some low-power designs. [ 58 ] [ 59 ]
The binary-reflected Gray code list for n bits can be generated recursively from the list for n − 1 bits by reflecting the list (i.e. listing the entries in reverse order), prefixing the entries in the original list with a binary 0 , prefixing the entries in the reflected list with a binary 1 , and then concatenating the original list with the reversed list. [ 13 ] For example, generating the n = 3 list from the n = 2 list:
The one-bit Gray code is G 1 = ( 0,1 ). This can be thought of as built recursively as above from a zero-bit Gray code G 0 = ( Λ ) consisting of a single entry of zero length. This iterative process of generating G n +1 from G n makes the following properties of the standard reflecting code clear:
These characteristics suggest a simple and fast method of translating a binary value into the corresponding Gray code. Each bit is inverted if the next higher bit of the input value is set to one. This can be performed in parallel by a bit-shift and exclusive-or operation if they are available: the n th Gray code is obtained by computing n ⊕ ⌊ n 2 ⌋ {\displaystyle n\oplus \left\lfloor {\tfrac {n}{2}}\right\rfloor } . Prepending a 0 bit leaves the order of the code words unchanged, prepending a 1 bit reverses the order of the code words. If the bits at position i {\displaystyle i} of codewords are inverted, the order of neighbouring blocks of 2 i {\displaystyle 2^{i}} codewords is reversed. For example, if bit 0 is inverted in a 3 bit codeword sequence, the order of two neighbouring codewords is reversed
If bit 1 is inverted, blocks of 2 codewords change order:
If bit 2 is inverted, blocks of 4 codewords reverse order:
Thus, performing an exclusive or on a bit b i {\displaystyle b_{i}} at position i {\displaystyle i} with the bit b i + 1 {\displaystyle b_{i+1}} at position i + 1 {\displaystyle i+1} leaves the order of codewords intact if b i + 1 = 0 {\displaystyle b_{i+1}={\mathtt {0}}} , and reverses the order of blocks of 2 i + 1 {\displaystyle 2^{i+1}} codewords if b i + 1 = 1 {\displaystyle b_{i+1}={\mathtt {1}}} . Now, this is exactly the same operation as the reflect-and-prefix method to generate the Gray code.
A similar method can be used to perform the reverse translation, but the computation of each bit depends on the computed value of the next higher bit so it cannot be performed in parallel. Assuming g i {\displaystyle g_{i}} is the i {\displaystyle i} th Gray-coded bit ( g 0 {\displaystyle g_{0}} being the most significant bit), and b i {\displaystyle b_{i}} is the i {\displaystyle i} th binary-coded bit ( b 0 {\displaystyle b_{0}} being the most-significant bit), the reverse translation can be given recursively: b 0 = g 0 {\displaystyle b_{0}=g_{0}} , and b i = g i ⊕ b i − 1 {\displaystyle b_{i}=g_{i}\oplus b_{i-1}} . Alternatively, decoding a Gray code into a binary number can be described as a prefix sum of the bits in the Gray code, where each individual summation operation in the prefix sum is performed modulo two.
To construct the binary-reflected Gray code iteratively, at step 0 start with the c o d e 0 = 0 {\displaystyle \mathrm {code} _{0}={\mathtt {0}}} , and at step i > 0 {\displaystyle i>0} find the bit position of the least significant 1 in the binary representation of i {\displaystyle i} and flip the bit at that position in the previous code c o d e i − 1 {\displaystyle \mathrm {code} _{i-1}} to get the next code c o d e i {\displaystyle \mathrm {code} _{i}} . The bit positions start 0, 1, 0, 2, 0, 1, 0, 3, ... [ nb 2 ] See find first set for efficient algorithms to compute these values.
The following functions in C convert between binary numbers and their associated Gray codes. While it may seem that Gray-to-binary conversion requires each bit to be handled one at a time, faster algorithms exist. [ 60 ] [ 55 ] [ nb 1 ]
On newer processors, the number of ALU instructions in the decoding step can be reduced by taking advantage of the CLMUL instruction set . If MASK is the constant binary string of ones ended with a single zero digit, then carryless multiplication of MASK with the grey encoding of x will always give either x or its bitwise negation.
In practice, "Gray code" almost always refers to a binary-reflected Gray code (BRGC). However, mathematicians have discovered other kinds of Gray codes. Like BRGCs, each consists of a list of words, where each word differs from the next in only one digit (each word has a Hamming distance of 1 from the next word).
It is possible to construct binary Gray codes with n bits with a length of less than 2 n , if the length is even. One possibility is to start with a balanced Gray code and remove pairs of values at either the beginning and the end, or in the middle. [ 61 ] OEIS sequence A290772 [ 62 ] gives the number of possible Gray sequences of length 2 n that include zero and use the minimum number of bits.
0 → 000 1 → 001 2 → 002 10 → 012 11 → 011 12 → 010 20 → 020 21 → 021 22 → 022 100 → 122 101 → 121 102 → 120 110 → 110 111 → 111 112 → 112 120 → 102 121 → 101 122 → 100 200 → 200 201 → 201 202 → 202 210 → 212 211 → 211 212 → 210 220 → 220 221 → 221
There are many specialized types of Gray codes other than the binary-reflected Gray code. One such type of Gray code is the n -ary Gray code , also known as a non-Boolean Gray code . As the name implies, this type of Gray code uses non- Boolean values in its encodings.
For example, a 3-ary ( ternary ) Gray code would use the values 0,1,2. [ 31 ] The ( n , k )- Gray code is the n -ary Gray code with k digits. [ 63 ] The sequence of elements in the (3, 2)-Gray code is: 00,01,02,12,11,10,20,21,22. The ( n , k )-Gray code may be constructed recursively, as the BRGC, or may be constructed iteratively . An algorithm to iteratively generate the ( N , k )-Gray code is presented (in C ):
There are other Gray code algorithms for ( n , k )-Gray codes. The ( n , k )-Gray code produced by the above algorithm is always cyclical; some algorithms, such as that by Guan, [ 63 ] lack this property when k is odd. On the other hand, while only one digit at a time changes with this method, it can change by wrapping (looping from n − 1 to 0). In Guan's algorithm, the count alternately rises and falls, so that the numeric difference between two Gray code digits is always one.
Gray codes are not uniquely defined, because a permutation of the columns of such a code is a Gray code too. The above procedure produces a code in which the lower the significance of a digit, the more often it changes, making it similar to normal counting methods.
See also Skew binary number system , a variant ternary number system where at most two digits change on each increment, as each increment can be done with at most one digit carry operation.
Although the binary reflected Gray code is useful in many scenarios, it is not optimal in certain cases because of a lack of "uniformity". [ 52 ] In balanced Gray codes , the number of changes in different coordinate positions are as close as possible. To make this more precise, let G be an R -ary complete Gray cycle having transition sequence ( δ k ) {\displaystyle (\delta _{k})} ; the transition counts ( spectrum ) of G are the collection of integers defined by
λ k = | { j ∈ Z R n : δ j = k } | , for k ∈ Z n {\displaystyle \lambda _{k}=|\{j\in \mathbb {Z} _{R^{n}}:\delta _{j}=k\}|\,,{\text{ for }}k\in \mathbb {Z} _{n}}
A Gray code is uniform or uniformly balanced if its transition counts are all equal, in which case we have λ k = R n n {\displaystyle \lambda _{k}={\tfrac {R^{n}}{n}}} for all k . Clearly, when R = 2 {\displaystyle R=2} , such codes exist only if n is a power of 2. [ 64 ] If n is not a power of 2, it is possible to construct well-balanced binary codes where the difference between two transition counts is at most 2; so that (combining both cases) every transition count is either 2 ⌊ 2 n 2 n ⌋ {\displaystyle 2\left\lfloor {\tfrac {2^{n}}{2n}}\right\rfloor } or 2 ⌈ 2 n 2 n ⌉ {\displaystyle 2\left\lceil {\tfrac {2^{n}}{2n}}\right\rceil } . [ 52 ] Gray codes can also be exponentially balanced if all of their transition counts are adjacent powers of two, and such codes exist for every power of two. [ 65 ]
For example, a balanced 4-bit Gray code has 16 transitions, which can be evenly distributed among all four positions (four transitions per position), making it uniformly balanced: [ 52 ]
whereas a balanced 5-bit Gray code has a total of 32 transitions, which cannot be evenly distributed among the positions. In this example, four positions have six transitions each, and one has eight: [ 52 ]
We will now show a construction [ 66 ] and implementation [ 67 ] for well-balanced binary Gray codes which allows us to generate an n -digit balanced Gray code for every n . The main principle is to inductively construct an ( n + 2)-digit Gray code G ′ {\displaystyle G'} given an n -digit Gray code G in such a way that the balanced property is preserved. To do this, we consider partitions of G = g 0 , … , g 2 n − 1 {\displaystyle G=g_{0},\ldots ,g_{2^{n}-1}} into an even number L of non-empty blocks of the form
{ g 0 } , { g 1 , … , g k 2 } , { g k 2 + 1 , … , g k 3 } , … , { g k L − 2 + 1 , … , g − 2 } , { g − 1 } {\displaystyle \left\{g_{0}\right\},\left\{g_{1},\ldots ,g_{k_{2}}\right\},\left\{g_{k_{2}+1},\ldots ,g_{k_{3}}\right\},\ldots ,\left\{g_{k_{L-2}+1},\ldots ,g_{-2}\right\},\left\{g_{-1}\right\}}
where k 1 = 0 {\displaystyle k_{1}=0} , k L − 1 = − 2 {\displaystyle k_{L-1}=-2} , and k L ≡ − 1 ( mod 2 n ) {\displaystyle k_{L}\equiv -1{\pmod {2^{n}}}} ). This partition induces an ( n + 2 ) {\displaystyle (n+2)} -digit Gray code given by
If we define the transition multiplicities
m i = | { j : δ k j = i , 1 ≤ j ≤ L } | {\displaystyle m_{i}=\left|\left\{j:\delta _{k_{j}}=i,1\leq j\leq L\right\}\right|}
to be the number of times the digit in position i changes between consecutive blocks in a partition, then for the ( n + 2)-digit Gray code induced by this partition the transition spectrum λ i ′ {\displaystyle \lambda '_{i}} is
λ i ′ = { 4 λ i − 2 m i , if 0 ≤ i < n L , otherwise {\displaystyle \lambda '_{i}={\begin{cases}4\lambda _{i}-2m_{i},&{\text{if }}0\leq i<n\\L,&{\text{ otherwise }}\end{cases}}}
The delicate part of this construction is to find an adequate partitioning of a balanced n -digit Gray code such that the code induced by it remains balanced, but for this only the transition multiplicities matter; joining two consecutive blocks over a digit i {\displaystyle i} transition and splitting another block at another digit i {\displaystyle i} transition produces a different Gray code with exactly the same transition spectrum λ i ′ {\displaystyle \lambda '_{i}} , so one may for example [ 65 ] designate the first m i {\displaystyle m_{i}} transitions at digit i {\displaystyle i} as those that fall between two blocks. Uniform codes can be found when R ≡ 0 ( mod 4 ) {\displaystyle R\equiv 0{\pmod {4}}} and R n ≡ 0 ( mod n ) {\displaystyle R^{n}\equiv 0{\pmod {n}}} , and this construction can be extended to the R -ary case as well. [ 66 ]
Long run (or maximum gap ) Gray codes maximize the distance between consecutive changes of digits in the same position. That is, the minimum run-length of any bit remains unchanged for as long as possible. [ 68 ]
Monotonic codes are useful in the theory of interconnection networks, especially for minimizing dilation for linear arrays of processors. [ 69 ] If we define the weight of a binary string to be the number of 1s in the string, then although we clearly cannot have a Gray code with strictly increasing weight, we may want to approximate this by having the code run through two adjacent weights before reaching the next one.
We can formalize the concept of monotone Gray codes as follows: consider the partition of the hypercube Q n = ( V n , E n ) {\displaystyle Q_{n}=(V_{n},E_{n})} into levels of vertices that have equal weight, i.e.
V n ( i ) = { v ∈ V n : v has weight i } {\displaystyle V_{n}(i)=\{v\in V_{n}:v{\text{ has weight }}i\}}
for 0 ≤ i ≤ n {\displaystyle 0\leq i\leq n} . These levels satisfy | V n ( i ) | = ( n i ) {\displaystyle |V_{n}(i)|=\textstyle {\binom {n}{i}}} . Let Q n ( i ) {\displaystyle Q_{n}(i)} be the subgraph of Q n {\displaystyle Q_{n}} induced by V n ( i ) ∪ V n ( i + 1 ) {\displaystyle V_{n}(i)\cup V_{n}(i+1)} , and let E n ( i ) {\displaystyle E_{n}(i)} be the edges in Q n ( i ) {\displaystyle Q_{n}(i)} . A monotonic Gray code is then a Hamiltonian path in Q n {\displaystyle Q_{n}} such that whenever δ 1 ∈ E n ( i ) {\displaystyle \delta _{1}\in E_{n}(i)} comes before δ 2 ∈ E n ( j ) {\displaystyle \delta _{2}\in E_{n}(j)} in the path, then i ≤ j {\displaystyle i\leq j} .
An elegant construction of monotonic n -digit Gray codes for any n is based on the idea of recursively building subpaths P n , j {\displaystyle P_{n,j}} of length 2 ( n j ) {\displaystyle 2\textstyle {\binom {n}{j}}} having edges in E n ( j ) {\displaystyle E_{n}(j)} . [ 69 ] We define P 1 , 0 = ( 0 , 1 ) {\displaystyle P_{1,0}=({\mathtt {0}},{\mathtt {1}})} , P n , j = ∅ {\displaystyle P_{n,j}=\emptyset } whenever j < 0 {\displaystyle j<0} or j ≥ n {\displaystyle j\geq n} , and
P n + 1 , j = 1 P n , j − 1 π n , 0 P n , j {\displaystyle P_{n+1,j}={\mathtt {1}}P_{n,j-1}^{\pi _{n}},{\mathtt {0}}P_{n,j}}
otherwise. Here, π n {\displaystyle \pi _{n}} is a suitably defined permutation and P π {\displaystyle P^{\pi }} refers to the path P with its coordinates permuted by π {\displaystyle \pi } . These paths give rise to two monotonic n -digit Gray codes G n ( 1 ) {\displaystyle G_{n}^{(1)}} and G n ( 2 ) {\displaystyle G_{n}^{(2)}} given by
G n ( 1 ) = P n , 0 P n , 1 R P n , 2 P n , 3 R ⋯ and G n ( 2 ) = P n , 0 R P n , 1 P n , 2 R P n , 3 ⋯ {\displaystyle G_{n}^{(1)}=P_{n,0}P_{n,1}^{R}P_{n,2}P_{n,3}^{R}\cdots {\text{ and }}G_{n}^{(2)}=P_{n,0}^{R}P_{n,1}P_{n,2}^{R}P_{n,3}\cdots }
The choice of π n {\displaystyle \pi _{n}} which ensures that these codes are indeed Gray codes turns out to be π n = E − 1 ( π n − 1 2 ) {\displaystyle \pi _{n}=E^{-1}\left(\pi _{n-1}^{2}\right)} . The first few values of P n , j {\displaystyle P_{n,j}} are shown in the table below.
These monotonic Gray codes can be efficiently implemented in such a way that each subsequent element can be generated in O ( n ) time. The algorithm is most easily described using coroutines .
Monotonic codes have an interesting connection to the Lovász conjecture , which states that every connected vertex-transitive graph contains a Hamiltonian path. The "middle-level" subgraph Q 2 n + 1 ( n ) {\displaystyle Q_{2n+1}(n)} is vertex-transitive (that is, its automorphism group is transitive, so that each vertex has the same "local environment" and cannot be differentiated from the others, since we can relabel the coordinates as well as the binary digits to obtain an automorphism ) and the problem of finding a Hamiltonian path in this subgraph is called the "middle-levels problem", which can provide insights into the more general conjecture. The question has been answered affirmatively for n ≤ 15 {\displaystyle n\leq 15} , and the preceding construction for monotonic codes ensures a Hamiltonian path of length at least 0.839 N , where N is the number of vertices in the middle-level subgraph. [ 70 ]
Another type of Gray code, the Beckett–Gray code , is named for Irish playwright Samuel Beckett , who was interested in symmetry . His play " Quad " features four actors and is divided into sixteen time periods. Each period ends with one of the four actors entering or leaving the stage. The play begins and ends with an empty stage, and Beckett wanted each subset of actors to appear on stage exactly once. [ 71 ] Clearly the set of actors currently on stage can be represented by a 4-bit binary Gray code. Beckett, however, placed an additional restriction on the script: he wished the actors to enter and exit so that the actor who had been on stage the longest would always be the one to exit. The actors could then be represented by a first in, first out queue , so that (of the actors onstage) the actor being dequeued is always the one who was enqueued first. [ 71 ] Beckett was unable to find a Beckett–Gray code for his play, and indeed, an exhaustive listing of all possible sequences reveals that no such code exists for n = 4. It is known today that such codes do exist for n = 2, 5, 6, 7, and 8, and do not exist for n = 3 or 4. An example of an 8-bit Beckett–Gray code can be found in Donald Knuth 's Art of Computer Programming . [ 13 ] According to Sawada and Wong, the search space for n = 6 can be explored in 15 hours, and more than 9500 solutions for the case n = 7 have been found. [ 72 ]
Snake-in-the-box codes, or snakes , are the sequences of nodes of induced paths in an n -dimensional hypercube graph , and coil-in-the-box codes, [ 73 ] or coils , are the sequences of nodes of induced cycles in a hypercube. Viewed as Gray codes, these sequences have the property of being able to detect any single-bit coding error. Codes of this type were first described by William H. Kautz in the late 1950s; [ 5 ] since then, there has been much research on finding the code with the largest possible number of codewords for a given hypercube dimension.
Yet another kind of Gray code is the single-track Gray code (STGC) developed by Norman B. Spedding [ 74 ] [ 75 ] and refined by Hiltgen, Paterson and Brandestini in Single-track Gray Codes (1996). [ 76 ] [ 77 ] The STGC is a cyclical list of P unique binary encodings of length n such that two consecutive words differ in exactly one position, and when the list is examined as a P × n matrix , each column is a cyclic shift of the first column. [ 78 ]
The name comes from their use with rotary encoders , where a number of tracks are being sensed by contacts, resulting for each in an output of 0 or 1 . To reduce noise due to different contacts not switching at exactly the same moment in time, one preferably sets up the tracks so that the data output by the contacts are in Gray code. To get high angular accuracy, one needs lots of contacts; in order to achieve at least 1° accuracy, one needs at least 360 distinct positions per revolution, which requires a minimum of 9 bits of data, and thus the same number of contacts.
If all contacts are placed at the same angular position, then 9 tracks are needed to get a standard BRGC with at least 1° accuracy. However, if the manufacturer moves a contact to a different angular position (but at the same distance from the center shaft), then the corresponding "ring pattern" needs to be rotated the same angle to give the same output. If the most significant bit (the inner ring in Figure 1) is rotated enough, it exactly matches the next ring out. Since both rings are then identical, the inner ring can be cut out, and the sensor for that ring moved to the remaining, identical ring (but offset at that angle from the other sensor on that ring). Those two sensors on a single ring make a quadrature encoder. That reduces the number of tracks for a "1° resolution" angular encoder to 8 tracks. Reducing the number of tracks still further cannot be done with BRGC.
For many years, Torsten Sillke [ 79 ] and other mathematicians believed that it was impossible to encode position on a single track such that consecutive positions differed at only a single sensor, except for the 2-sensor, 1-track quadrature encoder. So for applications where 8 tracks were too bulky, people used single-track incremental encoders (quadrature encoders) or 2-track "quadrature encoder + reference notch" encoders.
Norman B. Spedding, however, registered a patent in 1994 with several examples showing that it was possible. [ 74 ] Although it is not possible to distinguish 2 n positions with n sensors on a single track, it is possible to distinguish close to that many. Etzion and Paterson conjecture that when n is itself a power of 2, n sensors can distinguish at most 2 n − 2 n positions and that for prime n the limit is 2 n − 2 positions. [ 80 ] The authors went on to generate a 504-position single track code of length 9 which they believe is optimal. Since this number is larger than 2 8 = 256, more than 8 sensors are required by any code, although a BRGC could distinguish 512 positions with 9 sensors.
An STGC for P = 30 and n = 5 is reproduced here:
Each column is a cyclic shift of the first column, and from any row to the next row only one bit changes. [ 81 ] The single-track nature (like a code chain) is useful in the fabrication of these wheels (compared to BRGC), as only one track is needed, thus reducing their cost and size.
The Gray code nature is useful (compared to chain codes , also called De Bruijn sequences ), as only one sensor will change at any one time, so the uncertainty during a transition between two discrete states will only be plus or minus one unit of angular measurement the device is capable of resolving. [ 82 ]
Since this 30 degree example was added, there has been a lot of interest in examples with higher angular resolution. In 2008, Gary Williams, [ 83 ] [ user-generated source? ] based on previous work, [ 80 ] discovered a 9-bit single track Gray code that gives a 1 degree resolution. This Gray code was used to design an actual device which was published on the site Thingiverse . This device [ 84 ] was designed by etzenseep (Florian Bauer) in September 2022.
An STGC for P = 360 and n = 9 is reproduced here:
Two-dimensional Gray codes are used in communication to minimize the number of bit errors in quadrature amplitude modulation (QAM) adjacent points in the constellation . In a typical encoding the horizontal and vertical adjacent constellation points differ by a single bit, and diagonal adjacent points differ by 2 bits. [ 85 ]
Two-dimensional Gray codes also have uses in location identifications schemes, where the code would be applied to area maps such as a Mercator projection of the earth's surface and an appropriate cyclic two-dimensional distance function such as the Mannheim metric be used to calculate the distance between two encoded locations, thereby combining the characteristics of the Hamming distance with the cyclic continuation of a Mercator projection. [ 86 ]
If a subsection of a specific codevalue is extracted from that value, for example the last 3 bits of a 4-bit Gray code, the resulting code will be an "excess Gray code". This code shows the property of counting backwards in those extracted bits if the original value is further increased. Reason for this is that Gray-encoded values do not show the behaviour of overflow, known from classic binary encoding, when increasing past the "highest" value.
Example: The highest 3-bit Gray code, 7, is encoded as (0)100. Adding 1 results in number 8, encoded in Gray as 1100. The last 3 bits do not overflow and count backwards if you further increase the original 4 bit code.
When working with sensors that output multiple, Gray-encoded values in a serial fashion, one should therefore pay attention whether the sensor produces those multiple values encoded in 1 single Gray code or as separate ones, as otherwise the values might appear to be counting backwards when an "overflow" is expected.
The bijective mapping { 0 ↔ 00 , 1 ↔ 01 , 2 ↔ 11 , 3 ↔ 10 } establishes an isometry between the metric space over the finite field Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} with the metric given by the Hamming distance and the metric space over the finite ring Z 4 {\displaystyle \mathbb {Z} _{4}} (the usual modular arithmetic ) with the metric given by the Lee distance . The mapping is suitably extended to an isometry of the Hamming spaces Z 2 2 m {\displaystyle \mathbb {Z} _{2}^{2m}} and Z 4 m {\displaystyle \mathbb {Z} _{4}^{m}} . Its importance lies in establishing a correspondence between various "good" but not necessarily linear codes as Gray-map images in Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} of ring-linear codes from Z 4 {\displaystyle \mathbb {Z} _{4}} . [ 87 ] [ 88 ]
There are a number of binary codes similar to Gray codes, including:
The following binary-coded decimal (BCD) codes are Gray code variants as well:
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WRF-SFIRE is a coupled atmosphere - wildfire model, which combines the Weather Research and Forecasting Model (WRF) with a fire-spread model, implemented by the level-set method . A version from 2010 was released based on the WRF 3.2 as WRF-Fire .
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Web Service Atomic Transaction is an OASIS standard.
To achieve all-or-nothing property for a group of services, it defines three protocols (completion, volatile two-phase commit , and durable two-phase commit), and a set of services. These protocols and services together ensure automatic activation, registration, propagation and atomic termination of web services . The protocols are implemented via the WS-Coordination context management framework and emulate ACID transaction properties .
Following the standard, a distributed transaction has a coordinator, an initiator, and one or more participants.
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WS-Management ( Web Services-Management ) is a DMTF open standard defining a SOAP -based protocol for the management of servers, devices, applications and various Web services. WS-Management provides a common way for systems to access and exchange management information across the IT infrastructure .
The specification is based on DMTF open standards and Internet standards for Web services.
The specification is quite rich, supporting much more than get/set of simple variables, and in that it is closer to WBEM or Netconf than to SNMP . A mapping of the DMTF -originated Common Information Model into WS-Management was also defined.
WS-Management was originally developed by a coalition of vendors. The coalition started with AMD , Dell , Intel , Microsoft , Sun Microsystems and expanded to a total of 13 members before being subsumed by the DMTF in 2005.
The DMTF has published the standards document DSP0226 with version 1.2 of September 30, 2014. [ 1 ]
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WSO2 Carbon [ 1 ] is the core platform on which WSO2 middleware products are built. It is based on Java OSGi technology, which allows components to be dynamically installed, started, stopped, updated, and uninstalled, and it eliminates component version conflicts. In Carbon, this capability translates into a solid core of common middleware enterprise components, including clustering, security, logging, and monitoring, plus the ability to add components for specific features needed to solve a specific enterprise scenario.
WSO2 Carbon was introduced in 2009 and received InfoWorld's 2009 'Best of Open Source Software', or "Bossie", award. [ 2 ]
In February 2009, WSO2 introduced the WSO2 Carbon componentized framework based on the Open Source Gateway Initiative (OSGi), designed to serve as the basis for all WSO2 software products. [ 3 ] [ 4 ] Version 5.3.0 of the open-source WSO2 Carbon Kernel was released in December 2022 and updated in January 2023. [ 5 ]
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The WSSUS ( Wide-Sense Stationary Uncorrelated Scattering ) model provides a statistical description of the transmission behavior of wireless channels . "Wide-sense stationarity " means the second-order moments of the channel are stationary, which means that they depends only on the time difference, while "uncorrelated scattering " refers to the delay τ due to scatterers.
Modelling of mobile channels as WSSUS (wide sense stationary uncorrelated scattering) has become popular among specialists. The model was introduced by Phillip A. Bello in 1963. [ 1 ]
A commonly used description of time variant channel applies the set of Bello functions and the theory of stochastic processes.
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Tungsten diselenide is an inorganic compound with the formula WSe 2 . [ 6 ] The compound adopts a hexagonal crystalline structure similar to molybdenum disulfide . The tungsten atoms are covalently bonded to six selenium ligands in a trigonal prismatic coordination sphere while each selenium is bonded to three tungsten atoms in a pyramidal geometry. The tungsten–selenium bond has a length of 0.2526 nm, and the distance between selenium atoms is 0.334 nm. [ 7 ] It is a well studied example of a layered material . The layers stack together via van der Waals interactions . WSe 2 is a very stable semiconductor in the group-VI transition metal dichalcogenides.
The hexagonal (P6 3 /mmc) polymorph 2H-WSe 2 is isotypic with hexagonal MoS 2 . The two-dimensional lattice structure has W and Se arranged periodically in layers with hexagonal symmetry. Similar to graphite , van der Waals interactions hold the layers together; however, the 2D-layers in WSe 2 are not atomically thin. The large size of the W cation renders the lattice structure of WSe 2 more sensitive to changes than MoS 2 . [ 8 ]
In addition to the typical semiconducting hexagonal structure, a second metallic polymorph of WSe 2 exists. This phase, 1T-WSe 2 , is based on a tetragonal symmetry with one WSe 2 layer per repeating unit. The 1T-WSe 2 phase is less stable and transitions to the 2H-WSe 2 phase. [ 8 ] [ 9 ] WSe 2 can form a fullerene -like structure.
The Young's modulus varies greatly as a function of the number of layers in a flake. For a single monolayer, the reported Young's modulus is 258.6 ± 38.3 GPa. [ 10 ]
Heating thin films of tungsten under pressure from gaseous selenium and high temperatures (>800 K) using the sputter deposition technique leads to the films crystallizing in hexagonal structures with the correct stoichiometric ratio. [ 11 ]
The potential applications of transition metal dichalcogenides in solar cells and photonics are often discussed. [ 13 ] Bulk WSe 2 has an optical band gap of ~1.35 eV with a temperature dependence of −4.6 × 10 −4 eV/K. [ 14 ] WSe 2 photoelectrodes are stable in both acidic and basic conditions, making them potentially useful in electrochemical solar cells . [ 15 ] [ 16 ] [ 17 ]
The properties of WSe 2 monolayers differ from those of the bulk state, as is typical for semiconductors. Mechanically exfoliated monolayers of WSe 2 are transparent photovoltaic materials with LED properties . [ 18 ] The resulting solar cells pass 95 percent of the incident light, with one tenth of the remaining five percent converted into electrical power. [ 19 ] [ 20 ] The material can be changed from p-type to n-type by changing the voltage of an adjacent metal electrode from positive to negative, allowing devices made from it to have tunable bandgaps. [ 21 ]
Superconductivity has been reported in twisted bilayer WSe 2 , with a transition temperature of 200 mK. [ 22 ]
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WT1190F ( 9U01FF6 , UDA34A3 , or UW8551D ) was a small temporary satellite of Earth that impacted Earth on 13 November 2015 at 06:18:21.7 (± 0.1 seconds) UTC . [ 4 ] : 7–8 It is thought to have been space debris from the trans-lunar injection stage of the 1998 Lunar Prospector mission. [ 5 ] [ 6 ] It was first discovered on 18 February 2013 by the Catalina Sky Survey . [ 2 ] [ 7 ] It was then lost, and reacquired on 29 November 2013. It was again discovered on 3 October 2015 by astronomer Rose Garcia with the Catalina Sky Survey 60-inch telescope, and the object was soon identified to be the same as the two objects previously sighted by the team, who have been sharing their data through the International Astronomical Union 's Minor Planet Center (MPC). [ 8 ] An early orbit calculation showed that it was orbiting Earth in an extremely elliptical orbit, taking it from within the geosynchronous satellite ring to nearly twice the distance of the Moon. [ 1 ] It was also probably the same object as 9U01FF6, another object on a similar orbit discovered on 26 October 2009.
WT1190F had been orbiting Earth as a temporary satellite (named UWAIS ) since mid-2009, if not longer. While it has not been positively identified with any known artificial satellites, its estimated density of 0.1 g/cm 3 was much lower than would be expected of a natural object as even water has a density of 1 g/cm 3 . Hence, European Space Agency astronomers have concluded that the object was likely a fuel tank of some sort. [ 2 ] [ 7 ]
After more observations, astronomers determined that the object would impact Earth on 13 November 2015 at 06:18 UTC (11:48 local time), [ 9 ] south of Sri Lanka . [ 2 ] [ 7 ] Due to its small size, it was expected that most or all of the object would burn up in the atmosphere before impacting, but would be visible as a bright daytime fireball if the sky was not badly overcast . [ 2 ] [ 7 ]
A ground-based observational campaign was organized as a possible test for future collision events involving also natural bodies. [ 10 ]
WT1190F was first discovered by the Mount Lemmon Survey , a participant in the Catalina Sky Survey Near-Earth Object surveying program. [ 11 ] The object was identified with an apparent magnitude 19.5 on 18 February 2013, and given the temporary designation UDA34A3, but was lost soon after, with an observation arc of only 5 hours. [ 12 ] However, it was again seen by the same survey on 29 November 2013 and given the designation UW8551D and lost again, only being observed for 1 hour 35 minutes. [ 12 ]
Most recently, it was recovered on 3 October 2015 and given the designation WT1190F. Its orbit was soon calculated and found to be orbiting Earth, but not with the orbit of any known artificial satellite. The object's orbit was soon connected, allowing more observations to be made, and several precovery observations have been found of the object, dating back to June 2009. [ 13 ]
The type of orbit that WT1190F had was not stable long-term. An object in this type of orbit was likely to impact into Earth or the Moon, or acquire enough orbital speed to be ejected into orbit around the Sun. [ 14 ] It was not likely that it had been orbiting Earth for decades. [ 14 ] In 2011 the orbit had an eccentricity of 0.33 and perigee (closest approach to Earth) of 248,000 km (154,000 mi ). [ 13 ] It passed about 22,000 km (14,000 mi) from the Moon on 24 May 2012. [ 15 ] By 2013 the eccentricity had increased to 0.70 and the perigee decreased to 105,000 km (65,000 mi). [ 12 ]
During WT1190F's orbit, it changed significantly in brightness, from an apparent magnitude 16 at perigee , to magnitude 23 at apogee . It spent most of its time dimmer than magnitude 20. [ 1 ] This, combined with solar pressure acceleration , the Yarkovsky effect , and frequent orbital perturbations by the Moon, made it difficult to precisely predict its orbit and location. About one hour before atmospheric entry, the object had a R magnitude of 13.6, [ 16 ] [ a ] roughly the brightness of Pluto .
WT1190F made atmospheric entry at 11 kilometers per second (25,000 miles per hour). [ 17 ] Whatever was left from the re-entry was calculated to have fallen into the ocean about 100 kilometres (62 mi) from Galle , Sri Lanka . [ 8 ] The closest approach to Galle occurred during atmospheric flight when the object had an altitude of 45 km and a distance of 51 km. [ 18 ] For observers in Colombo , Sri Lanka, the object started out [ clarification needed ] 30 degrees above the horizon coming in from slightly south of due west. [ 19 ] Its mass was not sufficient to cause any risk to the area, but the event still produced a bright fireball. Scientists wanted to study WT1190F to better understand the trajectory and atmospheric entry of satellites, debris, and small asteroids from translunar orbit. [ 20 ] [ 8 ] The International Astronomical Center (IAC) and the United Arab Emirates Space Agency utilized a Gulfstream 450 jet to study the re-entry from above the clouds and haze. [ 20 ] The airborne observation team successfully captured the re-entry on video. [ 9 ] [ 21 ]
The International Astronomical Center (IAC) and the United Arab Emirates Space Agency observed WT1190F as it fell towards the Earth. The IAC chartered a Gulfstream 450 jet to bring researchers such as Peter Jenniskens to the area of WT1190F's impact, at a high altitude, to view the event over clouds or haze. [ 20 ] The Next TC3 Consortium Asteroid Detection and Early Warning team narrowed the atmospheric entry time to ± 1.3 seconds. [ 9 ]
Observers on the ground could not see the fireball because of rain, but the plane was able to find an opening in the clouds. The fireball was a bright naked eye object. Spectroscopic data was acquired to determine what the object was made of, [ 9 ] and the results published. [ 4 ] : 9
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Tungsten ditelluride ( W Te 2 ) is an inorganic semimetallic chemical compound . In October 2014, tungsten ditelluride was discovered to exhibit an extremely large magnetoresistance : 13 million percent resistance increase in a magnetic field of 60 tesla at 0.5 kelvin. [ 3 ] The resistance is proportional to the square of the magnetic field and shows no saturation. This may be due to the material being the first example of a compensated semimetal, in which the number of mobile holes is the same as the number of electrons. [ 4 ] Tungsten ditelluride has layered structure, similar to many other transition metal dichalcogenides , but its layers are so distorted that the honeycomb lattice many of them have in common is in WTe 2 hard to recognize. The tungsten atoms instead form zigzag chains, which are thought to behave as one-dimensional conductors. Unlike electrons in other two-dimensional semiconductors , the electrons in WTe 2 can easily move between the layers. [ 5 ]
When subjected to pressure, the magnetoresistance effect in WTe 2 is reduced. Above the pressure of 10.5 GPa magnetoresistance disappears and the material becomes a superconductor. At 13.0 GPa the transition to superconductivity happens below 6.5 K. [ 6 ]
WTe 2 was predicted to be a Weyl semimetal and, in particular, to be the first example of a Type II Weyl semimetal, where the Weyl nodes exist at the intersection of the electron and hole pockets. [ 7 ]
It has also been reported that terahertz-frequency light pulses can switch the crystal structure of W Te 2 between orthorhombic and monoclinic by altering the material's atomic lattice. [ 8 ]
Tungsten ditelluride can be exfoliated into thin sheets down to single layers. Monolayer WTe 2 was initially predicted to remain a Weyl semimetal [ 9 ] in the 1T' crystal phase. It was later shown with transport measurements that, below 50K, a single layer of WTe 2 instead acts like an insulator but with an offset current independent of doping by a local electrostatic gate. When using a contact geometry that shorted out conduction along the device edges, this offset current vanished, demonstrating that this nearly quantized conduction was localized to the edge—behavior consistent with monolayer WTe 2 being a two-dimensional topological insulator . [ 10 ] [ 11 ] Identical measurements with two- and three-layer thick samples showed the expected semimetallic response. Subsequent studies using other techniques have been consistent with the transport results, including those using angle-resolved photoemission spectroscopy [ 12 ] [ 13 ] and microwave-impedance microscopy. [ 14 ] Monolayer WTe 2 has also been observed to superconduct at moderate doping, [ 15 ] with a critical temperature tunable by doping level.
Two- and three-layer thick WTe 2 have also been observed to be polar metals , simultaneously hosting metallic behavior and switchable electric polarization. [ 16 ] The polarization was theorized to originate from vertical charge transfer between the layers, which is switched by interlayer sliding. [ 17 ]
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The W Window System , or simply W , is a discontinued windowing system and precursor, in name and concept, to the modern X Window System .
W was originally developed at Stanford University by Paul Asente and Brian Reid for the V operating system . In 1983, Paul Asente and Chris Kent ported the system to UNIX on the VS100 , giving a copy to those working at MIT 's Laboratory for Computer Science. [ 1 ]
In 1984, Bob Scheifler of MIT replaced the synchronous protocol of W with an asynchronous alternative and named the result X. [ 2 ]
Since this time, the X window system has gone through many fundamental changes and no longer bears any significant resemblance to W.
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The Waves in the Lower Solar Atmosphere ( WaLSA ) team is an international consortium that is focused on investigating wave activity in the Sun's lower atmosphere. The purpose of the group is to understand how magnetohydrodynamic (MHD) waves generated within the Sun's interior and lower atmosphere affect the dynamics and heating of its outer layers. [ 1 ]
The WaLSA team's research has been supported by organizations including the Research Council of Norway through the Rosseland Centre for Solar Physics, [ 2 ] the Royal Society , [ 3 ] and the International Space Science Institute . [ 4 ]
The WaLSA team's research focuses on understanding various wave modes propagating through solar structures. [ 5 ] They have investigated the coupling mechanisms between different wave modes [ 6 ] and measured energy carried by MHD waves. [ 7 ]
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In traditional Japanese aesthetics , wabi-sabi ( 侘び寂び ) centers on the acceptance of transience and imperfection. [ 2 ] It is often described as the appreciation of beauty that is "imperfect, impermanent, and incomplete". [ 3 ] It is prevalent in many forms of Japanese art. [ 4 ] [ 5 ]
Wabi-sabi combines two interrelated concepts: wabi ( 侘 ) and sabi ( 寂 ) . According to the Stanford Encyclopedia of Philosophy , wabi may be translated as "subdued, austere beauty", and sabi as "rustic patina ". [ 6 ] Wabi-sabi derives from the Buddhist teaching of the three marks of existence ( 三法印 , sanbōin ) , which include impermanence ( 無常 , mujō ) , suffering ( 苦 , ku ) , and emptiness or absence of self-nature ( 空 , kū ) . [ 7 ]
Characteristics of wabi-sabi aesthetics and principles include asymmetry , roughness, simplicity , economy, austerity, modesty, intimacy , and the appreciation of both natural objects and the forces of nature.
Wabi-sabi has been described as "the most conspicuous and characteristic feature of what we think of as traditional Japanese beauty. It occupies roughly the same position in the Japanese pantheon of aesthetic values as do the Greek ideals of beauty and perfection in the West." [ 3 ] Andrew Juniper writes that, "If an object or expression can bring about, within us, a sense of serene melancholy and a spiritual longing, then that object could be said to be wabi-sabi ." [ 8 ] According to Richard Powell, " Wabi-sabi nurtures all that is authentic by acknowledging three simple realities: nothing lasts, nothing is finished, and nothing is perfect." [ 9 ]
When considering an English translation of the words wabi and sabi , Juniper explains that "they have been used to express a vast range of ideas and emotions, and so their meanings are more open to personal interpretation than almost any other word in the Japanese vocabulary." As a result, attempts to translate wabi-sabi directly may obscure the ambiguity essential to its meaning. [ 8 ]
After centuries of incorporating artistic and Buddhist influences from China, wabi-sabi evolved into a distinctly Japanese ideal. Over time, the meanings of wabi and sabi became more lighthearted and hopeful. Around 700 years ago, particularly among the Japanese nobility, understanding emptiness and imperfection came to be regarded as a first step toward satori or enlightenment . In contemporary Japan, wabi-sabi is often summarized as "wisdom in natural simplicity". In art books, it is typically defined as "flawed beauty". [ 10 ] Works in the wabi-sabi style often emphasize process, with the piece understood as ultimately incomplete. [ 11 ]
From a design or engineering perspective, wabi may refer to the imperfect quality of an object resulting from inherent limitations in design and manufacture, especially under changing or unpredictable conditions. In this context, sabi could relate to impermanent reliability or the object's finite lifespan. This interpretation is further reflected in a phonological and etymological connection with the Japanese word sabi ( 錆 , lit. ' to rust ' ) . Although the kanji for "rust" differ from sabi ( 寂 ) in wabi-sabi , the original spoken term (from pre-kanji yamato-kotoba ) is believed to have been the same. [ 12 ] [ 13 ]
Wabi and sabi both convey feelings of desolation and solitude. Within Mahayana Buddhism , these can be considered positive traits, representing release from the material world and the possibility of transcendence to a simpler life. As Mahayana philosophy emphasizes direct experience over verbal explanation, wabi-sabi may be best understood in a non-verbal, experiential way.
Although wabi and sabi have religious origins, their usage in contemporary Japanese language is often informal, consistent with the syncretic nature of Japanese spiritual practice .
In one sense, wabi-sabi can be seen as a form of training. The student learns to observe and appreciate the simplest, most natural elements, such as fading autumn leaves. Over time, wabi-sabi reshapes perception so that even a chipped vase or a cracked bowl becomes meaningful and beautiful, not despite the flaw but because of it. These imperfections offer space for reflection. The same applies to materials like unfinished wood, paper, or fabric: as they age and change, those transformations can become quietly captivating. [ 14 ]
Wabi-sabi has roots in Zen Buddhism. It began to shape Japanese culture when the Zen priest Murata Jukō (村田珠光, 1423–1502) modified the tea ceremony . [ 15 ] He introduced simple, rough wooden and clay instruments in place of the gold, jade, and porcelain then popular in the Chinese-style tea service. About one hundred years later, the tea master Sen no Rikyū (千利休, 1522 to 21 April 1591) introduced wabi-sabi to the nobility through his design of the teahouse . "He constructed a teahouse with a door so low that even the emperor would have to bow in order to enter, reminding everyone of the importance of humility before tradition, mystery, and spirit." [ 15 ]
At first, something that exhibited wabi-sabi qualities could only be discovered. It could be "found in the simple dwellings of the farmers that dotted the landscape, epitomized in neglected stone lanterns overgrown with moss or in simple bowls and other household utensils used by the common folk." [ 16 ] However, toward the end of the late medieval period, the ruling class began using these aesthetic values to intentionally create "tea ceremony utensils, handicrafts, tea ceremony rooms and cottages, homes, gardens, even food and sweets, and above all manners and etiquette." [ 16 ]
Many forms of Japanese art have been influenced by Zen and Mahayana philosophy over the past thousand years. The contemplation and acceptance of imperfection, as well as the awareness of constant flux and impermanence , have been particularly important to Japanese arts and culture . [ 8 ] Accordingly, many Japanese art forms can be seen to encapsulate and exemplify the ideals of wabi-sabi . [ 8 ]
Japanese gardens began as simple open spaces intended to attract kami, or spirits. During the Kamakura period, Zen ideals began to influence Japanese garden design. [ 8 ] Temple gardens were arranged with large rocks and other natural materials to form Karesansui , or Zen rock gardens. "Their designs imbued the gardens with a sense of the surreal and beckoned viewers to forget themselves and become immersed in the seas of gravel and the forests of moss. By loosening the rigid sense of perception, the actual scales of the garden became irrelevant and the viewers were able to then perceive the huge landscapes deep within themselves." [ 8 ]
Due to the tea garden's close relationship with the tea ceremony, "the tea garden became one of the richest expressions of wabi sabi." [ 8 ] These small gardens typically incorporated elements of wabi-sabi design. They were meant to invite interpretation and place the visitor in a contemplative state, preparing them to take part in the tea ceremony. [ 8 ]
Japanese poetry such as tanka and haiku is typically very short and focuses on the defining attributes of a scene. "By withholding verbose descriptions, the poem entices the reader to actively participate in the fulfillment of its meaning and, as with the Zen gardens, to become an active participant in the creative process." [ 8 ] One of the most famous Japanese poets, Bashō , was credited with establishing sabi as a definitive emotive force in haiku. Many of his works, like other wabi-sabi expressions, avoid sentimentality or superfluous adjectives, instead presenting the "devastating imagery of solitude." [ 8 ]
As the preference for simplicity and modesty grew, Zen masters came to view ornate Chinese ceramics as overly decorative and ostentatious. [ 17 ] Japanese potters began to explore freer expressions of beauty, moving away from uniformity and symmetry. New kiln technologies introduced varied colors, forms, and textures, allowing the creation of pieces that were unique and nonuniform. A particular type of firing was favored for its natural, unpredictable effects and its contribution to organic ash glazes —considered a clear embodiment of wabi-sabi . [ 17 ]
One example is the white raku bowl Mount Fuji (Shiroraku-Chawan, Fujisan), made by Hon'ami Kōetsu (本阿弥 光悦; 1558 – 27 February 1637), which has been designated a national treasure by the Japanese government. [ 17 ]
Kintsugi , a technique that uses gold lacquer to repair broken pottery, is also regarded as an expression of wabi-sabi . [ 8 ]
Sen no Rikyū rejected the ornate rikka style popular at the time, disliking its rigid formalism and elaborate Chinese vases. Instead, he used simple vessels to display flowers, known as chabana , in his tea ceremonies. [ 8 ] Rather than selecting impressive or cultivated blooms, he preferred wildflowers. " Ikebana , like the gardens, uses a living medium in the creative process, and it is this ingredient of life that brings a unique feel to flower arrangements." [ 8 ]
Ikebana then became an important part of the tea ceremony, and the flowers were treated with great respect. [ 8 ] "When a tea-master has arranged a flower to his satisfaction he will place it on the tokonoma , the place of honour in a Japanese room. It rests there like an enthroned prince, and the guests or disciples on entering the room will salute it with a profound bow before making their addresses to the host." [ 18 ]
Other traditional expressions of wabi-sabi include:
Wabi-sabi has been employed in the Western world across a variety of contexts, including the arts, technology, media, and mental health.
Many Western designers, writers, poets, and artists have incorporated wabi-sabi ideals into their work to varying degrees. Some treat the concept as central to their practice, while others use it more selectively.
autumn twilight: the wreath on the door lifts in the wind
During the 1990s, the concept was adopted by computer software developers and used in contexts such as agile programming and wiki platforms. It described the acceptance of ongoing imperfection in software development produced through iterative methods. [ 22 ]
Wabi-sabi has also been cited in mental health contexts as a helpful concept for reducing perfectionist thinking . [ 23 ]
In 2009, Marcel Theroux presented In Search of Wabi Sabi on BBC Four as part of its Hidden Japan programming season. He traveled throughout Japan attempting to understand the aesthetic preferences of its people. Theroux began by humorously enacting a challenge from the book Living Wabi Sabi by Taro Gold , asking passersby on a Tokyo street to describe wabi-sabi . As Gold predicted, "they will likely give you a polite shrug and explain that Wabi Sabi is simply unexplainable." [ 24 ]
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Polythionic acid is an oxoacid which has a straight chain of sulfur atoms and has the chemical formula S n (SO 3 H) 2 ( n + 2 > 2). Trithionic acid (H 2 S 3 O 6 ), tetrathionic acid (H 2 S 4 O 6 ) are simple examples. They are the conjugate acids of polythionates . The compounds of n < 80 are expected to exist, and those of n < 20 have already been synthesized. Dithionic acid (H 2 S 2 O 6 ) does not belong to the polythionic acids due to strongly different properties.
All polythionates anion contains chains of sulfur atoms attached to the terminal SO 3 H-groups. Names of polythionic acids are determined by the number of atoms in the chain of sulfur atoms:
Numerous acids and salts of this group have a venerable history, and chemistry systems, where they exist, dates back to the studies John Dalton devoted to the behavior of hydrogen sulfide in aqueous solutions of sulfur dioxide (1808). This solution now has the name of Heinrich Wilhelm Ferdinand Wackenroder , who conducted a systematic study (1846). Over the next 60–80 years, numerous studies have shown the presence of ions, in particular tetrathionate and pentathionate anion ( S 4 O 2− 6 and S 5 O 2− 6 , respectively).
H 2 S react with SO 3 or HSO 3 Cl , forming thiosulfuric acid H 2 S 2 O 3 , as the analogous reaction with H 2 S 2 forms disulfonomonosulfonic acid HS 2 SO 3 H ; similarly polysulfanes H 2 S n ( n = 2–6) give HS n SO 3 H. Reactions from both ends of the polysulfane chain lead to the formation of polysulfonodisulfonic acid HO 3 SS n SO 3 H.
Many methods exist for the synthesis of these acids, but the mechanism is unclear because of the large number of simultaneously occurring and competing reactions such as redox , chain transfer , and disproportionation . Typical examples are:
Anhydrous polythionic acids can be formed in diethyl ether solution by the following three general ways:
Polythionic acids with a small number of sulfur atoms in the chain ( n = 3, 4, 5, 6) are the most stable. Polythionic acids are stable only in aqueous solutions, and are rapidly destroyed at higher concentrations with the release of sulfur , sulfur dioxide and - sometimes - sulfuric acid . Acid salts of polythionic acids do not exist. Polythionate ions are significantly more stable than the corresponding acids.
Under the action of oxidants ( potassium permanganate , potassium dichromate ) polythionic acids and their salts are oxidized to sulfate , and the interaction with strong reducing agents ( amalgam of sodium) converts them into sulfites and dithionites.
Polythionic acids are rarely encountered, but polythion ates are common and important.
Polythionic acids have been identified in crater lakes . [ 2 ] The phenomenon may be useful to predict volcanic activity .
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The Wacker process or the Hoechst-Wacker process (named after the chemical companies of the same name) refers to the oxidation of ethylene to acetaldehyde in the presence of palladium(II) chloride and copper(II) chloride as the catalyst . [ 1 ] This chemical reaction was one of the first homogeneous catalysis with organopalladium chemistry applied on an industrial scale. [ 2 ]
The Wacker reaction was first reported by Smidt et al. [ 3 ] [ 4 ] [ 5 ]
The development of the chemical process now known as the Wacker process began in 1956 at Wacker Chemie . [ 6 ] At the time, many industrial compounds were produced from acetylene , derived from calcium carbide , an expensive and environmentally unfriendly technology. The construction of a new oil refinery in Cologne by Esso close to a Wacker site, combined with the realization that ethylene would be a cheaper feedstock prompted Wacker to investigate its potential uses. As part of the ensuing research effort, a reaction of ethylene and oxygen over palladium on carbon in a quest for ethylene oxide unexpectedly gave evidence for the formation of acetaldehyde (simply based on smell). More research into this ethylene to acetaldehyde conversion resulted in a 1957 patent describing a gas-phase reaction using a heterogeneous catalyst. [ 7 ] In the meanwhile Hoechst AG joined the race and after a patent filing forced Wacker into a partnership called Aldehyd GmbH . The heterogeneous process ultimately failed due to catalyst inactivation and was replaced by the water-based homogeneous system for which a pilot plant was operational in 1958. Problems with the aggressive catalyst solution were solved by adopting titanium (newly available for industrial use) as construction material for reactors and pumps. Production plants went into operation in 1960.
The reaction mechanism for the industrial Wacker process (olefin oxidation via palladium(II) chloride) has received significant attention for several decades. Aspects of the mechanism are still debated. A modern formulation is described below:
The initial stoichiometric reaction was first reported by Francis Clifford Phillips in his doctoral dissertation on the composition of Pennsylvanian natural gas defended in 1893. [ 9 ] This net reaction can also be described as follows:
This conversion is followed by reactions that regenerate the Pd(II) catalyst:
Only the alkene and oxygen are consumed. Without copper(II) chloride as an oxidizing agent , Pd(0) metal (resulting from beta-hydride elimination of Pd(II) in the final step) would precipitate, stopping Philips' reaction after one cycle. Air, pure oxygen, or a number of other reagents can then oxidise the resultant CuCl -chloride mixture back to CuCl 2 , allowing the cycle to continue.
Early mechanistic studies from the 1960s elucidated several key points: [ 10 ] [ 8 ]
Many mechanistic studies on the Wacker process have focused on pathway for formation of the C-O bond, the hydroxypalladation step. Henry inferred that coordinated hydroxide attacks the ethylene ligand, an internal (syn-) pathway. [ 11 ] Later, stereochemical studies by Stille and coworkers [ 12 ] [ 13 ] [ 14 ] support an anti-addition pathway, whereby free hydroxide attacks the ethylene ligand. The conditions for Stille's experiments differ significantly from industrial process conditions. Other studies using normal industrial Wacker conditions (except with high chloride and high copper chloride concentrations) also yielded products that inferred nucleophilic attack was an anti-addition reaction. [ 15 ]
Kinetic studies were conducted on isotopically substituted allyl alcohols at standard industrial conditions (with low-chloride concentrations) to probe the reaction mechanisms. [ 16 ] [ 17 ] Those results showed that nucleophilic attack is a slow process, while the proposed mechanisms explaining the earlier stereochemical studies assumed nucleophilic attack to be a fast process.
Subsequent stereochemical studies indicated that both pathways occur and are dependent on chloride concentrations. [ 18 ] [ 19 ] However, these studies too are disputed since allyl-alcohols may be sensitive to isomerization reactions, and different stereoisomers may be formed from those reactions and not from the standard Wacker process.
In summary, experimental evidence seems to support that syn-addition occurs under low-chloride reaction concentrations (< 1 mol / L , industrial process conditions), while anti-addition occurs under high-chloride (> 3mol/L) reaction concentrations, probably due to chloride ions saturating the catalyst and inhibiting the inner-sphere mechanism. However, the exact pathway and the reason for this switching of pathways is still unknown.
Further complicating the Wacker process mechanism is questions about the role of copper chloride. Most theories assumed copper does not play a role in the olefin oxidation mechanisms. Yet, experiments by Stangl and Jira [ 20 ] found chlorohydrin formation was dependent on copper chloride concentrations. Work by Hosokawa and coworkers [ 21 ] yielded a crystallized product containing copper chloride, indicating it may have a non-innocent role in olefin oxidation. Finally, an ab initio study by Comas-Vives, et al. [ 22 ] involving no copper co-catalyst found anti-addition was the preferred pathway. This pathway was later confirmed by copper-free experiments by Anderson and Sigman. [ 23 ] A different kinetic rate law with no proton dependence was found under copper-free conditions, indicating the possibility that even small amounts of copper co-catalysts may have non-innocent roles on this chemistry. While these works complicate the picture of the Wacker process mechanism, one should probably infer that this and related chemistry can be sensitive to reaction conditions, and multiple different reaction pathways may be in play.
Another key step in the Wacker process is the migration of the hydrogen from oxygen to chloride and formation of the C-O double bond. This step is generally thought to proceed through a so-called β-hydride elimination with a cyclic four-membered transition state :
In silico studies [ 24 ] [ 25 ] [ 26 ] argue that the transition state for this reaction step is unfavorable and an alternative reductive elimination reaction mechanism is in play. The proposed reaction steps are likely assisted by water molecule in solution acting as a catalyst.
Two routes are commercialized for the production of acetaldehyde: one-stage process and two-stage.
Ethene and oxygen are passed co-currently in a reaction tower at about 130 °C and 400 kPa. [ 27 ] The catalyst is an aqueous solution of PdCl 2 and CuCl 2 . The acetaldehyde is purified by extractive distillation followed by fractional distillation . Extractive distillation with water removes the lights ends having lower boiling points than acetaldehyde ( chloromethane , chloroethane , and carbon dioxide ) at the top, while water and higher-boiling byproducts, such as acetic acid , crotonaldehyde or chlorinated acetaldehydes, are withdrawn together with acetaldehyde at the bottom. [ 27 ] Due to the corrosive nature of catalyst, the reactor is lined with acid-proof ceramic material and the tubing is made of titanium .
In two-stage process, reaction and oxidation are carried out separately in tubular reactors. Unlike one-stage process, air can be used instead of oxygen. Ethylene is passed through the reactor along with catalyst at 105–110 °C and 900–1000 kPa. [ 27 ] Catalyst solution containing acetaldehyde is separated by flash distillation . The catalyst is oxidized in the oxidation reactor at 1000 kPa using air as oxidizing medium. Oxidized catalyst solution is separated and sent back to reactor. Oxygen from air is used up completely and the exhaust air is circulated as inert gas. Acetaldehyde – water vapor mixture is preconcentrated to 60–90% acetaldehyde by utilizing the heat of reaction and the discharged water is returned to the flash tower to maintain catalyst concentration. A two-stage distillation of the crude acetaldehyde follows. In the first stage, low-boiling substances, such as chloromethane , chloroethane and carbon dioxide , are separated. In the second stage, water and higher-boiling by-products, such as chlorinated acetaldehydes and acetic acid , are removed and acetaldehyde is obtained in pure form overhead. [ 27 ] Due to corrosive nature of the catalyst, the equipments in contact with it are lined with titanium .
In both one- and two-stage processes the acetaldehyde yield is about 95% [ 27 ] and the production costs are virtually the same. The advantage of using dilute gases in the two-stage method is balanced by higher investment costs. Both methods yield chlorinated hydrocarbons, chlorinated acetaldehydes, and acetic acid as byproducts. Generally, the choice of method is governed by the raw material and energy situations as well as by the availability of oxygen at a reasonable price.
In general, 100 parts of ethene gives:
and other minor side products
The advent of Wacker Process has spurred on many investigations into the utility and applicability of the reactions to more complex terminal olefins. The Tsuji-Wacker oxidation is the palladium(II)-catalyzed transformation of such olefins into carbonyl compounds. Clement and Selwitz [ 28 ] were the first to find that using an aqueous DMF as solvent allowed for the oxidation of 1-dodecene to 2-dodecanone, which addressed the insolubility problem of higher order olefins in water. Fahey [ 29 ] noted the use of 3-methylsulfolane in place of DMF as solvent increased the yield of oxidation of 3,3-Dimethylbut-1-ene. Two years after, Tsuji [ 30 ] applied the Selwitz conditions for selective oxidations of terminal olefins with multiple functional groups, and demonstrated its utility in synthesis of complex substrates. [ 31 ] Further development of the reaction has led to various catalytic systems to address selectivity of the reaction, as well as introduction of intermolecular and intramolecular oxidations with non-water nucleophiles.
The Tsuji-Wacker oxidation oxidizes terminal olefin to the corresponding methyl ketone under the Wacker process condition. Almost identical to that of Wacker Process, the proposed catalytic cycle [ 32 ] (Figure 1) begins with complexation of PdCl 2 and two chloride anions to PdCl 4 , which then undergoes subsequent ligand exchange of two chloride ligand for water and alkene to form Pd(Cl 2 )(H 2 O)(alkene) complex. A water molecule then attacks the olefin regioselectively through an outer sphere mechanism in a Markovnikov fashion, to form the more thermodynamically stable Pd(Cl 2 )(OH)(-CH 2 -CHOH-R) complex. Dissociation of a chloride ligand to the three coordinate palladium complex promotes β-hydride elimination, then subsequent 1,2-hydride migratory insertion generates Pd(Cl 2 )(OH)(-CHOHR-CH 3 ) complex. This undergoes β-hydride elimination to release the ketone, and subsequent reductive elimination produces HCl, water, and palladium(0). Finally palladium(0) is reoxidized to PdCl 2 with two equivalents of Cu(II)Cl 2 , which in turn can be reoxidized by O 2 .
The oxidation of terminal olefins generally provide the Markovnikov ketone product, however in cases where substrate favors the aldehyde (discussed below), different ligands can be used to enforce the Markovnikov regioselectivity. The use of sparteine as a ligand (Figure 2, A) [ 33 ] favors nucleopalladation at the terminal carbon to minimize steric interaction between the palladium complex and substrate. The Quinox-ligated palladium catalyst is used to favor ketone formation when substrate contains a directing group (Figure 2, B). [ 34 ] When such substrate bind to Pd(Quinox)(OOtBu), this complex is coordinately saturated which prevents the binding of the directing group, and results in formation of the Markovnikov product. The efficiency of this ligand is also attributed to its electronic property, where anionic TBHP prefers to bind trans to the oxazoline and olefin coordinate trans to the quinoline. [ 35 ]
The anti-Markovnikov addition selectivity to aldehyde can be achieved through exploiting inherent stereoelectronics of the substrate. [ 36 ] Placement of directing group at homo-allylic (i.e. Figure 3, A) [ 37 ] and allylic position (i.e. Figure 3, B) [ 38 ] to the terminal olefin favors the anti-Markovnikov aldehyde product, which suggests that in the catalytic cycle the directing group chelates to the palladium complex such that water attacks at the anti-Markovnikov carbon to generate the more thermodynamically stable palladacycle. Anti-Markovnikov selectivity is also observed in styrenyl substrates (i.e. Figure 3, C), [ 39 ] presumably via η 4 -palladium-styrene complex after water attacks anti-Markovnikov. More examples of substrate-controlled, anti-Markovnikov Tsuji-Wacker Oxidation of olefins are given in reviews by Namboothiri, [ 40 ] Feringa, [ 36 ] and Muzart. [ 41 ]
Grubbs and co-workers paved way for anti-Markovnikov oxidation of stereoelectronically unbiased terminal olefins, through the use of palladium-nitrite system (Figure 2, D). [ 42 ] In his system, the terminal olefin was oxidized to the aldehyde with high selectivity through a catalyst-control pathway. The mechanism is under investigation, however evidence [ 40 ] suggests it goes through a nitrite radical adds into the terminal carbon to generate the more thermodynamically stable, secondary radical. Grubbs expanded this methodology to more complex, unbiased olefins. [ 43 ] [ 44 ]
The intermolecular oxidations of olefins with alcohols as nucleophile typically generate ketals , where as the palladium-catalyzed oxidations of olefins with carboxylic acids as nucleophile generates vinylic or allylic carboxylates . In case of diols , their reactions with alkenes typically generate ketals, whereas reactions of olefins bearing electron-withdrawing groups tend to form acetals . [ 45 ]
Palladium-catalyzed intermolecular oxidations of dienes with carboxylic acids and alcohols as donors give 1,4-addition products. In the case of cyclohexadiene (Figure 4, A), Backvall found that stereochemical outcome of product was found to depend on concentration of LiCl. [ 46 ] This reaction proceeds by first generating the Pd(OAc)(benzoquinone)(allyl) complex, through anti-nucleopalladation of diene with acetate as nucleophile. The absence of LiCl induces an inner sphere reductive elimination to afford the trans-acetate stereochemistry to give the trans-1,4-adduct. The presence of LiCl displaces acetate with chloride due to its higher binding affinity, which forces an outer sphere acetate attack anti to the palladium, and affords the cis-acetate stereochemistry to give the cis-1,4-adduct. Intramolecular oxidative cyclization: 2-(2-cyclohexenyl)phenol cyclizes to corresponding dihydro-benzofuran (Figure 4, B); [ 47 ] 1-cyclohexadiene-acetic acid in presence of acetic acid cyclizes to corresponding lactone-acetate 1,4 adduct (Figure 4, C), [ 48 ] with cis and trans selectivity controlled by LiCl presence.
The oxidative aminations of olefins are generally conducted with amides or imides ; amines are thought to be protonated by the acidic medium or to bind the metal center too tightly to allow for the catalytic chemistry to occur. [ 45 ] These nitrogen nucleophiles are found to be competent in both intermolecular and intramolecular reactions, some examples are depicted (Figure 5, A, [ 49 ] B [ 50 ] )
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Wad is an old mining term for any black manganese oxide or hydroxide mineral-rich rock in the oxidized zone of various ore deposits. Typically closely associated with various iron oxides. Specific mineral varieties include pyrolusite , lithiophorite , nsutite , takanelite and vernadite . [ 1 ] Wad can be considered to be the manganese equivalent to the iron mineraloid limonite .
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Wadja solves the problem of conversation relevance (social noise) by giving users a way to label social activity , and curate that activity into meaningful conversations . Wadja is based in Cyprus and had its BETA launch in August 2006. [ 1 ] As of December 2009, Wadja had over 5,000,000 registered users. [ 2 ]
Wadja users can create interest labels, capturing an idea, an insightful topic and even a special offer or hot deal.
Wadja.com supports multiple languages and users can translate the messages in other languages via integration with the Google Translate API. [ 3 ] Almost all features of the Wadja website are also available on the mobile platform and are optimized for both the iPhone [ 4 ] and the BlackBerry . iPhone and Windows Mobile applications are available on m.wadja.com.
Wadja can organize real time conversations and social content under customized “label” tags. Wadja's label feature lets individuals follow very specific topics and group discussions and can be applied to a variety of social content including real-time tweets and uploaded media ( YouTube and Flickr ). Labels can also be applied to communication activity including tweets and status updates. More than one label can be added to a conversation. Once a label is created, all the content and feeds within that label are easily searched or accessed by clicking the label name. Real-time, label driven conversations are completely searchable, and distributable across a variety of devices and platforms including email and web apps.
Wadja services include:
Wadja.com enables its members to restrict who has access to their profile and data and choose what information they want to appear on their profile. Members' contact lists restrict who can contact them. Wadja's login supports OpenID . [ 6 ]
Users' logins and API calls have their source IPs logged and Wadja explicitly warns users that their actions are not anonymous.
The website was a recipient of several awards, including the Mashable Top Mobile Social Network : People's Choice Award in 2006 [ 7 ] , the Blogger's Choice award at Mashable's Open Web Awards in the category of Niche Social Networks in 2008 [ 8 ] and the 3rd Prize in the 8th Annual VC Forum, Athens , Greece . [ 9 ]
Wadja's API for sending text messages has been criticized for using HTTP GET instead of POST. [ 10 ]
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The "Wadley-drift-canceling-loop" , also known as a "Wadley loop" , is a system of two oscillators , a frequency synthesizer , and two frequency mixers in the radio-frequency signal path. The system was designed by Dr. Trevor Wadley in the 1940s in South Africa . The circuit was first used for a stable wavemeter . (A wavemeter is used for measuring the wavelength and therefore also the frequency of a signal).
There is no regulation loop in a "Wadley-loop" , which is why the term is in quotation marks. However, the circuit configuration is not known by more accurate names. [ 2 ]
The "Wadley loop" was used in radio receivers from the 1950s to approximately 1980. The "Wadley loop" was mostly used in more expensive stationary radio receivers, but the "Wadley loop" was also used in a portable radio receiver (Barlow-Wadley XCR-30 Mark II). [ 3 ] [ 4 ]
In a traditional superheterodyne radio receiver , most oscillator drift and instability occur in the first frequency converter stage because it is tunable and operating at a high frequency.
Unlike other drift-reducing techniques (such as crystal control or frequency synthesis ), the Wadley Loop does not attempt to stabilize the oscillator. Instead, it cancels the drift mathematically.
The Wadley loop works by:
Since the high-IF of part 1 drifts in the same direction and the same amount as the "synthetic oscillator" of part 3, when they are mixed in part 4, the drift terms cancel out and the result is a crystal-stable signal at a second intermediate frequency.
However, the drift makes it impossible to use high-IF selectivity to reject undesired signals. Instead, the high IF is designed with a band-pass characteristic. Also, since the first oscillator is cancelled out, it cannot be used to tune a particular signal. Instead, it selects an entire band of signals - which one depends on which harmonic was chosen in part 3 above. The size of the band is equal to the spacing of the crystal harmonics. A conventionally tuned "back end" selects the desired signal from the band of signals presented at the second IF.
An example would be picking up signals from 0 to 30 MHz. This is divided into 30 1 MHz bands, which are then translated to a band at 44-45 MHz. To convert 0-1 MHz, the first oscillator must be 45 MHz; to convert 1-2 MHz it must be 46 MHz; and so on. Meanwhile, the first oscillator is also mixed with harmonics from a 1 MHz crystal and the results pass through a 42 MHz filter. Only one harmonic gets through. When the first oscillator is 45 MHz, it is the third harmonic, because 45 - 3 = 42. At 46 MHz, it is the fourth harmonic, and so on. The oscillator does not have to be exactly 45, 46, and so on, only close enough to get through the 42 MHz band-pass filter . Let's say it is 45.1 . Then we get 42.1 from the filter, and 45.1 - 42.1 is still 3. When the high IF is mixed with the 42 MHz, the result is a band of signals from 3 MHz to 2 MHz, from which the desired signal is selected. This can potentially be accomplished with a conventional superheterodyne back-end converting 3-2 MHz to 455 kHz and finally demodulating the signal back to audio. The overall receiver drift consists of the crystal's drift plus the 3 MHz back-end. When we're listening to a 30 MHz signal, this receiver is about ten times as stable as one using a high-frequency tunable VFO .
To a new user, the feel of the first oscillator tuning control is counterintuitive. Although the knob moves in a continuous, analog fashion, its effect on the receiver operation is discrete , that is, the tuning advances in 1 MHz jumps.
An example is Yaesu 's FRG-7 communications receiver, [ 5 ] which uses the system to remove local oscillator drift. The Racal RA17 and Realistic DX-302 [ 6 ] also used the Wadley Loop in their design.
An optical implementation of a Wadley Loop has recently been proposed. This allows a compact relatively unstable laser to be used as a local oscillator. The system's stability being obtained from a master 'comb source' (usually a pulsed laser, such as a mode-locked laser), possibly common to many receivers within an exchange. [ 7 ]
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Wafer bond characterization refers to the process of evaluating the quality and strength of a bond between two semiconductor wafers . The wafer bond characterization is based on different methods and tests. Considered a high importance of the wafer are the successful bonded wafers without flaws. Those flaws can be caused by void formation in the interface due to unevenness or impurities . The bond connection is characterized for wafer bond development or quality assessment of fabricated wafers and sensors.
Wafer bonds are commonly characterized by three important encapsulation parameters: bond strength, hermeticity of encapsulation and bonding induced stress. [ 1 ]
The bond strength can be evaluated using double cantilever beam or chevron respectively micro-chevron tests. Other pull tests as well as burst, direct shear tests or bend tests enable the determination of the bond strength. [ 2 ] The packaging hermeticity is characterized using membrane, He-leak, resonator/pressure tests. [ 1 ]
Three additional possibilities to evaluate the bond connection are optical, electron and Acoustical measurements and instrumentation . At first, optical measurement techniques are using an optical microscope , IR transmission microscopy and visual inspection. Secondly, the electron measurement is commonly applied using an electron microscope , e.g. scanning electron microscopy (SEM), high voltage transmittance electron microscopy (HVTEM) and high resolution scanning electron microscopy (HRSEM). And finally, typical acoustic measurement approaches are scanning acoustic microscope (SAM), scanning laser acoustic microscope (SLAM) and C-mode scanning acoustic microscope (C-SAM).
The specimen preparation is sophisticated and the mechanical, electronic properties are important for the bonding technology characterization and comparison. [ 3 ]
Infrared (IR) void imaging is possible if the analyzed materials are IR transparent, i.e. silicon . This method gives a rapid qualitative examination [ 4 ] and is very suitable due to its sensitivity to the surface and to the buried interface. It obtains information on chemical nature of surface and interface.
Infrared transmitted light is based on the fact that silicon is translucent at wavelength ≥ 1.2 μm. The equipment consists of an infrared lamp as light source and an infrared video system (compare to figure "Schematic infrared transmission microscopy setup").
The IR imaging system enables the analysis of the bond wave and additionally micro mechanical structures as well as deformities in the silicon. This procedure allows also to analyze multiple layer bonds. [ 3 ] The image contrast depends on the distance between the wafers . Usually if using monochromatic color IR the center of the wafers is display brighter based on the vicinity. Particles in the bond interface generate highly visible spots with differing contrast because of the interference (wave propagation) fringes. [ 5 ] Unbonded areas can be shown if the void opening (height) is ≥ 1 nm. [ 4 ]
The Fourier transform infrared (FT-IR) spectroscopy is a non-destructive hermeticity characterization method. The radiation absorption enables the analysis with a specific wavelength for gases. [ 6 ]
Ultrasonic microscopy uses high frequency sound waves to image bonded interfaces. Deionized water is used as the acoustic interconnect medium between the electromagnetic acoustic transducer and the wafer. [ 4 ] [ 7 ]
This method works with an ultrasonic transducer scanning the wafer bond. The reflected sound signal is used for the image creation. The lateral resolutions depends on the ultrasonic frequency, the acoustic beam diameter and the signal-to-noise ratio (contrast).
Unbonded areas, i.e. impurities or voids, do not reflect the ultrasonic beam like bonded areas, therefore a quality assessment of the bond is possible. [ 3 ]
Double cantilever beam test , also referred to as crack opening or razor blade method, is a method to define the strength of the bond. This is achieved by determining the energy of the bonded surfaces. A blade of a specific thickness is inserted between the bonded wafer pair. This leads to a split-up of the bond connection. [ 3 ] The crack length L {\displaystyle L} equals the distance between the blade tip and the crack tip and is determined using IR transmitted light. The IR light is able to illuminate the crack, when using materials transparent to IR or visible light. [ 8 ] If the fracture surface toughness is very high, it is very difficult to insert the blade and the wafers are endangered to break at the slide in of the blade. [ 3 ]
The DCB test characterizes the time dependent strength by mechanical fracture evaluation and is therefore well suited for lifetime predictions. [ 9 ] A disadvantage of this method is, that between the entering of the blade and the time to take the IR image, the results can be influenced. In addition, the measurement inaccuracy increases with a high surface fracture toughness resulting in a smaller crack length or broken wafers at the blade insertion as well as the influence of the fourth power of the measured crack length. The measured crack length determines surface energy γ {\displaystyle \gamma } in relation to a rectangular, beam-shaped specimen.
γ = 3 t b 2 E 1 t w 1 3 E 2 t w 2 3 16 L 4 ( E 1 t w 1 3 + E 2 t w 2 3 ) {\displaystyle \gamma ={\frac {3t_{b}^{2}E_{1}t_{w1}^{3}E_{2}t_{w2}^{3}}{16L^{4}(E_{1}t_{w1}^{3}+E_{2}t_{w2}^{3})}}}
Thereby is E {\displaystyle E} the Young's modulus , t w {\displaystyle t_{w}} the wafer thickness, t b {\displaystyle t_{b}} the blade thickness and L {\displaystyle L} the measured crack length. [ 10 ] In literature different DCB models are mentioned, i.e. measurement approaches by Maszara, Gillis and Gilman, Srawley and Gross, Kanninen or Williams. The most commonly used approaches are by Maszara or Gillis and Gilman. [ 8 ]
The Maszara model neglects shear stress as well as stress in the un-cleaved part for the obtained crack lengths. The compliance of a symmetric DCB specimen is described as follows:
C = 8 L 3 E ∗ w t 3 {\displaystyle C={\frac {8L^{3}}{E^{*}wt^{3}}}}
The compliance is determined out of the crack length L {\displaystyle L} , the width w {\displaystyle w} and the beam thickness t {\displaystyle t} . E ∗ {\displaystyle E^{*}} defines the Young's modulus. The surface fracture energy G I C {\displaystyle G_{IC}} is:
G I C = 3 E ∗ δ 2 t 3 16 L 4 {\displaystyle G_{IC}={\frac {3E^{*}\delta ^{2}t^{3}}{16L^{4}}}}
with δ {\displaystyle \delta } as load-point displacement.
The Gillis and Gilman approach considers bend and shear forces in the beam. The compliance equation is:
C = 8 L 3 E ∗ w t 3 ( 1 + 3 c ( t L ) 2 − n + α s E ∗ 4 μ ( t L ) 2 ) {\displaystyle C={\frac {8L^{3}}{E^{*}wt^{3}}}\left(1+3c\left({\frac {t}{L}}\right)^{2-n}+{\frac {\alpha _{s}E^{*}}{4\mu }}\left({\frac {t}{L}}\right)^{2}\right)}
The first term 8 L 3 E ∗ w t 3 {\displaystyle {\frac {8L^{3}}{E^{*}wt^{3}}}} describes the strain energy in the cantilever due to bending. The second term is the contribution from elastic deformations in the un-cleaved specimen part and the third term considers the shear deformation. Therefore, n {\displaystyle n} and c {\displaystyle c} are dependent on the conditions of the fixed end of the cantilever. The shear coefficient α S {\displaystyle \alpha _{S}} is dependent on the cross-section geometry of the beam.
The chevron test is used to determine the fracture toughness K I C {\displaystyle K_{IC}} of brittle construction materials. The fracture toughness is a basic material parameter for analyzing the bond strength.
The chevron test uses a special notch geometry for the specimen that is loaded with an increasing tensile force. The chevron notch geometry is commonly in shape of a triangle with different bond patterns. At a specific tensile load the crack starts at the chevron tip and grows with continuous applied load until a critical length is reached. [ 11 ] The crack growth becomes unstable and accelerates resulting in a fracture of the specimen. [ 8 ] The critical length depends only on the specimen geometry and the loading condition. The fracture toughness commonly K I C {\displaystyle K_{IC}} is determined by measuring the recorded fracture load of the test. This improves the test quality and accuracy and decreases measurement scatter. [ 11 ]
Two approaches, based on energy release rate G I {\displaystyle G_{I}} or stress intensity factor K I {\displaystyle K_{I}} , can be used for explaining the chevron test method. [ 8 ] The fracture occurs when K I {\displaystyle K_{I}} or G I {\displaystyle G_{I}} reach a critical value, describing the fracture toughness K I C {\displaystyle K_{IC}} or G I C {\displaystyle G_{IC}} .
The advantage using chevron notch specimen is due to the formation of a specified crack of well-defined length. [ 12 ] The disadvantage of the approach is that the gluing required for loading is time consuming and may induce data scatter due to misalignment. [ 8 ]
The micro chevron (MC) test is a modification of the chevron test using a specimen of defined and reproducible size and shape. The test allows the determination of the critical energy release rate G I C {\displaystyle G_{IC}} and the critical fracture toughness K I C {\displaystyle K_{IC}} . [ 13 ] It is commonly used to characterize the wafer bond strength as well as the reliability. The reliability characterization is determined based on the fracture mechanical evaluation of critical failure. [ 9 ] The evaluation is determined by analyzing the fracture toughness as well as the resistance against crack propagation. [ 10 ]
The fracture toughness allows comparison of the strength properties independent on the particular specimen geometry. [ 12 ] In addition, bond strength of the bonded interface can be determined. [ 11 ] The chevron specimen is designed out of bonded stripes in shape of a triangle. The space of the tip of the chevron structure triangle is used as lever arm for the applied force. This reduces the force required to initiate the crack. The dimensions of the micro chevron structures are in the range of several millimeters and usually an angle of 70 ° chevron notch. [ 13 ] This chevron pattern is fabricated using wet or reactive ion etching. [ 12 ]
The MC test is applied with special specimen stamp glued onto the non-bonded edge of the processed structures. The specimen is loaded in a tensile tester and the load is applied perpendicular to the bonded area. When the load equals the maximum bearable conditions, a crack is initiated at the tip of the chevron notch.´ [ 13 ]
By increasing the mechanical stress by means of a higher loading, two opposing effects can be observed. First, the resistance against the crack expansion increases based on the increasing bonding of the triangular shaped first half of the chevron pattern. Second, the lever arm is getting longer with increased crack length a {\displaystyle a} . From the critical crack length a c {\displaystyle a_{c}} an instable crack expansion and the destruction of the specimen is initiated. [ 13 ] The critical crack length a c {\displaystyle a_{c}} corresponds to the maximum force F m a x {\displaystyle F_{max}} in a force-length-diagram and a minimum of the geometric function Y M I N {\displaystyle Y_{MIN}} . [ 14 ]
The fracture toughness K I C {\displaystyle K_{IC}} can be calculated with maximum force, width w {\displaystyle w} and thickness t {\displaystyle t} :
K I C = F M A X t ⋅ w ⋅ Y M I N {\displaystyle K_{IC}={\frac {F_{MAX}}{t\cdot {\sqrt {w}}}}\cdot Y_{MIN}}
The maximum force F M A X {\displaystyle F_{MAX}} is determined during the test and the minimal stress intensity coefficient Y M I N {\displaystyle Y_{MIN}} is determined by FE Simulation. [ 15 ] In addition, the energy release rate G I C {\displaystyle G_{IC}} can be determined with E {\displaystyle E} as modulus of elasticity and v {\displaystyle v} as Poisson's ratio in the following way.´ [ 13 ]
G I C = K I C 2 E ⋅ ( 1 − v 2 ) {\displaystyle G_{IC}={\frac {K_{IC}^{2}}{E}}\cdot (1-v^{2})}
The advantage of this test is the high accuracy compared to other tensile or bend tests. It is an effective, reliable and precise approach for the development of wafer bonds as well as for the quality control of the micro mechanical device production. [ 12 ]
Bond strength measurement or bond testing is performed in two basic methods: pull testing and shear testing. Both can be done destructively, which is more common (also on wafer level), or non destructively. They are used to determine the integrity of materials and manufacturing procedures, and to evaluate the overall performance of the bonding frame, as well as to compare various bonding technologies with each other. The success or failure of the bond is based on measuring the applied force, the failure type due to the applied force and the visual appearance of the residual medium used.
A development in bond strength testing of adhesively bonded composite structures is laser bond inspection (LBI). LBI provides a relative strength quotient derived from the fluence level of the laser energy delivered onto the material for the strength test compared to the strength of bonds previously mechanically tested at the same laser fluence. LBI provides nondestructive testing of bonds that were adequately prepared and meet engineering intent. [ 16 ]
Measuring bond strength by pull testing is often the best way to get the failure mode in which you are interested. Additionally, and unlike a shear test, as the bond separates, the fracture surfaces are pulled away from each other, cleanly enabling accurate failure mode analysis. To pull a bond requires the substrate and interconnect to be gripped; because of size, shape and material properties, this can be difficult, particularly for the interconnection. In these cases, a set of accurately formed and aligned tweezer tips with precision control of their opening and closing is likely to make the difference between success and failure. [ 17 ]
The most common type of pull tests is a Wire Pull test. Wire Pull testing applies an upward force under the wire, effectively pulling it away from the substrate or die.
Shear testing is the alternative method to determine the strength a bond can withstand. Various variants of shear testing exist. Like with pull testing, the objective is to recreate the failure mode of interest in the test. If that is not possible, the operator should focus on putting the highest possible load on the bond. [ 18 ]
White light interferometry is commonly used for detecting deformations of the wafer surface based on optical measurements. Low-coherence light from a white light source passes through the optical top wafer, e.g. glass wafer, to the bond interface. Usually there are three different white light interferometers:
For the white light interferometer the position of zero order interference fringe and the spacing of the interference fringes needs to be independent of wavelength. [ 19 ] White light interferometry is utilized to detect deformations of the wafer. Low coherence light from a white light source passes through the top wafer to the sensor. The white light is generated by a halogen lamp and modulated. The spectrum of the reflected light of the sensor cavity is detected by a spectrometer. The captured spectrum is used to obtain the cavity length of the sensor. The cavity length d corresponds to the applied pressure and is determined by the spectrum of the reflection of the light of the sensor. This pressure value is subsequently displayed on a screen. The cavity length d {\displaystyle d} is determined using
d = λ 1 λ 2 2 n ( λ 2 − λ 1 ) {\displaystyle d={\frac {\lambda _{1}\lambda _{2}}{2n(\lambda _{2}-\lambda _{1})}}}
with n {\displaystyle n} as refractive index of the sensor cavity material, λ 1 {\displaystyle \lambda _{1}} and λ 2 {\displaystyle \lambda _{2}} as adjacent peaks in the reflection spectrum.
The advantage of using white light interferometry as characterization method is the influence reduction of the bending loss. [ 20 ]
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https://en.wikipedia.org/wiki/Wafer_bond_characterization
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Wafer bonding is a packaging technology on wafer -level for the fabrication of microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS), microelectronics and optoelectronics , ensuring a mechanically stable and hermetically sealed encapsulation. The wafers' diameter range from 100 mm to 200 mm (4 inch to 8 inch) for MEMS/NEMS and up to 300 mm (12 inch) for the production of microelectronic devices. Smaller wafers were used in the early days of the microelectronics industry, with wafers being just 1 inch in diameter in the 1950s.
In microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS), the package protects the sensitive internal structures from environmental influences such as temperature, moisture, high pressure and oxidizing species. The long-term stability and reliability of the functional elements depend on the encapsulation process, as does the overall device cost. [ 1 ] The package has to fulfill the following requirements: [ 2 ]
The commonly used and developed bonding methods are as follows:
The bonding of wafers requires specific environmental conditions which can generally be defined as follows: [ 3 ]
The actual bond is an interaction of all those conditions and requirements. Hence, the applied technology needs to be chosen in respect to the present substrate and defined specification like max. bearable temperature, mechanical pressure or desired gaseous atmosphere.
The bonded wafers are characterized in order to evaluate a technology's yield, bonding strength and level of hermeticity either for fabricated devices or for the purpose of process development. Therefore, several different approaches for the bond characterization have emerged. On the one hand non-destructive optical methods to find cracks or interfacial voids are used beside destructive techniques for the bond strength evaluation, like tensile or shear testing. On the other hand, the unique properties of carefully chosen gases or the pressure depending vibration behavior of micro resonators are exploited for hermeticity testing.
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https://en.wikipedia.org/wiki/Wafer_bonding
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Wafer fabrication equipment is equipment that is used in the process of semiconductor fabrication to process raw semiconductor wafers into finished chips, such as integrated circuits . [ 1 ]
Wafer fabrication equipment is meant to be installed in cleanrooms .
Referred to respectively as the wafer fab equipment [ 2 ] or wafer front end [ 3 ] (equipment) market, both using the acronym WFE, the market is that of the manufacturers of the machines which in turn manufacture semiconductors. The apexresearch link in 2020 identified Applied Materials , ASML , KLA-Tencor , Lam Research , TEL and Dainippon Screen Manufacturing as market participants [ 2 ] while the 2019 electronicsweekly.com report, citing The Information Network's president Robert Castellano, focused on the respective market shares commanded by the two leaders, Applied Materials and ASML. [ 3 ]
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https://en.wikipedia.org/wiki/Wafer_fabrication_equipment
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A waffle slab or two-way joist slab is a concrete slab made of reinforced concrete with concrete ribs running in two directions on its underside. [ 1 ] The name waffle comes from the grid pattern created by the reinforcing ribs. Waffle slabs are preferred for spans greater than 40 feet (12 m), because, for a given mass of concrete, they are much stronger than flat slabs, flat slabs with drop panels, two-way slabs, one-way slabs , and one-way joist slabs. [ 2 ]
A waffle slab is flat on top, while joists create a grid like surface on the bottom. The grid is formed by the removal of molds after the concrete sets. This structure was designed to be more solid when used on longer spans and with heavier loads. [ 3 ] This type of structure, because of its rigidity, is recommended for buildings that require minimal vibration, like laboratories and manufacturing facilities. [ 3 ] It is also used in buildings that require big open spaces, like theatres or train stations . [ 2 ] Waffle slabs are composed by intricate formwork , and may be more expensive than other types of slabs, but depending on the project and the quantity of concrete needed it may be cheaper to build.
There are two types of waffle slab system:
A waffle slab can be made in different ways but generic forms are needed to give the waffle shape to the slab. The formwork is made up of many elements: waffle pods , horizontal supports , vertical supports , cube junctions , hole plates , clits [ clarification needed ] and steel bars . [ 4 ] First the supports are built, then the pods are arranged in place, and finally the concrete is poured.
This process may occur in three different approaches, however the basic method is the same in each:
Different guides have been made for architects and engineers to determine various parameters of waffle slabs, primarily the overall thickness and rib dimensions. The following are rules of thumb, which are explained further in the accompanying diagrams:
The waffle slab floor system has several advantages:
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https://en.wikipedia.org/wiki/Waffle_slab
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Wagner's gene network model is a computational model of artificial gene networks, which explicitly modeled the developmental and evolutionary process of genetic regulatory networks . A population with multiple organisms can be created and evolved from generation to generation. It was first developed by Andreas Wagner in 1996 [ 1 ] and has been investigated by other groups to study the evolution of gene networks , gene expression , robustness , plasticity and epistasis . [ 2 ] [ 3 ] [ 4 ]
The model and its variants have a number of simplifying assumptions. Three of them are listing below.
The model represents individuals as networks of interacting transcriptional regulators. Each individual expresses n {\displaystyle n} genes encoding transcription factors. The product of each gene can regulate the expression level of itself and/or the other genes through cis-regulatory elements . The interactions among genes constitute a gene network that is represented by a N {\displaystyle N} × N {\displaystyle N} regulatory matrix ( R ) {\displaystyle (R)} in the model. The elements in matrix R represent the interaction strength. Positive values within the matrix represent the activation of the target gene, while negative ones represent repression. Matrix elements with value 0 indicate the absence of interactions between two genes.
The phenotype of each individual is modeled as the gene expression pattern at time t {\displaystyle t} . It is represented by a state vector S ( t ) {\displaystyle S(t)} in this model.
S ( t ) := ( s 1 ( t ) , . . . , s N ( t ) ) {\displaystyle S(t)\ :=\ (s_{1}(t),\ ...,\ s_{N}(t))}
whose element s i ( t ) {\displaystyle s_{i}(t)} denotes the expression state of gene i at time t . In the original Wagner model,
s i ( t ) {\displaystyle s_{i}(t)} ∈ { − 1 , 1 } {\displaystyle \{-1,1\}}
where 1 represents the gene is expressed while -1 implies the gene is not expressed. The expression pattern can only be ON or OFF. The continuous expression pattern between -1 (or 0) and 1 is also implemented in some other variants. [ 2 ] [ 3 ] [ 4 ]
The development process is modeled as the development of gene expression states. The gene expression pattern S ( 0 ) {\displaystyle S(0)} at time t = 0 {\displaystyle t=0} is defined as the initial expression state. The interactions among genes change the expression states during the development process. This process is modeled by the following differential equations
S l ( t + τ ) = σ [ ∑ j = 1 N w i j S j ( t ) ] = σ [ h i ] ( t ) , {\displaystyle S_{l}(t+\tau )=\sigma [\sum _{j=1}^{N}w_{ij}S_{j}(t)]=\sigma [h_{i}](t),}
where S l ( t + {\displaystyle S_{l}(t+} τ) represents the expression state of G l {\displaystyle G_{l}} at time t + τ {\displaystyle t+\tau } . It is determined by a filter function σ ( x ) {\displaystyle (x)} . h i ( t ) {\displaystyle h_{i}(t)} represents the weighted sum of regulatory effects ( w i j {\displaystyle w_{ij}} ) of all genes on gene G i {\displaystyle G_{i}} at time t {\displaystyle t} . In the original Wagner model, the filter function is a step function
σ ( x ) = { − 1 , ( x < 0 ) 1 , ( x > 0 ) 0 , ( x = 0 ) . {\displaystyle \sigma (x)={\begin{cases}-1,&(x<0)\\1,&(x>0)\\0,&(x=0).\end{cases}}}
In other variants, the filter function is implemented as a sigmoidal function
σ ( x ) = 2 1 + e − a x − 1 {\displaystyle \sigma (x)={\frac {2}{1+e^{-ax}}}-1}
In this way, the expression states will acquire a continuous distribution. The gene expression will reach the final state if it reaches a stable pattern.
Evolutionary simulations are performed by reproduction-mutation-selection life cycle. Populations are fixed at size N {\displaystyle N} and they will not go extinct. Non-overlapping generations are employed. In a typical evolutionary simulation, a single random viable individual that can produce a stable gene expression pattern is chosen as the founder. Cloned individuals are generated to create a population of N {\displaystyle N} identical individuals. According to the asexual or sexual reproductive mode, offspring are produced by randomly choosing (with replacement) parent individual(s) from current generation. Mutations can be acquired with probability μ and survive with probability equal to their fitness. This process is repeated until N individuals are produced that go on to found the following generation.
Fitness in this model is the probability that an individual survives to reproduce. In the simplest implementation of the model, developmentally stable genotypes survive (i.e. their fitness is 1 {\displaystyle 1} ) and developmentally unstable ones do not (i.e. their fitness is 0 {\displaystyle 0} ).
Mutations are modeled as the changes in gene regulation , i.e., the changes of the elements in the regulatory matrix R {\displaystyle R} .
Both sexual and asexual reproductions are implemented. Asexual reproduction is implemented as producing the offspring's genome (the gene network) by directly copying the parent's genome. Sexual reproduction is implemented as the recombination of the two parents' genomes.
An organism is considered viable if it reaches a stable gene expression pattern. An organism with oscillated expression pattern is discarded and cannot enter the next generation.
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https://en.wikipedia.org/wiki/Wagner's_gene_network_model
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The Wagner-Jauregg reaction is a classic organic reaction in organic chemistry , named after Theodor Wagner-Jauregg [ de ] (son of Julius Wagner-Jauregg ), describing the double Diels–Alder reaction of 2 equivalents of maleic anhydride with a 1,1-diarylethylene. After aromatization of the bis-adduct, the ultimate reaction product is a naphthalene compound with one phenyl substituent. [ 1 ] [ 2 ]
The reaction is unusual in that the anhydride reacts with the aromatic ring. The presence of the additional alpha-phenyl group on the phenylethene (the styryl group) activates the styryl for a Diels–Alder reaction even at the expense of its aromaticity. In contrast, unactivated styrene reacts instead at the alkene alone via a linear polymerization reaction. Styrene maleic anhydride copolymer is formed, retaining the aromaticity of the styrene.
The Diels–Alder product can be re-aromatized using elemental sulfur at high temperature, followed by a second rearomatization by decarboxylation with barium hydroxide and copper : [ 3 ]
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https://en.wikipedia.org/wiki/Wagner-Jauregg_reaction
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In computer science , the Wagner–Fischer algorithm is a dynamic programming algorithm that computes the edit distance between two strings of characters.
The Wagner–Fischer algorithm has a history of multiple invention . Navarro lists the following inventors of it, with date of publication, and acknowledges that the list is incomplete: [ 1 ] : 43
The Wagner–Fischer algorithm computes edit distance based on the observation that if we reserve a matrix to hold the edit distances between all prefixes of the first string and all prefixes of the second, then we can compute the values in the matrix by flood filling the matrix, and thus find the distance between the two full strings as the last value computed.
A straightforward implementation, as pseudocode for a function Distance that takes two strings, s of length m , and t of length n , and returns the Levenshtein distance between them, looks as follows. The input strings are one-indexed, while the matrix d is zero-indexed, and [i..k] is a closed range.
Two examples of the resulting matrix (hovering over an underlined number reveals the operation performed to get that number):
The invariant maintained throughout the algorithm is that we can transform the initial segment s[1..i] into t[1..j] using a minimum of d[i,j] operations. At the end, the bottom-right element of the array contains the answer.
As mentioned earlier, the invariant is that we can transform the initial segment s[1..i] into t[1..j] using a minimum of d[i,j] operations. This invariant holds since:
This proof fails to validate that the number placed in d[i,j] is in fact minimal; this is more difficult to show, and involves an argument by contradiction in which we assume d[i,j] is smaller than the minimum of the three, and use this to show one of the three is not minimal.
Possible modifications to this algorithm include:
By initializing the first row of the matrix with zeros, we obtain a variant of the Wagner–Fischer algorithm that can be used for fuzzy string search of a string in a text. [ 1 ] This modification gives the end-position of matching substrings of the text. To determine the start-position of the matching substrings, the number of insertions and deletions can be stored separately and used to compute the start-position from the end-position. [ 4 ]
The resulting algorithm is by no means efficient, but was at the time of its publication (1980) one of the first algorithms that performed approximate search. [ 1 ]
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https://en.wikipedia.org/wiki/Wagner–Fischer_algorithm
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A Wagner–Meerwein rearrangement is a class of carbocation 1,2-rearrangement reactions in which a hydrogen , alkyl or aryl group migrates from one carbon to a neighboring carbon. [ 1 ] [ 2 ] They can be described as cationic [1,2]- sigmatropic rearrangements, proceeding suprafacially and with stereochemical retention. As such, a Wagner–Meerwein shift is a thermally allowed pericyclic process with the Woodward-Hoffmann symbol [ ω 0 s + σ 2 s ]. They are usually facile, and in many cases, they can take place at temperatures as low as –120 °C. The reaction is named after the Russian chemist Yegor Yegorovich Vagner ; he had German origin and published in German journals as Georg Wagner; and Hans Meerwein .
Several reviews have been published. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]
The rearrangement was first discovered in bicyclic terpenes for example the conversion of isoborneol to camphene : [ 8 ]
The story of the rearrangement reveals that many scientists were puzzled with this and related reactions and its close relationship to the discovery of carbocations as intermediates. [ 9 ]
In a simple demonstration reaction of 1,4-dimethoxybenzene with either 2-methyl-2-butanol or 3-methyl-2-butanol in sulfuric acid and acetic acid yields the same disubstituted product, [ 10 ] the latter via a hydride shift of the cationic intermediate:
Currently, there are works relating to the use of skeletal rearrangement in the synthesis of bridged azaheterocycles . These data are summarized in [ 11 ]
Plausible mechanisms of the Wagner–Meerwein rearrangement of diepoxyisoindoles :
The related Nametkin rearrangement , named after Sergey Namyotkin , involves the rearrangement of methyl groups in certain terpenes. In some cases the reaction type is also called a retropinacol rearrangement (see pinacol rearrangement ).
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https://en.wikipedia.org/wiki/Wagner–Meerwein_rearrangement
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A wah-wah pedal , or simply wah pedal , is a type of effects pedal designed for electric guitar that alters the timbre of the input signal to create a distinctive sound, mimicking the human voice saying the onomatopoeic name "wah-wah". The pedal sweeps a band-pass filter up and down in frequency to create a spectral glide . The wah-wah effect originated in the 1920s, with trumpet or trombone players finding they could produce an expressive crying tone by moving a mute in, and out of the instrument's bell. This was later simulated with electronic circuitry for the electric guitar when the wah-wah pedal was invented. It is controlled by movement of the player's foot on a rocking pedal connected to a potentiometer . Wah-wah effects may be used without moving the treadle as a fixed filter to alter an instrument’s timbre (known as a "cocked-wah" [ 1 ] ), or to create a "wacka-wacka" funk -styled rhythm for rhythm guitar playing. [ 2 ]
An auto-wah pedal uses an envelope follower to control the filter instead of a potentiometer.
The first wah pedal was created by Bradley J. Plunkett at Warwick Electronics Inc./ Thomas Organ Company in November 1966. This pedal is the original prototype made from a transistorized MRB (mid-range boost) potentiometer bread-boarded circuit and the housing of a Vox Continental Organ volume pedal . The concept, however, was not new. Country guitar virtuoso Chet Atkins had used a similar, self-designed device on his late 1950s recordings of "Hot Toddy" and "Slinkey". Jazz guitarist Peter Van Wood had a modified Hammond organ expression
pedal; he recorded in 1955 a version of George Gershwin 's " Summertime " with a "crying" tone, and other recordings including humorous "novelty" effects. A DeArmond Tone and Volume pedal was used in the early 1960s by Big Jim Sullivan , notably in some Krew Cats instrumental tracks, and in Dave Berry 's song " The Crying Game ".
The creation of the modern wah pedal was an accident which stemmed from the redesign of the Vox Super Beatle guitar amplifier in 1966. Warwick Electronics Inc. also owned Thomas Organ Company and had earlier entered into an agreement with Jennings Musical Instruments (JMI) of England for Thomas to distribute the Vox name and products in the United States. In addition to distributing the British-made Vox amplifiers, the Thomas Organ Company also designed and manufactured much of the Vox equipment sold in the US. The more highly regarded British Vox amplifiers were designed by Dick Denney and made by JMI, the parent company of Vox. Warwick assigned Thomas Organ Company to create a new product line of solid state Vox amplifiers called Vox Amplifonic Orchestra, which included the Super Beatle amplifier, named to capitalize on the Vox brand name's popularity in association with the Beatles , who used the JMI English Vox amplifiers such as the famous Vox AC30 . The US-made Vox product line development was headed by musician and bandleader Bill Page . While creating the Vox Amplifonic Orchestra, the Thomas Organ Company decided to create an American-made equivalent of the British Vox amplifier but with transistorized (solid state) circuits, rather than vacuum tubes , which would be less expensive to manufacture. During the re-design of the USA Vox amplifier, Stan Cuttler, head engineer of Thomas Organ Company, assigned Brad Plunkett, a junior electronics engineer, to replace the expensive Jennings 3-position mid-range boost (MRB) circuit switch with a transistorized solid state MRB circuit.
Plunkett had lifted and bread-boarded a transistorized tone-circuit from the Thomas Organ (an electric solid state transistorized organ) to duplicate the Jennings 3-position circuit. After adjusting and testing the amplifier with an electronic oscillator and oscilloscope , Plunkett connected the output to the speaker and tested the circuit audibly. At that point, several engineers and technical consultants, including Bill Page and Del Casher , noticed the sound effect caused by the circuit. Page insisted on testing this bread-boarded circuit while he played his saxophone through an amplifier. John Glennon, an assistant junior electronics engineer with the Thomas Organ Company, was summoned to bring a volume control pedal which was used in the Vox Continental Organ so that the transistorized MRB potentiometer bread-boarded circuit could be installed in the pedal's housing. After the installation, Page began playing his saxophone through the pedal and asked Joe Banaron, CEO of Warwick Electronics Inc./Thomas Organ Company, to listen to the effect. At this point, the first electric guitar was plugged into the prototype wah pedal by guitarist Del Casher who suggested to Joe Banaron that this was a guitar effects pedal rather than a wind instrument effects pedal. Banaron, being a fan of the big band style of music, was interested in marketing the wah pedal for wind instruments as suggested by Page rather than for the electric guitar as suggested by Casher. After a remark by Casher to Banaron regarding the Harmon mute style of trumpet playing in the famous recording of " Sugar Blues " from the 1930s, Banaron decided to market the wah-wah pedal using Clyde McCoy 's name for endorsement.
After the invention of the wah pedal, the prototype was modified by Casher and Plunkett to better accommodate the harmonic qualities of the electric guitar. However, since Vox had no intention of marketing the wah pedal for electric guitar players, the prototype wah-wah pedal was given to Del Casher for performances at Vox press conferences and film scores for Universal Pictures . The un-modified version of the Vox wah pedal was released to the public in February 1967 with an image of Clyde McCoy on the bottom of the pedal.
Warwick Electronics Inc. assigned Lester L. Kushner, an engineer with the Thomas Organ Company, and Brad Plunkett to write and submit the documentation for the wah-wah pedal patent. The patent application was submitted on 24 February 1967, which included technical diagrams of the pedal being connected to a four-stringed "guitar" (as noted from the "Description of the Preferred Embodiment"). Warwick Electronics Inc. was granted U.S. patent 3,530,224 ("foot-controlled continuously variable preference circuit for musical instruments") on 22 September 1970.
Early versions of the Clyde McCoy featured an image of McCoy on the bottom panel, which soon gave way to only his signature. Thomas Organ then wanted the effect branded as their own for the American market, changing it to Cry Baby which was sold in parallel to the Italian Vox V846. Thomas Organ's failure to trademark the Cry Baby name soon led to the market being flooded with Cry Baby imitations from various parts of the world, including Italy, where all of the original Vox and Cry Babys were made. [ 4 ] JEN, who had been responsible for the manufacture of Thomas Organ and Vox wah pedals, also made rebranded pedals for companies such as Fender and Gretsch and under their own JEN brand. When Thomas Organ moved production completely to Sepulveda, California and Chicago, Illinois these Italian models continued to be made and are among the more collectible wah pedals today.
Some of the most famous electric guitarists of the day were keen to adopt the wah-wah pedal soon after its release. Among the first recordings featuring wah-wah pedal were " Tales of Brave Ulysses " by Cream with Eric Clapton on guitar and " Burning of the Midnight Lamp " by the Jimi Hendrix Experience , [ 5 ] both released in 1967. Hendrix also used wah wah on his famous song " Voodoo Child ", in intro and in soloing. According to Del Casher, Hendrix learned about the pedal from Frank Zappa , another well-known early user. [ 6 ] [ 7 ] Clapton, in particular, used the device on many of the Cream songs included on their second and third albums, Disraeli Gears (1967) and Wheels of Fire (1968) respectively. Clapton would subsequently employ it again on " Wah-Wah ", from his good friend George Harrison 's solo album All Things Must Pass , upon the dissolution of The Beatles in 1970.
The wah-wah pedal increased in popularity in the following years, and was employed by guitarists such as Terry Kath of Chicago , Martin Barre of Jethro Tull , Jimmy Page of Led Zeppelin , and Tony Iommi of Black Sabbath . Kirk Hammett of Metallica would later use the pedal on many Metallica songs, most notably the guitar solo of Enter Sandman . David Gilmour of Pink Floyd used the pedal to create the "whale" effect during Echoes . He discovered this effect as a result of a roadie accidentally plugging his guitar into the output of the pedal and the input being plugged into his amp. The effect was first used during live performances of The Embryo during 1970 but was then switched into Echoes as it was being developed before being released on the Meddle album on 31 October 1971. [ 8 ] Mick Ronson used a Cry Baby while recording The Rise and Fall of Ziggy Stardust and the Spiders from Mars . [ 9 ] Michael Schenker also utilized the pedal in his work. [ 10 ]
One of the most famous uses of this effect is heard on Isaac Hayes 's " Theme from Shaft " (1971), with Charles Pitts (credited as Charles 'Skip' Pitts) playing the guitar. [ 11 ]
In addition to rock music, many R&B artists have also used the wah-wah effect, including Lalo Schifrin on " Enter the Dragon " (1973), Johnny Pate on "Shaft in Africa" (1973) and James Brown on " Funky President " (1974). [ 12 ] Funk band Kool & the Gang , B. T. Express , and Jimmy Castor Bunch used the wah-wah pedal also. Melvin Ragin, better known by the nickname Wah Wah Watson , [ 13 ] was a member of the Motown Records studio band, The Funk Brothers, where he recorded with artists such as The Temptations on " Papa Was a Rollin' Stone ", [ 14 ] Marvin Gaye on " Let's Get It On ", The Four Tops , Gladys Knight & the Pips , The Supremes , and The Undisputed Truth on " Smiling Faces Sometimes ". [ 15 ]
In the late 1980s, the wah-wah pedal was revived in the British music industry by John Squire of The Stone Roses , who bought a wah-wah pedal to differentiate his sound from other contemporary acts of the time. [ citation needed ] Afterwards, the wah-wah pedal would also be used by bands such as the Happy Mondays and the Charlatans , and became one of the defining sounds of British guitar music in the late '80s and early '90s. [ citation needed ]
The main use of the wah-wah pedal is by rocking the pedal up and down. By doing this motion, the pedal reacts by sweeping through the peak response of a frequency filter up and down in frequency to create a spectral glide.
A different function of the pedal is to use it in a fixed position, which changes how an instrument sounds by selecting a certain frequency range. A guitarist using the wah in this way selects a position on the pedal and leaves the pedal there. Depending on the position of the pedal, this will boost or cut a specific frequency. This can be used for emphasizing the "sweet spot" in the tonal spectrum of a particular instrument. One electric guitar player to use the pedal in this way was Jimi Hendrix , who revolutionized its application by combining a Fender Stratocaster with stacked Marshall Amplifiers (in both static and modulated mode) for lead and rhythm guitar applications unheard of before then.
Another famous style of wah-wah playing is utilizing it for a percussive "wacka-wacka" effect during rhythm guitar parts. This is done by muting strings, holding down a chord and moving the pedal at the same time. This was first heard on the song "Little Miss Lover" (1967) on " Axis: Bold as Love ," by the Jimi Hendrix Experience.
The "wah-wah" and "wacka-wacka" effects are often associated with the bands on 1970s TV variety shows , like those of Sonny and Cher , Flip Wilson , or Donny and Marie Osmond ; or with the soundtracks of pornographic films , the sound referenced in TV commercials for Axe body spray as "bow chicka wow wow."
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In applied mathematics , Wahba's problem , first posed by Grace Wahba in 1965, seeks to find a rotation matrix ( special orthogonal matrix ) between two coordinate systems from a set of (weighted) vector observations. Solutions to Wahba's problem are often used in satellite attitude determination utilising sensors such as magnetometers and multi-antenna GPS receivers . The cost function that Wahba's problem seeks to minimise is as follows:
where w k {\displaystyle \mathbf {w} _{k}} is the k -th 3-vector measurement in the reference frame, v k {\displaystyle \mathbf {v} _{k}} is the corresponding k -th 3-vector measurement in the body frame and R {\displaystyle \mathbf {R} } is a 3 by 3 rotation matrix between the coordinate frames. [ 1 ] a k {\displaystyle a_{k}} is an optional set of weights for each observation.
A number of solutions to the problem have appeared in literature, notably Davenport's q-method, [ 2 ] QUEST and methods based on the singular value decomposition (SVD). Several methods for solving Wahba's problem are discussed by Markley and Mortari.
This is an alternative formulation of the orthogonal Procrustes problem (consider all the vectors multiplied by the square-roots of the corresponding weights as columns of two matrices with N columns to obtain the alternative formulation). A compact and elegant derivation can be found in Appel (2015). [ 3 ]
One solution can be found using a singular value decomposition (SVD).
1. Obtain a matrix B {\displaystyle \mathbf {B} } as follows:
2. Find the singular value decomposition of B {\displaystyle \mathbf {B} }
3. The rotation matrix is simply:
where M = diag ( [ 1 1 det ( U ) det ( V ) ] ) {\displaystyle \mathbf {M} =\operatorname {diag} ({\begin{bmatrix}1&1&\det(\mathbf {U} )\det(\mathbf {V} )\end{bmatrix}})}
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https://en.wikipedia.org/wiki/Wahba's_problem
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The wait/walk dilemma occurs when waiting for a bus at a bus stop , when the duration of the wait may exceed the time needed to arrive at a destination by another means, especially walking .
Some work on this problem was featured in the 2008 "Year in Ideas" issue of The New York Times Magazine . [ 1 ]
The dilemma has been studied in an unpublished report entitled "Walk Versus Wait: The Lazy Mathematician Wins." [ 2 ] [ 3 ] Anthony B. Morton's paper "A Note on Walking Versus Waiting" supports and extends Chen et al.'s results. [ 4 ] Ramnik Arora's "A Note on Walk versus Wait: Lazy Mathematician Wins" discusses what he believes to be some of the errors in Chen et al.'s argument; the result of Chen et al.'s paper still holds following Arora's alleged corrections. [ 5 ] As early as 1990, writer Tom Parker had observed that "walking is faster than waiting for a bus if you're going less than a mile". [ 6 ]
As an undergraduate mathematics major at Harvard , Scott D. Kominers first began fixating on the problem while walking from MIT to Harvard , [ 2 ] which are more than a mile apart in Cambridge, Massachusetts along MBTA bus route 1 . He enlisted the help of Caltech physics major Justin G. Chen and Harvard statistics major Robert W. Sinnott to perform the analysis. [ 2 ]
Their paper concludes that it is usually mathematically quicker to wait for the bus [ dubious – discuss ] , at least for a little while. But once made, the decision to walk should be final instead of waiting again at subsequent stops. [ 2 ] [ 1 ] The paper also showed potential applications to the field of cryptography.
The corresponding problem in interstellar travel is called the wait calculation , which tries to determine the optimal time to wait for technological progress to improve spaceship speeds before committing to the journey.
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https://en.wikipedia.org/wiki/Wait/walk_dilemma
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A wajū ( 輪中 , lit. ' inside the circle ' ) Japanese pronunciation: [wa(d)ʑɯː] is a hydraulic engineering and flood control structure unique to the alluvial floodplain of the Kiso Three Rivers in central Japan. [ 1 ] It is comparable to the European polder , although a wajū is usually not reclaimed . The hardships endured for centuries by farmers whose lives revolved around the wajū has given rise to the term " wajū spirit" ( 輪中根性 , wajū konjō ) .
Since prehistoric times sudden freshets along the course of the major rivers of Owari and Mino in late spring caused by snowmelt in the snow country , especially in the Japanese Alps and Koshi , created great suffering for agricultural communities. The wajū was developed to protect fertile riparian farmland from becoming submerged by rising water levels during these freshets. [ 1 ] Wajū are known to have been in use since at least the 16th century, [ 2 ] but some wajū are reputed to be much older, such as Takasu wajū [ ja ] which was allegedly completed in 1319. [ 3 ]
To develop a wajū , an area of land, usually a river island , was enclosed by a levee ring. In the event of a levee failure, most wajū incorporated structures allowing for vertical evacuation .
One evacuation system used by those who could afford to build it, such as the well-to-do gōnō , was the mizuya ( 水屋 ) , a sort of tower house above the high water line built on a foundation in ishigaki style. For lower class people, including peasants and rural samurai (gōshi), who couldn't afford to build mizuya , there was the inochizuka ( 命塚 , lit. ' life [preserving] mound ' ) an artificial earthen high ground similar to the terps of Northern Europe or the cattle mounds built on American ranches.
Over the centuries, the wajū suffered numerous failures due to engineering deficiencies. In the 18th century, Izawa Yasobē [ ja ] was among the first to suggest redirecting the rivers to relieve water pressure on the wajū and compensate for the inadequacies of the existing system of pressure-regulating aqueducts , known as hayodoyu ( 夙樋 ) . In the late 19th century, the wajū were improved and reinforced using technology imported from Europe.
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https://en.wikipedia.org/wiki/Wajū
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Wake-on-Ring ( WOR ) or Wake-on-Modem ( WOM ) is a specification that allows supported computers and devices to "wake up" or turn on from a sleeping, hibernating or "soft off" state (e.g. ACPI state G1 or G2), and begin operation.
The basic premise is that a special signal is sent over phone lines to the computer through its dial-up modem , telling it to fully power-on and begin operation. Common uses were archive databases and BBSes , although hobbyist use was significant.
Fax machines use a similar system, in which they are mostly idle until receiving an incoming fax signal, which spurs operation.
This style of remote operation has mostly been supplanted by Wake-on-LAN , which is newer but works in much the same way.
This computing article is a stub . You can help Wikipedia by expanding it .
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In fluid dynamics , a wake may either be:
The wake is the region of disturbed flow (often turbulent ) downstream of a solid body moving through a fluid, caused by the flow of the fluid around the body.
For a blunt body in subsonic external flow, for example the Apollo or Orion capsules during descent and landing, the wake is massively separated and behind the body is a reverse flow region where the flow is moving toward the body. This phenomenon is often observed in wind tunnel testing of aircraft, and is especially important when parachute systems are involved, because unless the parachute lines extend the canopy beyond the reverse flow region, the chute can fail to inflate and thus collapse. Parachutes deployed into wakes suffer dynamic pressure deficits which reduce their expected drag forces. High-fidelity computational fluid dynamics simulations are often undertaken to model wake flows, although such modeling has uncertainties associated with turbulence modeling (for example RANS versus LES implementations), in addition to unsteady flow effects. Example applications include rocket stage separation and aircraft store separation.
In incompressible fluids (liquids) such as water, a bow wake is created when a watercraft moves through the medium; as the medium cannot be compressed, it must be displaced instead, resulting in a wave. As with all wave forms , it spreads outward from the source until its energy is overcome or lost, usually by friction or dispersion .
The non-dimensional parameter of interest is the Froude number .
Waterfowl and boats moving across the surface of water produce a wake pattern, first explained mathematically by Lord Kelvin and known today as the Kelvin wake pattern . [ 1 ]
The above describes an ideal wake, where the body's means of propulsion has no other effect on the water. In practice the wave pattern between the V-shaped wavefronts is usually mixed with the effects of propeller backwash and eddying behind the boat's (usually square-ended) stern.
The Kelvin angle is also derived for the case of deep water in which the fluid is not flowing in different speed or directions as a function of depth ("shear"). In cases where the water (or fluid) has shear, the results may be more complicated. [ 2 ] Also, the deep water model neglects surface tension, which implies that the wave source is large compared to capillary length .
"No wake zones" may prohibit wakes in marinas , near moorings and within some distance of shore [ 3 ] in order to facilitate recreation by other boats and reduce the damage wakes cause. Powered narrowboats on British canals are not permitted to create a breaking wash (a wake large enough to create a breaking wave ) along the banks, as this erodes them. This rule normally restricts these vessels to 4 knots (4.6 mph; 7.4 km/h) or less.
Wakes are occasionally used recreationally. Swimmers, people riding personal watercraft, and aquatic mammals such as dolphins can ride the leading edge of a wake. In the sport of wakeboarding the wake is used as a jump. The wake is also used to propel a surfer in the sport of wakesurfing . In the sport of water polo , the ball carrier can swim while advancing the ball, propelled ahead with the wake created by alternating armstrokes in crawl stroke , a technique known as dribbling . Furthermore, in the sport of canoe marathon, competitors use the wake of fellow kayaks in order to save energy and gain an advantage, through the practice of sitting their boats on the wake of another, so their kayak is propelled by the wash.
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https://en.wikipedia.org/wiki/Wake_(physics)
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The Wake Forest Institute for Regenerative Medicine ( WFIRM ) is a research institute affiliated with Wake Forest School of Medicine and located in Winston-Salem , North Carolina , United States .
WFIRM's goal is to apply the principles of regenerative medicine to repair or replace diseased tissues and organs. Among other goals, WFIRM scientists are looking for ways to create insulin-producing cells in the laboratory, engineered blood vessels for heart bypass surgery and treat knee injuries through regenerated meniscus tissues. [ 1 ] WFIRM has also led two federal initiatives to regenerate tissues from battlefield injuries (AFIRM I and AFIRM II), with a combined funding of $160 million from the U.S. Department of Defense . [ 2 ] WFIRM is working to develop more than 40 different organs and tissues in the laboratory.
Anthony Atala , M.D., is the director of the institute, which is located in Wake Forest Innovation Quarter in downtown Winston-Salem . Atala was recruited by Wake Forest Baptist Medical Center in 2004, and brought many of his team members from the Laboratory for Tissue Engineering and Cellular Therapeutics at the Children's Hospital Boston and Harvard Medical School . Notable achievements announced at WFIRM have been the first lab-grown organ , a urinary bladder . The artificial urinary bladder was the first to be implanted into a human. [ 3 ] [ 4 ] WFIRM research also discovered stem cells harvested from the amniotic fluid of pregnant women. These stems cells are pluripotent , meaning that they can be manipulated to differentiate into various types of mature cells that make up nerve, muscle, bone, and other tissues while avoiding the problems of tumor formation and ethical concerns that are associated with embryonic stem cells . [ 5 ] Research at WFIRM was also essential towards developing the field of bioprinting . This was first accomplished by converting a Hewlett Packard paper and ink printer to deposit cells, which is now on display at the National Museum of Health and Medicine . [ 6 ] Later, the more advanced Integrated Tissue-Organ Printer (ITOP) was developed at the institute. [ 7 ]
In 2019, the U.S. federal Department of Health and Human Services (HHS) provided a 5-year grant through BARDA to support further development of WFIRM technology to better understand damage to the body caused by inhaling chlorine gas . The technology is called "lung-on-a-chip" and is a part of a "miniaturized system of human organs" developed by WFIRM that can allow researchers to create models of the body's response to harmful agents. [ 8 ]
The Institute also is involved in research on energy fields and the human biofield. This led to a retracted article on Energy Medicine. [ 9 ]
This article about a United States health organization is a stub . You can help Wikipedia by expanding it .
This North Carolina –related article is a stub . You can help Wikipedia by expanding it .
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In probability theory , Wald's equation , Wald's identity [ 1 ] or Wald's lemma [ 2 ] is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantities. In its simplest form, it relates the expectation of a sum of randomly many finite-mean, independent and identically distributed random variables to the expected number of terms in the sum and the random variables' common expectation under the condition that the number of terms in the sum is independent of the summands.
The equation is named after the mathematician Abraham Wald . An identity for the second moment is given by the Blackwell–Girshick equation . [ 3 ]
Let ( X n ) n ∈ N {\displaystyle \mathbb {N} } be a sequence of real-valued, independent and identically distributed random variables and let N ≥ 0 be an integer-valued random variable that is independent of the sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } . Suppose that N and the X n have finite expectations. Then
Roll a six-sided dice . Take the number on the die (call it N ) and roll that number of six-sided dice to get the numbers X 1 , . . . , X N , and add up their values. By Wald's equation, the resulting value on average is
Let ( X n ) n ∈ N {\displaystyle \mathbb {N} } be an infinite sequence of real-valued random variables and let N be a nonnegative integer-valued random variable.
Assume that:
Then the random sums
are integrable and
If, in addition,
then
Remark: Usually, the name Wald's equation refers to this last equality.
Clearly, assumption ( 1 ) is needed to formulate assumption ( 2 ) and Wald's equation. Assumption ( 2 ) controls the amount of dependence allowed between the sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } and the number N of terms; see the counterexample below for the necessity . Note that assumption ( 2 ) is satisfied when N is a stopping time for a sequence of independent random variables ( X n ) n ∈ N {\displaystyle \mathbb {N} } . [ citation needed ] Assumption ( 3 ) is of more technical nature, implying absolute convergence and therefore allowing arbitrary rearrangement of an infinite series in the proof.
If assumption ( 5 ) is satisfied, then assumption ( 3 ) can be strengthened to the simpler condition
Indeed, using assumption ( 6 ),
and the last series equals the expectation of N [ Proof ] , which is finite by assumption ( 5 ). Therefore, ( 5 ) and ( 6 ) imply assumption ( 3 ).
Assume in addition to ( 1 ) and ( 5 ) that
Then all the assumptions ( 1 ), ( 2 ), ( 5 ) and ( 6 ), hence also ( 3 ) are satisfied. In particular, the conditions ( 4 ) and ( 8 ) are satisfied if
Note that the random variables of the sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } don't need to be independent.
The interesting point is to admit some dependence between the random number N of terms and the sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } . A standard version is to assume ( 1 ), ( 5 ), ( 8 ) and the existence of a filtration ( F n ) n ∈ N {\displaystyle \mathbb {N} } 0 such that
Then ( 10 ) implies that the event { N ≥ n } = { N ≤ n – 1} c is in F n –1 , hence by ( 11 ) independent of X n . This implies ( 2 ), and together with ( 8 ) it implies ( 6 ).
For convenience (see the proof below using the optional stopping theorem) and to specify the relation of the sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } and the filtration ( F n ) n ∈ N {\displaystyle \mathbb {N} } 0 , the following additional assumption is often imposed:
Note that ( 11 ) and ( 12 ) together imply that the random variables ( X n ) n ∈ N {\displaystyle \mathbb {N} } are independent.
An application is in actuarial science when considering the total claim amount follows a compound Poisson process
within a certain time period, say one year, arising from a random number N of individual insurance claims, whose sizes are described by the random variables ( X n ) n ∈ N {\displaystyle \mathbb {N} } . Under the above assumptions, Wald's equation can be used to calculate the expected total claim amount when information about the average claim number per year and the average claim size is available. Under stronger assumptions and with more information about the underlying distributions, Panjer's recursion can be used to calculate the distribution of S N .
Let N be an integrable, N {\displaystyle \mathbb {N} } 0 -valued random variable, which is independent of the integrable, real-valued random variable Z with E[ Z ] = 0 . Define X n = (–1) n Z for all n ∈ N {\displaystyle \mathbb {N} } . Then assumptions ( 1 ), ( 5 ), ( 7 ), and ( 8 ) with C := E[| Z |] are satisfied, hence also ( 2 ) and ( 6 ), and Wald's equation applies. If the distribution of Z is not symmetric, then ( 9 ) does not hold. Note that, when Z is not almost surely equal to the zero random variable, then ( 11 ) and ( 12 ) cannot hold simultaneously for any filtration ( F n ) n ∈ N {\displaystyle \mathbb {N} } , because Z cannot be independent of itself as E[ Z 2 ] = (E[ Z ]) 2 = 0 is impossible.
Let ( X n ) n ∈ N {\displaystyle \mathbb {N} } be a sequence of independent, symmetric, and {–1, +1 }-valued random variables. For every n ∈ N {\displaystyle \mathbb {N} } let F n be the σ-algebra generated by X 1 , . . . , X n and define N = n when X n is the first random variable taking the value +1 . Note that P( N = n ) = 1/2 n , hence E[ N ] < ∞ by the ratio test . The assumptions ( 1 ), ( 5 ) and ( 9 ), hence ( 4 ) and ( 8 ) with C = 1 , ( 10 ), ( 11 ), and ( 12 ) hold, hence also ( 2 ), and ( 6 ) and Wald's equation applies. However, ( 7 ) does not hold, because N is defined in terms of the sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } . Intuitively, one might expect to have E[ S N ] > 0 in this example, because the summation stops right after a one, thereby apparently creating a positive bias. However, Wald's equation shows that this intuition is misleading.
Consider a sequence ( X n ) n ∈ N {\displaystyle \mathbb {N} } of i.i.d. (Independent and identically distributed random variables) random variables, taking each of the two values 0 and 1 with probability 1 / 2 (actually, only X 1 is needed in the following). Define N = 1 – X 1 . Then S N is identically equal to zero, hence E[ S N ] = 0 , but E[ X 1 ] = 1 / 2 and E[ N ] = 1 / 2 and therefore Wald's equation does not hold. Indeed, the assumptions ( 1 ), ( 3 ), ( 4 ) and ( 5 ) are satisfied, however, the equation in assumption ( 2 ) holds for all n ∈ N {\displaystyle \mathbb {N} } except for n = 1 . [ citation needed ]
Very similar to the second example above, let ( X n ) n ∈ N {\displaystyle \mathbb {N} } be a sequence of independent, symmetric random variables, where X n takes each of the values 2 n and –2 n with probability 1 / 2 . Let N be the first n ∈ N {\displaystyle \mathbb {N} } such that X n = 2 n . Then, as above, N has finite expectation, hence assumption ( 5 ) holds. Since E[ X n ] = 0 for all n ∈ N {\displaystyle \mathbb {N} } , assumptions ( 1 ) and ( 4 ) hold. However, since S N = 1 almost surely, Wald's equation cannot hold.
Since N is a stopping time with respect to the filtration generated by ( X n ) n ∈ N {\displaystyle \mathbb {N} } , assumption ( 2 ) holds, see above. Therefore, only assumption ( 3 ) can fail, and indeed, since
and therefore P( N ≥ n ) = 1/2 n –1 for every n ∈ N {\displaystyle \mathbb {N} } , it follows that
Assume ( 1 ), ( 5 ), ( 8 ), ( 10 ), ( 11 ) and ( 12 ). Using assumption ( 1 ), define the sequence of random variables
Assumption ( 11 ) implies that the conditional expectation of X n given F n –1 equals E[ X n ] almost surely for every n ∈ N {\displaystyle \mathbb {N} } , hence ( M n ) n ∈ N {\displaystyle \mathbb {N} } 0 is a martingale with respect to the filtration ( F n ) n ∈ N {\displaystyle \mathbb {N} } 0 by assumption ( 12 ). Assumptions ( 5 ), ( 8 ) and ( 10 ) make sure that we can apply the optional stopping theorem , hence M N = S N – T N is integrable and
Due to assumption ( 8 ),
and due to assumption ( 5 ) this upper bound is integrable. Hence we can add the expectation of T N to both sides of Equation ( 13 ) and obtain by linearity
Remark: Note that this proof does not cover the above example with dependent terms .
This proof uses only Lebesgue's monotone and dominated convergence theorems .
We prove the statement as given above in three steps.
We first show that the random sum S N is integrable. Define the partial sums
Since N takes its values in N {\displaystyle \mathbb {N} } 0 and since S 0 = 0 , it follows that
The Lebesgue monotone convergence theorem implies that
By the triangle inequality,
Using this upper estimate and changing the order of summation (which is permitted because all terms are non-negative), we obtain
where the second inequality follows using the monotone convergence theorem. By assumption ( 3 ), the infinite sequence on the right-hand side of ( 15 ) converges, hence S N is integrable.
We now show that the random sum T N is integrable. Define the partial sums
of real numbers. Since N takes its values in N {\displaystyle \mathbb {N} } 0 and since T 0 = 0 , it follows that
As in step 1, the Lebesgue monotone convergence theorem implies that
By the triangle inequality,
Using this upper estimate and changing the order of summation (which is permitted because all terms are non-negative), we obtain
By assumption ( 2 ),
Substituting this into ( 17 ) yields
which is finite by assumption ( 3 ), hence T N is integrable.
To prove Wald's equation, we essentially go through the same steps again without the absolute value, making use of the integrability of the random sums S N and T N in order to show that they have the same expectation.
Using the dominated convergence theorem with dominating random variable | S N | and the definition of the partial sum S i given in ( 14 ), it follows that
Due to the absolute convergence proved in ( 15 ) above using assumption ( 3 ), we may rearrange the summation and obtain that
where we used assumption ( 1 ) and the dominated convergence theorem with dominating random variable | X n | for the second equality. Due to assumption ( 2 ) and the σ-additivity of the probability measure,
Substituting this result into the previous equation, rearranging the summation (which is permitted due to absolute convergence, see ( 15 ) above), using linearity of expectation and the definition of the partial sum T i of expectations given in ( 16 ),
By using dominated convergence again with dominating random variable | T N | ,
If assumptions ( 4 ) and ( 5 ) are satisfied, then by linearity of expectation,
This completes the proof.
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In game theory , the Waldegrave problem is a problem first described in the second edition of Pierre Raymond de Montmort `s Essay d'analyse sur les jeux de hazard , which is the first discussion of a mixed strategy to derive a solution in game theory. Montmort originally called Waldegrave's Problem the Problème de la Poulle or the Problem of the Pool. He provides a minimax mixed strategy solution to a two-person version of the card game le her .
The general description of the problem is as follows: Suppose there are n+1 players with each player putting one unit into the pot or pool. The first two players play each other and the winner plays the third player. The loser of each game puts one unit into the pot. Play continues in like fashion through all the players until one of the players has beaten all the others in succession. The original problem, stated in a letter dated 10 April 1711, from Montmort to Nicholas Bernoulli is for n = 2 and is attributed to M. de Waldegrave . The problem, according to Montmort, is to find the expectation of each player and the probability that the pool will be won within a specified number of games. [ 1 ]
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Walden inversion is the inversion of a stereogenic center in a chiral molecule in a chemical reaction . Since a molecule can form two enantiomers around a stereogenic center, the Walden inversion converts the configuration of the molecule from one enantiomeric form to the other. For example, in an S N 2 reaction , Walden inversion occurs at a tetrahedral carbon atom. It can be visualized by imagining an umbrella turned inside-out in a gale . In the Walden inversion, the backside attack by the nucleophile in an S N 2 reaction gives rise to a product whose configuration is opposite to the reactant. Therefore, during S N 2 reaction, 100% inversion of product takes place. This is known as Walden inversion.
It was first observed by chemist Paul Walden in 1896. He was able to convert one enantiomer of a chemical compound into the other enantiomer and back again in a so-called Walden cycle which went like this: (+)- chlorosuccinic acid ( 1 in the illustration) was converted to (+)- malic acid 2 by action of silver oxide in water with retention of configuration. In the next step the hydroxyl group was replaced by chlorine to the other isomer of chlorosuccinic acid 3 by reaction with phosphorus pentachloride . A reaction with silver oxide yielded (−)-malic acid 4 and finally a reaction with PCl 5 returned the cycle to its starting point. [ 1 ]
In this reaction, the silver oxide in the first step acts as a hydroxide donor while the silver ion plays no role in the reaction. The intermediates are the carboxyl dianion A which gives an intramolecular nucleophilic substitution by the β-carboxylate anion to produce a four-membered β- lactone ring B . The α-carboxyl group is also reactive but in silico data suggests that the transition state for the formation of the three-membered α-lactone is very high. A hydroxyde ion ring-opens the lactone to form the alcohol C and the net effect of two counts of inversion is retention of configuration. [ 2 ]
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The Walden reductor is a reduction column filled with metallic silver which can be used to reduce a metal ion in aqueous solution to a lower oxidation state . It can be used e.g. to reduce UO 2 2+ to U 4+ . [ 1 ] The method is named after George H. Walden , who developed it jointly with a Ph.D. student, Sylvan M. Edmonds, at Columbia University . [ 2 ]
A copper wire is submerged in a solution of silver nitrate . Dendritic crystals of silver immediately form on the copper wire according to the following redox reaction:
Cu + 2 Ag + → Cu 2+ + 2 Ag
The silver crystals are then removed from the copper wire, washed with pure water to remove the copper nitrate and the excess of silver nitrate and packed in a small glass column. [ 2 ] [ 3 ]
To use the reductor, the solution to be reduced is poured at the top of the glass tube, and then drawn through it. The reactive front progresses along the column as in chromatography and the extent of reduction reaches up to 100 % as the solution passes down the tube and the product becomes completely separated from the starting material. [ 2 ] [ 3 ]
The Walden reductor can be used to obtain chemical species in their low valence state if required for chemical analyses or to obtain small amounts of the compound in the appropriate form. [ 1 ] [ 2 ] [ 3 ]
Other reductor
Other oxidizing reagents (opposite)
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In mathematics , Waldspurger's theorem , introduced by Jean-Loup Waldspurger ( 1981 ), is a result that identifies Fourier coefficients of modular forms of half-integral weight k +1/2 with the value of an L-series at s = k /2.
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Professor Abiodun Adewale Oladipo (born January 1, 1958, Ile-Ife , Nigeria) [ 1 ] is a Nigerian academician, administrator , and politician. [ 2 ] His Contribution includes, the field of nuclear chemistry, as well as his involvement in Nigerian politics. He serves as the Pro-chancellor [ 3 ] [ 4 ] and Chairman of the Governing Council of Osun State University . [ 5 ] [ 6 ]
Oladipo attended St. John's Catholic Grammar School, Ile-Ife, from 1972 to 1976. During this period, he achieved a Grade 1 in the West African Senior Certificate Examination . He then pursued his bachelor's degree in Chemistry (Education) at Obafemi Awolowo University (formerly University of Ife), Ile-Ife, graduating with Second Class (Upper Division) honors in 1981. [ 7 ] Following his undergraduate studies, he continued his education abroad at the Université Claude Bernard, Lyon I, Villeurbanne, France , where he obtained an MPhil and a PhD in Analytical Chemistry (Nuclear Techniques) With more than five publications in 1984-1988, under the active supervision of Professor JP Thomas. [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ]
In 2005, Oladipo achieved the rank of Research Professor at the Centre for Energy Research and Development (CERD) at Obafemi Awolowo University. He began his career as a Senior Research Fellow in CERD in 1993. He is also a member of Nigerian Association of Medical Physicists. [ 13 ]
Throughout his career, Oladipo has held various positions, including Head of Division, Environmental and Earth Sciences, CERD, OAU, and membership on the Academic Board, CERD, OAU. [ 14 ]
He has authorised many articles [ 12 ] [ 15 ] [ 11 ] and also served as keynote speakers at several local and international conferences. His work on nuclear chemistry includes the use of Cryogenically Produced Heavy Cluster ions of Hydrogen in the Study of Plasma Desorption Mass Spectrometry, as well as the establishment of a fully Automated AAS Laboratory with Graphite Atomization and Cold Vapor Hg Detection Option.
Professor Oladipo is active in various civic roles, including serving as a Nominee Director for Odu’a Investment Company Ltd in 1992, a Part-time Member of the Osun State Sports Council from 1998 to 1999, and a Part-time Member of the Osun State Local Govt. Service Commission from Feb. 2000 to 2002. He also served as a Member of the Ife Development Board for three years.
In 2008, he was appointed as the Chairman of the Osun State Universal Basic Education Board (SUBEB [ 16 ] ). Additionally, he served as the Chairman of the Governing Board of the Federal Neuropsychiatric Hospital, Yaba, from 2009 to 2011.
In July 2013, he was nominated as the National Secretary of the Peoples Democratic Party (PDP) [ 17 ] and was subsequently elected for a substantive four-year tenure in December 2014 at the Party's Special National Convention held in Abuja. [ 18 ] [ 19 ] [ 20 ]
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Walgreens Boots Alliance, Inc. ( WBA ) is an American multinational holding company headquartered in Deerfield, Illinois . [ 2 ] The company was formed on December 31, 2014, after Walgreens bought the 55% stake in Alliance Boots (owner of Boots UK Limited ) that it did not already own. The total price of the acquisition was $4.9 billion in cash and 144.3 million common shares with fair value of $10.7 billion. [ 3 ] Walgreens had previously purchased 45% of the company for $4.0 billion and 83.4 million common shares in August 2012 with an option to purchase the remaining shares within three years. [ 4 ] Walgreens became a subsidiary of the newly created company after the transactions were completed. [ 5 ] As of 2022 [update] , Walgreens Boots Alliance is ranked #18 on the Fortune 500 rankings of the largest United States corporations by total revenue. [ 6 ]
In fiscal year 2022, the company saw sales of $132.7 billion, up 0.1% from fiscal 2021, and saw net earnings increase to $4.3 billion. The combined business has operations in 9 countries, as of August 31, 2022 [update] . Walgreens had formerly operated solely within the United States and its territories, while Alliance Boots operated a more multinational business. [ 7 ]
The company began trading on the Nasdaq in its inception, under the symbol WBA. [ 8 ] On June 26, 2018, Walgreens Boots Alliance replaced General Electric on the Dow Jones Industrial Index . [ 9 ] [ 10 ] Walgreens Boots Alliance was subsequently replaced by Amazon on the Dow Jones Industrial Index on February 26, 2024. The company is also a component of the S&P 500 index; it was formerly a Nasdaq-100 company until 2024.
In March 2025, the company announced that it had agreed to be acquired by Sycamore Partners . The private equity firm will pay $11.45 per share for the company. [ 11 ]
Walgreens and Duane Reade operate within the Retail Pharmacy USA division of Walgreens Boots Alliance. Both businesses sell prescription and non-prescription drugs, and a range of household items, including personal care and beauty products. Walgreens provides access to consumer goods and services, plus pharmacy, photo department, health and wellness services in the United States through its retail drugstores. The division has 9,021 drugstores as of August 31, 2020. [ 12 ] Walgreens runs, or ran, [ vague ] several online stores, such as: Beauty.com, Drugstore.com , VisionDirect.com, and Walgreens.com. [ citation needed ]
Walgreens has stores in all 50 U.S. states, the District of Columbia , Puerto Rico , and the U.S. Virgin Islands .
On October 27, 2015, Walgreens announced the purchase of competitor Rite Aid for $17.2 billion (equivalent to $21.6 billion in 2023). [ 13 ] [ 14 ] However, that deal was later scrapped due to antitrust concerns in favor of a $5.18 billion deal (equivalent to $6.33 billion in 2023), [ 13 ] in which Walgreens only acquired half of Rite Aid locations. [ 15 ]
On September 19, 2017, the Federal Trade Commission approved a fourth deal agreement to purchase 1,932 Rite Aid stores for $4.38 billion total (equivalent to $5.36 billion in 2023), [ 13 ] which was completed in January 2018. [ 16 ]
In June 2024, Walgreens announced that only 75% of its 8,600 U.S. locations were profitable and that the company was planning to shutter more than 2,000 locations by the year 2027. The stock price of Walgreens Boots Alliance (WBA) fell by more than 55% between January and July of 2024. [ 17 ]
Boots forms the main part of the Retail Pharmacy International division of the company. The Boots brand has a history stretching back over 170 years [ 18 ] in the United Kingdom (UK) and is a familiar sight on Britain's high streets . [ 19 ] Stores are located in prominent high street and city center locations as well as in local communities. Most branches include a pharmacy and focus on healthcare, personal care, and cosmetic products, with most stores selling over-the-counter medicines. Larger stores typically offer a variety of healthcare services in addition to dispensing prescriptions, and chlamydia testing and treatment (private service). Optician services are also offered in many larger stores, with Boots Opticians providing eye tests along with the sale of spectacles and contact lenses. [ citation needed ]
Many stores also feature traditional photo processing and/or a Cewe picture kiosk where users of digital cameras and camera phones can create prints via Bluetooth, USB, or CD. Larger stores usually offer a range of electrical equipment such as hairdryers, curlers , and foot massagers, while selected stores offer a range of sandwiches, baguettes, wraps, salads, and beverages. [ citation needed ]
Since 1936, there have been Boots stores outside the UK. Stores in countries as widely spread as New Zealand, Canada (see Pharma Plus ), and France were all closed in the 1980s. As of 2022 [update] , there are Boots-branded stores outside the UK in Ireland , Norway and Thailand , with Boots franchise operations in the Middle East and Indonesia. [ 20 ]
The remainder of the division is made up of the pharmacies Benavides in Mexico and Farmacias Ahumada (FASA) in Chile . [ 20 ]
With the acquisition of Alliance Boots, the company gained a pharmaceutical wholesale division, operating twice-daily deliveries to more than 16,500 delivery points in the UK alone. [ 21 ] Internationally, the Pharmaceutical Wholesale Division, which mainly operated under the Alliance Healthcare brand, supplied medicines, other healthcare products and related services to more than 115,000 pharmacies, doctors, health centers and hospitals each year from 306 distribution centers in 11 countries. [ 22 ]
In June 2021, the majority of the Alliance Healthcare wholesale division was sold to AmerisourceBergen for $6.28 billion (equivalent to $6.96 billion in 2023) [ 13 ] in cash. [ 23 ]
For the fiscal year 2020, Walgreens Boots Alliance reported earnings of US$456 million, with an annual revenue of US$139.5 billion, an increase of 2.5% over the previous fiscal cycle. Numbers before 2014 are for Walgreens only. [ 24 ] As of 2022 [update] , Walgreens Boots Alliance is ranked #18 on the Fortune 500 rankings of the largest United States corporations by total revenue. [ 6 ]
Boots produces a large number of brands, including No. 7 , Soltan and Botanics, Boots Pharmaceuticals, and Boots Laboratories, that Alliance Boots and Walgreens sought to launch internationally following the first share purchase in 2012. [ 27 ]
Launched in 1935, the No. 7 brand is best known for its anti-aging beauty serums, developed in Nottingham, England . The range comprises products designed to target the aging concerns of specific age groups. [ 19 ] No. 7 became available in Walgreens and Duane Reade stores in the US from November 2012, beginning in Los Angeles . [ citation needed ]
Launched in 1939, Soltan markets its UVA 5-star suncare protection, a standard of protection developed by Boots and now adopted as the benchmark for suncare products in the UK. [ citation needed ] However, in both 2004 and 2015, Watchdog , a BBC consumer investigative TV program and cited on BBC News , plus the consumer Which? magazine, each did an investigation finding the SPF rating to be lower than stated on the packaging, according to their tests. [ 28 ] [ 29 ]
First launched in 1995, the Botanics range, developed in partnership with the Royal Botanic Gardens, Kew , uses plant extracts in a variety of products and includes a range of organic products. The Boots Botanics range is also available through third party retailers. [ citation needed ]
The Boots own brand range of products includes skincare, medicines, healthcare products, and many more. Boots Laboratories skincare range for independent pharmacy customers was launched in France and Portugal in 2008/09 and is also sold in Spain, Italy, and Germany. [ 30 ]
Boots now owns Almus Pharmaceuticals, a brand of generic prescription drugs, launched in 2003. [ 31 ] It is now sold in five countries and is an umbrella brand for a wide range of lower cost generic medicines. Almus placed considerable emphasis on the design of the packaging in an attempt to reduce the number of errors by the dispensing chemist and by the patient relating to incorrect dosage which can result in either a dangerous accidental overdose or an equally dangerous under dose. [ citation needed ]
Walgreens has a self-branded line of products, "Well at Walgreens". [ 32 ]
In 2015, Walgreens Boots Alliance paid £140 million (equivalent to £179 million in 2023) [ 33 ] for UK skincare brand Liz Earle Naturally Active, an Avon Products subsidiary since 2010. [ 34 ] Liz Earle Beauty Co co-founder Liz Earle , 'one of the biggest names in the beauty industry' [ 35 ] stayed on as an 'ambassador' [ 36 ] after selling the company for an undisclosed sum [ 37 ] and told her own Liz Earle Wellbeing magazine's website that '...alongside my new digital and print publishing venture...at the moment I'm still connected to Liz Earle Beauty Co and continue to work as a consultant to the brand that carries my name. I'm involved in new product development...' [ 38 ] In 2012, Liz Earle announced that she had left the company. [ 39 ]
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In graph theory , a walk-regular graph is a simple graph where the number of closed walks of any length ℓ {\displaystyle \ell } from a vertex to itself does only depend on ℓ {\displaystyle \ell } but not depend on the choice of vertex. Walk-regular graphs can be thought of as a spectral graph theory analogue of vertex-transitive graphs .
While a walk-regular graph is not necessarily very symmetric , all its vertices still behave identically with respect to the graph's spectral properties.
Suppose that G {\displaystyle G} is a simple graph. Let A {\displaystyle A} denote the adjacency matrix of G {\displaystyle G} , V ( G ) {\displaystyle V(G)} denote the set of vertices of G {\displaystyle G} , and Φ G − v ( x ) {\displaystyle \Phi _{G-v}(x)} denote the characteristic polynomial of the vertex-deleted subgraph G − v {\displaystyle G-v} for all v ∈ V ( G ) . {\displaystyle v\in V(G).} Then the following are equivalent:
A graph is k {\displaystyle k} -walk-regular if for any two vertices v {\displaystyle v} and w {\displaystyle w} of distance at most k , {\displaystyle k,} the number of walks of length ℓ {\displaystyle \ell } from v {\displaystyle v} to w {\displaystyle w} depends only on k {\displaystyle k} and ℓ {\displaystyle \ell } . [ 2 ]
For k = 0 {\displaystyle k=0} these are exactly the walk-regular graphs.
In analogy to walk-regular graphs generalizing vertex-transitive graphs, 1-walk-regular graphs can be thought of as generalizing symmetric graphs , that is, graphs that are both vertex- and edge-transitive. For example, the Hoffman graph is 1-walk-regular but not symmetric.
If k {\displaystyle k} is at least the diameter of the graph, then the k {\displaystyle k} -walk-regular graphs coincide with the distance-regular graphs .
In fact, if k ≥ 2 {\displaystyle k\geq 2} and the graph has an eigenvalue of multiplicity at most k {\displaystyle k} (except for eigenvalues d {\displaystyle d} and − d {\displaystyle -d} , where d {\displaystyle d} is the degree of the graph), then the graph is already distance-regular. [ 3 ]
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In computer science , GSAT and WalkSAT are local search algorithms to solve Boolean satisfiability problems .
Both algorithms work on formulae in Boolean logic that are in, or have been converted into conjunctive normal form . They start by assigning a random value to each variable in the formula. If the assignment satisfies all clauses , the algorithm terminates, returning the assignment. Otherwise, a variable is flipped and the above is then repeated until all the clauses are satisfied. WalkSAT and GSAT differ in the methods used to select which variable to flip.
Both algorithms may restart with a new random assignment if no solution has been found for too long, as a way of getting out of local minima of numbers of unsatisfied clauses.
Many versions of GSAT and WalkSAT exist. WalkSAT has been proven particularly useful in solving satisfiability problems produced by conversion from automated planning problems. The approach to planning that converts planning problems into Boolean satisfiability problems is called satplan .
MaxWalkSAT is a variant of WalkSAT designed to solve the weighted satisfiability problem , in which each clause has associated with a weight, and the goal is to find an assignment—one which may or may not satisfy the entire formula—that maximizes the total weight of the clauses satisfied by that assignment.
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Walk Again Project is an international, non-profit consortium led by Miguel Nicolelis , created in 2009 in a partnership between Duke University and the IINN/ELS , where researchers come together to find neuro-rehabilitation treatments for spinal cord injuries, [ 1 ] [ 2 ] [ 3 ] which pioneered the development and use of the brain–machine interface , including its non-invasive version, [ 4 ] with an EEG . [ 5 ]
Nicolelis, a Brazilian neuroscientist working at Duke University , who had been proposing the use of BMI in his laboratory since 2006, [ 6 ] but had been exploring this area since 1999. [ 7 ] [ a ] He had demonstrated the viability of BMI alongside scientist John Chapin, [ 15 ] in 2008, together with Gordon Cheng, in an experiment where they tested the first continental BMI, where an ape in North Carolina controlled a robot in Kyoto . This was a precursor of the Walk Again Project. [ 16 ] Previously, in 2000, Nicolelis had already demonstrated, in a publication in Nature , the possibility of a computer decoding an ape's brain signals in order to move a robotic arm. [ 17 ] [ 18 ] The project, which began in 2009, [ 19 ] [ 3 ] is a partnership between institutions in the US, Switzerland, Germany, and Brazil. [ 20 ] [ 21 ]
In one of its first steps, published in 2011, the project team made a monkey control a mechanical arm and receive tactile information from this tool, [ 22 ] [ 23 ] [ 24 ] including in the virtual world, with the team's research being welcomed "as an important advance by the scientific community", according to Veja magazine. [ 25 ] That year, in his book “Beyond boundaries”, Nicolelis described his plan to make a patient take the opening kick of the FIFA World Cup, [ 20 ] in a project budgeted at R$33 million at the time (U$S 15,305,489.56 in 2013), [ 26 ] and funded by Finep . [ 19 ]
In 2012, in the process of creating the BRA-Santos Dumont exoskeleton for the 2014 FIFA World Cup , [ b ] the project team recorded 1847 neurons simultaneously, something, until then, unprecedented. [ 28 ] [ 29 ] The next research project saw mice being able to sense tactile information from infrared light, as a possible new form of BMI communication. [ 30 ] [ 31 ] The following year, the project received authorization to test the exoskeleton in Brazil, [ 32 ] with volunteers from the Association for Assistance to Disabled Children [ pt ] testing the equipment since the beginning of November 2013. [ 33 ] [ 34 ]
When he returned to Brazil for the project, Nicolelis found that the patients did not want to undergo surgery as a way of regaining movement. This led his team to develop non-invasive techniques that were able to help patients chronically, something, according to the scientist, “that had never been done in decades of research and treatment of spinal cord injuries.” [ 35 ]
In 2013, the project team revealed that they had been able to make two rhesus monkeys control two virtual arms, using only their thoughts. The research was published in Science Translational Medicine . [ 36 ] [ 37 ] In March 2014 the two exoskeletons were already in Brazil. [ 38 ]
The initial contact with FIFA was made in 2012, but the plan to give the inaugural kick, which would even involve the patient getting up from his wheelchair and crossing 25 meters of the pitch, was abandoned by the entity. Nicolelis has been aware of the time limitation since March. 2014. In the end the demonstration, carried out by the patient Juliano Alves Pinto during the 2014 FIFA World Cup opening ceremony , was reduced to just three seconds on the world network, which was the subject of controversy. [ 39 ] [ 40 ] [ 41 ]
The Walk Again team, made up of 150–156 people for the World Cup, had no control over image production, but the rest of the project was carried out successfully. [ 42 ] [ 43 ] [ 19 ] The “ MIT Technology Review ” listed the exoskeleton as one of the “main failures” in technology in 2014, something Nicolelis refuted, while “ The Verge ” identified him as “one of the 50 world personalities of 2014”. [ 44 ] [ 45 ]
On March 3, 2016, the team demonstrated the use of BMI on apes so that they could move wheelchairs using only their thoughts. [ 46 ] On August 11 of the same year, a new study was published in Scientific Reports . Eight paraplegic patients, who had lost all movement in their lower limbs due to spinal cord injuries, experienced a partial neurological recovery after 12 months of training with virtual reality, a robot, and an exoskeleton. [ 7 ] [ 47 ] [ 48 ]
The experiment described above involved 6 men and 2 women: in four cases, the patients became “partially paralyzed”; a 32-year-old woman who had been paralyzed for more than a decade became able to walk with support after 13 months. One of the two women was able to become pregnant after restoring sensation inside and outside the body, as well as some men regaining sexual ability. The patients reported that the treatment had improved their quality of life. [ 49 ] [ 50 ]
The researchers were surprised by the improvements, since the damage to the spinal cord would have prevented the brain from communicating with the rest of the body. Nicolelis then theorized, still without evidence via imaging tests, that the immersion and mental focus on the training would have stimulated brain plasticity, possibly causing the brain to transmit information through what remained of the nerves. [ 29 ]
In 2018, in an article published in PLOS One , the project demonstrated seven complete paraplegic patients becoming partial paraplegics due to the 28-month-long training with the BMI. [ 4 ] [ 51 ] In 2019, in a study published in Scientific Reports , three paraplegic patients tested the “brain–muscle interface”, where small electrical charges in their legs helped them to move without an exoskeleton. [ 4 ] [ 52 ] [ 53 ] [ 2 ] In a study published on May 1, 2021, in Scientific Reports, two patients suffering from chronic paraplegia were shown to be able to walk on 70% of their own weight, in addition to taking 4580 steps, [ 1 ] [ 53 ] also with the help of non-invasive techniques. [ 5 ]
A study published in 2022 demonstrated the superior clinical effect that the use of non-invasive BMI has compared to putting patients on robots that don't have the same technology. [ 54 ] [ 4 ] Between 2023 and 2024, Nicolelis began to criticize the company Neuralink , founded by two of his former students. He raised ethical concerns about how the company works, as well as criticizing the way they advertised as new a type of research that Nicolelis' team had already carried out over the previous two decades. [ 55 ] [ 35 ] [ 56 ] [ 4 ] Also in 2023, Nicolelis announced the creation of the Nicolelis Institute for Advanced Brain Studies, which aims to bring low-cost solutions, based on BMI, to the treatment of neurological and psychiatric diseases for 1 billion people. The first hub will be created in Milan, Italy, developed with the IRCCS San Raffaele Hospital and the Vita-Salute San Raffaele University , as announced in March 2024. [ 57 ] [ 58 ] [ 59 ]
Unrelated to “Walking Again”, on July 9, 2015, two studies were published in Scientific Reports, demonstrating brain–brain interaction , inside the concept of Brainet . [ 60 ] [ 61 ] [ 62 ]
In 2010, Nicolelis won the U$S 2.5 million prize from the National Institute of Health , becoming the first Brazilian to receive this award. [ 63 ] For his research with BMI, in 2016 Nicolelis won the Daniel E. Noble Award in the category of emerging technologies. [ 64 ]
In 2019, the laboratory responsible for the project published a two-volume compilation of 20 years of scientific articles by the group, which can be downloaded free of charge. [ 65 ]
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Walker Haden Land, Jr. (born May 29, 1932) is a former research professor in the Department of Bioengineering at Binghamton University . Land joined the faculty at Binghamton after a long career at IBM , and has publications in the fields of complex adaptive systems , statistical learning theory, bioinformatics , and cancer research.
With his background in creating code and years of work at companies like IBM, Land was instrumental in perfecting the weights and bias for codes that are capable of solving complex adaptive systems.
Land worked at IBM for 27 years after being honorably discharged from the United States Air Force . He was responsible for research and development in statistical and stochastic processes , Bayesian inference , artificial intelligence , expert systems, coherent processing, neural networks , and guidance and location systems. Land also participated in development and evaluation of guidance systems for the Saturn and Apollo vehicles, as well as worked with post-Apollo space configurations, including the Space Shuttle . He made calculations for the original Apollo mission to circle the Moon and come back to Earth. The initial conditions in his calculation included the then-nine planets as well as all of their then-known moons.
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Walker–Warburg syndrome (WWS), also called Warburg syndrome , Chemke syndrome , HARD syndrome (Hydrocephalus, Agyria and Retinal Dysplasia), Pagon syndrome , cerebroocular dysgenesis (COD) or cerebroocular dysplasia-muscular dystrophy syndrome (COD-MD), [ 1 ] is a rare form of autosomal recessive congenital muscular dystrophy . [ 2 ] It is associated with brain ( lissencephaly , hydrocephalus , cerebellar malformations) and eye abnormalities. [ 3 ] This condition has a worldwide distribution. Walker-Warburg syndrome is estimated to affect 1 in 60,500 newborns worldwide. [ 4 ]
The clinical manifestations present at birth are generalized hypotonia , muscle weakness, developmental delay with intellectual disability and occasional seizures . [ 5 ] The congenital muscular dystrophy is characterized by hypoglycosylation of α-dystroglycan.
Those born with the disease also experience severe ocular and brain defects. Half of all children with WWS are born with encephalocele, which is a gap in the skull that will not seal. The meninges of the brain protrude through this gap due to the neural tube failing to close during development. A malformation of the a baby's cerebellum is often a sign of this disease. Common ocular issues associated with WWS are abnormally small eyes and retinal abnormalities cause by an underdeveloped light-sensitive area in the back of the eye. [ 6 ]
Several genes have been implicated in the etiology of Walker–Warburg syndrome, [ 7 ] and others are as yet unknown. Several mutations were found in the protein O-Mannosyltransferase POMT1 and POMT2 genes, and one mutation was found in each of the fukutin and fukutin-related protein genes. Another gene that has been linked to this condition is Beta-1,3-N-acetylgalactosaminyltransferase 2 ( B3GALNT2 ). [ 8 ]
Laboratory investigations usually show elevated creatine kinase , myopathic/dystrophic muscle pathology and altered α-dystroglycan. Antenatal diagnosis is possible in families with known mutations. Prenatal ultrasound may be helpful for diagnosis in families where the molecular defect is unknown. [ 9 ]
No specific treatment is available. Management is only supportive and preventive.
Those who are diagnosed with the disease often die within the first few months of life. Almost all children with the disease die by the age of three. [ 9 ]
WWS is named for Arthur Earl Walker and Mette Warburg . [ 10 ] [ 11 ] [ 12 ] Its alternative names include Chemke’s syndrome and Pagon’s syndrome, named after Juan M. Chemke and Roberta A. Pagon . [ 10 ]
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The term walking excavator may apply to two different forms of heavy equipment , the historic walking power shovel or dragline excavator that began to appear already early in the 20th century, or the contemporary version of all-terrain excavator popularly known as a spider excavator .
The original walking excavators were enormous and unwieldy machines which alternately raised and lowered sets of foot plates or sections of tracks to maneuver in all directions - albeit typically very slowly. The modern equally highly-specialized excavators (which followed a different evolutionary path and are still little known by the general public) [ 1 ] more closely resembles as standard small excavator (complete with boom , stick, bucket and cab on a rotating platform known as the "house"). However, in place of a fixed undercarriage its house sits atop articulated limb-like extensions with or without wheels. Each can move independently when necessary, moving in spider-like motion to overcome obstacles or set itself up as a stable platform to work on uneven ground.
The first walking excavators were power shovels and dragline excavators that moved by lifting plates or sections of tracked wheels to go forward, backward, or turn. Some of these evolved into some of the largest machines on earth.
Largely independent of this line of evolution, most traditional excavators followed that of tractors and tanks , employing tracks or standard wheels attached to fixed undercarriage, limiting their usability on steep inclines, uneven terrain or positions beyond their safe range of operation. Unlike roadgoing vehicles they typically lack suspensions to accommodate uneven ground conditions, indeed far less, with far less suspension travel and mobility, than modern tanks.
The modern walking excavator largely eliminated the fixed undercarriage in favor of an articulating one, which incorporates independently articulating "limbs" similar to those of a quaduped , characteristically ending in independently powered wheels.
The first development along this line was made in 1966 by Edwin Ernst Menzi (1897–1984) and Joseph Kaiser (1928–1993), who created a prototype excavator suitable for work on mountain slopes. Subsequently, Kaiser AG, Schaanwald, Liechtenstein , and Menzi Muck AG, Kriessern, Switzerland , developed excavators separately. [ 2 ]
The walking excavator's main feature is the ability to move in a crab- or spider-like fashion and hence overcome any terrain obstacle. The undercarriage design varies widely from model to model and between specialized roles. The number of legs or wheels can also vary from three (Menzi Muck 5000T2) to four. The leg design can also vary from fixed to telescoping. Most walking excavators now have rotating or powered wheels, allowing them to roll or drive depending on the need.
As with backhoe operation, the boom is often employed in moving, in the walking excavator's case to overcome gaps that are wider than the reach of its legs. [ citation needed ]
Despite the advantages of the design, it has not yet been widely used for a number of reasons, including the relatively small gain in mobility; the fact that most excavation is done in urban areas; and the high cost, both of the electro-hydraulic controls and of maintenance. [ 2 ]
Today, only spider excavators and some forest harvesters, such as the Ecolog forest harvester or the TimberPro tilt cab, are designed to move and work in mountains. [ 2 ] In 2007, Kaiser AG, Schaanwald, Liechtenstein, realized a turnover of nearly 60 million Swiss francs . [ 2 ]
In 2013, Menzi Muck AG had a turnover of 56.93 million Swiss francs. [ 3 ] In 2014, Kaiser AG had a turnover of 70 million Swiss francs. [ 4 ]
Menzi Muck AG, the walking excavator manufacturer, in collaboration with ETH Zurich , have demonstrated such remotely operated excavator at Bauma Fair 2019. [ 5 ]
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The Walkman effect is the way music listened to via headphones grants the listener more control over their environment. The term was coined by Shuhei Hosokawa , a professor at the International Research Center for Japanese Studies , in an article published in Popular Music in 1984. [ 1 ] While the term was named after the dominant portable music technology of the time, the Sony Walkman , it generically applies to all such devices and has been cited numerous times to refer to similar products released later, such as the Apple iPod .
When Sony released the first Walkmans , they featured two headphone jacks and a "hotline" switch. When pressed, this button activated a microphone and lowered the volume to enable those listening to have a conversation without removing their headphones. [ 2 ] Sony Chairman Akio Morita added these features to the design for fear the technology would be isolating. Although Morita "thought it would be considered rude for one person to be listening to his music in isolation", [ 3 ] people bought their own units rather than share and these features were removed for later models. [ 3 ] [ 4 ]
The initial Walkman marketing campaign showcased the freedom it brought. The first presentation to the press involved young people riding bikes and skateboarding while listening to Walkmans. [ 2 ] Hosokawa points to this ability to listen to music and do something else as making those experiences more pleasurable. The Walkman, he says, is the "autonomy-of-the-walking-self." [ 1 ]
Sony's vice president in charge of audio products said that Walkman's achievement was that it "provided listeners with a personal soundtrack to their lives", [ 3 ] allowing its users "to make even the most boring daily activities interesting, adding a bit of personal style to everything they do."
University of Sussex Professor Michael Bull (aka "Professor iPod") argues that a personal stereo changes the way its user processes the world, allowing for greater confidence and control over personal experiences in space and time. [ 5 ] From an interview in Wired : "People like to control their environment, and the iPod is the perfect way to manage your experience. Music is the most powerful medium for thought, mood and movement control." [ 6 ]
The appeal of personal experience management seems to be strongest in cities. As Hosokawa puts it, "To think about [the Walkman effect] is to reflect on the urban itself: [W]alkman as urban strategy, as urban sonic/musical device." [ 1 ]
One specific effect noted by both Patton [ 3 ] and Bull [ 5 ] is what Bull calls "auditized looking", [ 7 ] the ability of those listening to a personal stereo to make or escape eye contact with others in ways they would not otherwise. Traditional messages carried by eye contact are, to some extent, dissolved by the music's protective bubble, with the listener seen as unavailable.
The Walkman was the first of a long line of mobile devices to attract criticism for isolating its users, promoting narcissism , detachment, and rude behavior, while at the same time preventing interactions that are the basis for traditional place-based communities.
In his phenomenological analysis of this effect, Rainer Schönhammer argues that wearing headphones interrupts a form of contact between people in a shared situation, even if there is no explicit communication, thereby violating "an unwritten law of interpersonal reciprocity: the certainty of common sensual presence in shared situations." [ 8 ] He goes on to draw a similarity with the wearing of dark sunglasses, which irritates because there is an inequality in the balance of looking at and being looked at. Similarly, according to Hosokawa, Walkman users blatantly "confess" that they have a secret (something that you can not hear), which can cause negative feelings in observers.
Both men, however, make an effort to counter negative accusations of detachment, isolation, and narcissism. Perhaps most importantly, Walkman listeners are generally happier, more confident, and calmer. The users are "unified in the autonomous and singular moment—neither as persons nor as individuals—with the real," [ 1 ] when "absence does not mean that the world is no longer worth attention. On the contrary, the subject's disengagement sets him free to enjoy the world attentively as a colorful and rich spectacle." [ 8 ]
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The Wall mansion ( Chinese : 壁宿 ; pinyin : Bì Xiù ) [ 1 ] is one of the Twenty-eight mansions of the Chinese constellations . It is one of the northern mansions of the Black Tortoise .
This constellation -related article is a stub . You can help Wikipedia by expanding it .
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A wall footing , or strip footing , is a continuous strip of concrete that serves to spread the weight of a load-bearing wall across an area of soil. [ 1 ] It is a component of a shallow foundation . [ 1 ]
Wall footings carrying direct vertical loads might be designed either in plain concrete or in reinforced concrete. Since a wall footing deflects essentially in one way, it is analyzed by considering as a strip of unit width and its length.
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"Wall of Shame" ( German : Schandmauer ) is a phrase that is most commonly associated with the Berlin Wall . [ 1 ] In this context, the phrase was coined by Willy Brandt , and it was used by the government of West Berlin , and later popularized in the English-speaking world and elsewhere from the beginning of the 1960s. Inspired by its usage in reference to the Berlin Wall, the term has later been used more widely.
For example, the term "Wall of Shame" can be applied to things, including physical barriers (walls, fences, etc.) serving dishonourable or disputed separation purposes (like the Berlin Wall and the American border wall), physical and virtual bulletin boards listing names or images for purposes of shaming, and even lists in print (i.e., walls of text naming people, companies, etc. for the purpose of shaming them, or as record of embarrassment).
Additionally, "Wall of Shame" may be a significant part in the building of a "Hall of Shame", although, more often, a "Wall of Shame" is a monument in its own right (i.e., a wall not having been erected as part of any "Hall of Shame" endeavour). More recently, the term "Wall of Shame" has been used in reference to the Mexico–United States barrier , [ 2 ] the Egypt–Gaza barrier , [ 3 ] the Israeli West Bank barrier , [ 4 ] the Moroccan Western Sahara Wall . [ 5 ] and the barriers of the same name in Peru . [ 6 ] [ 7 ]
The earliest use of the term, which is a translation of a Japanese phrase, may have been by Ruth Benedict , in her influential book, The Chrysanthemum and the Sword (1948), and other anthropologists discussing the honor shame culture of Japan. [ 8 ]
The term was used by the government of West Berlin to refer to the Berlin Wall , which surrounded West Berlin and separated it from East Berlin and the GDR. In 1961, the government of East Germany named the erected wall as the "Anti-Fascist Protection Rampart", a part of the inner German border ; many Berliners, however, called it " Schandmauer " ("Wall of Shame").
The term was coined by governing mayor Willy Brandt . [ 9 ] Outside Germany it first appeared as "Wall of Shame" in a cover story published by TIME in 1962, [ 10 ] and President of the United States John F. Kennedy used the term in his Annual Message to the US Congress on the State of the Union , 14 January 1963. [ 11 ] Often, graffiti would be painted on points, where a street would intersect with the wall, often reading, "Road blocked by Wall of Shame".
The Berlin Wall was referred to as the "Wall of Shame" in many more recent notable contexts, such as:
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A plate or wall plate is a horizontal, structural, load-bearing member in wooden building framing.
A plate in timber framing is "A piece of Timber upon which some considerable weight is framed...Hence Ground-Plate...Window-plate [obsolete]..." etc. [ 1 ] Also called a wall plate , [ 2 ] raising plate , [ 3 ] or top plate , [ 4 ] An exception to the use of the term plate for a large, load-bearing timber in a wall is the bressummer , a timber supporting a wall over a wall opening (see also: lintel ). These are common in Australia.
The terms sole plate or sill plate are used for the members at the bottom of a wall at the foundation but are most often just called a sole or sill without the word plate . Other load-bearing timbers use the term plate but are not in the wall such as crown plate , a purlin -like beam carried by crown posts in roof framing, and a purlin plate which supports common rafters.
In platform framing there are three types of wall plates and are located at the top and bottom of a wall section, and the two hold the wall studs parallel and spaced at the correct interval. Each type continues in a piecewise fashion around the whole perimeter of the structure.
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In mathematics, a Wall polynomial is a polynomial studied by Wall (1963) in his work on conjugacy classes in classical groups , and named by Andrews (1984) .
This polynomial -related article is a stub . You can help Wikipedia by expanding it .
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Wall studs are framing components in timber or steel -framed walls , that run between the top and bottom plates. It is a fundamental element in frame building. The majority non- masonry buildings rely on wall studs, with wood being the most common and least-expensive material used for studs. Studs are positioned perpendicular to the wall they’re forming to give strength and create space for wires, pipes and insulation . Studs are sandwiched between two horizontal boards called top and bottom plates . These boards are nailed or screwed to the top and bottom ends of the studs, forming the complete wall frame. Studs are usually spaced 16 in. or 24 in. apart. [ 1 ]
Stud is an ancient word related to similar words in Old English, Old Norse, Middle High German, and Old Teutonic generally meaning prop or support . [ 2 ] Other historical words with similar meaning are quarter [ 2 ] and scantling [ 1 ] (one sense meaning a smaller timber, not necessarily the same use). Stick is a colloquial term for both framing lumber (timber) and a "timber tree" [ 3 ] (a tree trunk good for using as lumber (timber)); thus, the names "stick and platform" , "stick and frame" , "stick and box" , or simply stick framing . The stud height usually determines the ceiling height, thus sayings like: "...These rooms were usually high in stud..." [ 2 ]
Studs form walls and may carry vertical structural loads or be non load-bearing , such as in partition walls, which only separate spaces. They hold in place the windows, doors, interior finish, exterior sheathing or siding, insulation and utilities and help give shape to a building. Studs run from sill plate to wall plate . In modern construction, studs are anchored to the plates in a way, such as using fasteners , to prevent the building from being lifted off the foundation by severe wind or earthquake.
Studs are usually slender, so more studs are needed than in post and beam framing. Sometimes studs are long, as in balloon framing , where the studs extend two stories and carry a ledger which carries joists. Balloon framing has been made illegal in new construction in many jurisdictions for fire safety reasons because the open wall cavities allow fire to quickly spread such as from a basement to an attic; the plates and platforms in platform framing provide a passive fire stop inside the walls, and so are deemed much safer by fire safety officials. Being thinner and lighter, stick construction techniques are easier to cut and carry and is speedier than the timber framing.
In the United States and Canada, studs are traditionally made of wood, usually 2×4 or 2×6 by name; however, these historical dimensions have been reduced but still carry the name of "two by four" and "two by six". Typical dimensions of today's "two by four" is 1.5 by 3.5 inches (38 mm × 89 mm) dimensional lumber prior to sanding and are typically placed 16 inches (406 mm) from each other's center, but sometimes also at 12 inches (305 mm) or 24 inches (610 mm). The wood needs to be dry when used, or problems may occur as the studs shrink and twist as they dry out. Steel studs are gaining popularity as a non-combustible alternative, especially for non load-bearing walls, and are required in some firewalls .
In New Zealand, the required lumber size and spacing of wall studs are determined using NZS 3604 Timber-framed buildings table 8.2 for loadbearing walls and table 8.4 for non-loadbearing walls. [ 4 ]
The studs used to frame around window and door openings are sometimes given different names, including:
A building technique mostly associated with Lincolnshire, England, and parts of Scotland gets part of its name from the studs: mud and stud ( stud and mud ). This building method uses studs in a framework which is then totally covered with mud which resembles the building material cob . [ 5 ] Another traditional building method is called stud and plaster where the plaster walls are held by lath on the studs. Studs are also the namesake of a type of timber framing called close studding .
Based on the American West Coast Lumber Inspection Bureau (WCLIB) grading rules , [ 6 ] there is only one grade of stud: STUD. A stud is graded for vertical application and its stress requirements and allowable visual defects reflect that application. A stud is most similar to a #2 grade, which is held to a higher standard during grading. The biggest difference between the two is the frequency, placement and size of knots and overall allowable wane.
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The Wallace Line or Wallace's Line is a faunal boundary line drawn in 1859 by the British naturalist Alfred Russel Wallace and named by the English biologist Thomas Henry Huxley .
It separates the biogeographic realms of Asia and ' Wallacea ', a transitional zone between Asia and Australia formerly also called the Malay Archipelago and the Indo-Australian Archipelago (Present day Indonesia ). To the west of the line are found organisms related to Asiatic species; to the east, a mixture of species of Asian and Australian origins is present. Wallace noticed this clear division in both land mammals and birds during his travels through the East Indies in the 19th century.
The line runs through Indonesia , such as Makassar Strait between Borneo and Sulawesi (Celebes), and through the Lombok Strait between Bali and Lombok , where the distance is strikingly small, only about 35 kilometers (22 mi), but enough for a contrast in species present on each island.
The complex biogeography of the Indo-Australian Archipelago is a result of its location at the merging point of four major tectonic plates and other semi-isolated microplates in combination with ancient sea levels. Those caused the isolation of different taxonomic groups on islands at present relatively close to each other. Wallace's Line is one of the many boundaries drawn by naturalists and biologists since the mid-1800s intended to delineate constraints on the distribution of the fauna and flora of the archipelago. [ 1 ]
One of the earliest descriptions of the biodiversity in the Indo-Australian Archipelago dates back to 1521 when Venetian explorer Pigafetta recorded the biological contrasts between the Philippines and the Maluku Islands (Spice Islands) (on opposite sides of Wallace's Line) during the continuation of the voyage of Ferdinand Magellan , after Magellan had been killed on Mactan . Later on, the English navigator G.W. Earl published his observations in faunal differences between the islands in the Indo-Australian archipelago.
In 1845, G.W. Earl described how shallow seas connected islands on the west ( Sumatra , Java , etc.) with the Asian continent and with similar wildlife, and islands on the east such as New Guinea were connected to Australia and were characterized by the presence of marsupials . [ 2 ]
These early investigations assisted Wallace in developing his theories about the biogeography which he stated publicly in his 1859 paper after extensively traveling the region. [ 1 ] He proposed a line to the east of Bali since "all the islands eastward of Borneo and Java formed part of an Australian or Pacific continent, from which they were separated." [ 3 ]
The proposal of the line, however, was not the main objective of Wallace's endeavours: His primary purpose was in fact to understand the geological phenomena and the colonization events that caused the boundaries in faunal distribution in the region through the development of his theories of evolution and biogeography. [ 1 ] Wallace's studies in Indonesia demonstrated the emerging theory of evolution , at about the same time as J.D. Hooker and Asa Gray published essays also supporting Darwin 's hypothesis. [ 4 ] On the other hand, the lack of knowledge of tectonic plates , and the uncertainty about biodiversity in the Philippines , left Wallace with some contradicting points he had to deal with concerning his theory on biogeography. [ 1 ]
In fact, Wallace did not include the Philippines in his 1859 paper, and the determination of a line in honor of his name was suggested by T.H. Huxley (1868). [ 5 ] [ 6 ] Huxley studied the distribution of gallinaceous birds in the archipelago, and noticed that species in the Philippines were remarkably distinct from those in the Asiatic realm. Based on that, he redrew Wallace's boundary placing it to the west of the Philippines and named it "Wallace's Line", although Wallace himself had refused to include the Philippines on the east side of the line. [ 1 ]
Because of the complexity of the geographical landscape and the differences in diversity of organisms around the archipelago, continuous attempts to characterize faunal and botanical boundaries were carried out after Wallace. Some of them are
In addition, several smaller transition sub-regional boundaries were also proposed. [ 1 ]
More recent work assessing biodiversity assemblages, phylogeny, and using computer-based geospatial tools to analyze previous boundaries have led to patterns of division similar to those proposed through the 19th century, although some special cases not explained before are reinforced by these modern analyses. [ 8 ] [ full citation needed ] for instance, evaluated the distribution of land mammals, birds, and amphibians in Wallace's realms and concluded that the boundaries suggested by Wallace remain valid. Ali et al . (2020), in a different attempt, studied the fauna of Christmas Island and indicated that most of the ancestral colonizers of the island's land mammals and amphibians disappeared from the Lombok Strait . Therefore, they propose a re-conformation of Wallace's Line so that Christmas Island would be sited on the Australasian side of the biogeographical divide, instead of the oriental side. [ 1 ]
Understanding of the biogeography of the region centers on the relationship of ancient sea levels to the continental shelves . Wallace's Line is visible geographically when the continental shelf contours are examined. It figures as a deep-water channel that separates the southeastern edge of the Sunda Shelf from the Sahul Shelf . The Sunda Shelf links Borneo, Bali, Java, and Sumatra underwater to the mainland of southeastern Asia, while the Sahul Shelf connects Australia to New Guinea and their adjacent islands. [ 9 ]
During the Pleistocene, when the ocean levels were up to 120 metres (390 ft) lower , islands became connected, but never uniting Asia with Australia. Consequently, for over 50 million years, deep water between those two large continental shelf areas created a barrier that kept the flora and fauna of Australia separated from those of Asia. It can reasonably be concluded it was an ocean barrier preventing species migration because the physical aspects of the separated islands are very similar. [ 9 ] Thus, the Wallacea region consists of islands that remained isolated on their respective continental land masses, with only those organisms capable of crossing the straits between islands populating them. [ 10 ]
Alternatively, " Weber's line " runs through this transitional area (to the east of center), at the tipping point between Asian species against those with Australian origins. [ 10 ]
The distributions of many bird species follow the limits of the line, since many birds do not cross even the shortest stretches of open ocean water. Among mammals, bats have distributions that can cross the line, but larger terrestrial mammals are generally limited to one side or the other. On the Australian side, many species of marsupials are present, and some monotremes, alongside native rodents—although the occurrence of rodents in this case is derived from more recent colonization events. [ 1 ]
By contrast, to the Asian side, marsupials are excluded, and placental mammals such as apes, cats, elephants, monkeys, rhinoceroses, and other species are found. [ 1 ] Exceptions to this include macaques , pigs, and tarsiers on Sulawesi.
Other groups of plants and animals show differing patterns, but the overall pattern is striking and reasonably consistent. Flora do not follow the Wallace Line to the same extent as fauna , since their colonization events differ in their ability to spread across bodies of water. One genus of plants that does not cross the line is the Australasian genus Eucalyptus , except for one species, E. deglupta , which naturally occurs on the island of Mindanao in the Philippines. [ 3 ]
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Wallacea / w ɒ ˈ l eɪ s i ə / is a biogeographical designation for a group of mainly Indonesian islands separated by deep-water straits from the Asian and Australian continental shelves . Wallacea includes Sulawesi , the largest island in the group, as well as Lombok , Sumbawa , Flores , Sumba , Timor , Halmahera , Buru , Seram , and many smaller islands. The islands of Wallacea lie between the Sunda Shelf (the Malay Peninsula , Sumatra , Borneo , Java , and Bali ) to the west, and the Sahul Shelf including Australia and New Guinea to the south and east. The total land area of Wallacea is 347,000 km 2 (134,000 sq mi). [ 1 ]
Wallacea is defined as the series of islands stretching between the two continental shelves of Sunda and Sahul , but excluding the Philippines . Its eastern border (separating Wallacea from Sahul) is represented by a zoogeographical boundary known as Lydekker's Line , while the Wallace Line (separating Wallacea from Sunda) defines its western border. [ 2 ] [ 3 ]
The Weber Line is the midpoint, at which Asian and Australian fauna and flora are approximately equally represented. It follows the deepest straits traversing the Indonesian Archipelago .
The Wallace Line is named after the Welsh naturalist Alfred Russel Wallace , who recorded the differences between mammal and bird fauna between the islands on either side of the line. The islands of Sundaland to the west of the line, including Sumatra, Java, Bali, and Borneo, share a mammal fauna similar to that of East Asia, which includes tigers, rhinoceros, and apes; whereas the mammal fauna of Lombok and areas extending eastwards are mostly populated by marsupials and birds similar to those in Australasia. Sulawesi shows signs of both. [ 4 ]
During the ice ages, sea levels were lower, exposing the Sunda shelf that links the islands of Sundaland to one another and to Asia [ 5 ] and allowing Asian land animals to inhabit these islands.
The islands of Wallacea have few land mammals, land birds, or freshwater fish of continental origin, which find it difficult to cross open ocean . Many species of birds, reptiles, and insects were better able to cross the straits, and many such species of Australian and Asian origin are found there. Wallacea's plants are predominantly of Asian origin, and botanists include Sundaland, Wallacea, and New Guinea as the floristic province of Malesia . [ citation needed ]
Similarly, Australia and New Guinea to the east are linked by a shallow continental shelf, and were linked by a land bridge during the ice ages, forming a single continent that scientists variously call Australia-New Guinea , Meganesia, Papualand, or Sahul. Consequently, Australia, New Guinea, and the Aru Islands share many marsupial mammals, land birds, and freshwater fish that are not found in Wallacea. [ 3 ]
Although the distant ancestors of Wallacea's flora and fauna may have been from Asia or Australia-New Guinea, Wallacea is home to many endemic species. There is extensive autochthonous speciation and proportionately large numbers of endemics; the area is an important contributor to the overall mega- biodiversity of the Indonesian Archipelago. [ 6 ]
Fauna includes the lowland and mountain anoa , or dwarf buffalo ( Bubalus sp.), and the babirusa, or "deer-pig" ( Babyrousa sp.), both found on Sulawesi, among other islands. Maluku shares a number of similar species with Sulawesi, albeit with fewer total, given the differences in size between the two islands—Sulawesi has at least 4,000 recorded terrestrial plant and animal species, [ 7 ] while Maluku has just over 1,000, by comparison. Sulawesi is home to over 2,000 invertebrate species (with over 1,000 known species of arthropod , not including nearly 900 lepidopterans ), 100 species of reptiles and amphibians , and 288 bird species. Maluku has around 70 reptile and amphibian, 250 avian, and over 550 invertebrate species. Seram Island is particularly noted for its butterflies and birds, including the Moluccan king parrot . Smaller mammals, including some carnivorans (such as civets ), marsupials (such as the cuscus ), primates and rodents are common throughout the region.
A large portion of the waters surrounding Wallacea are part of the Coral Triangle , considered to be the richest coral reef and marine ecosystems on earth, with the highest number of species, adding to the total biodiversity of the region.
Wallacea was originally almost completely forested, mostly tropical moist broadleaf forests , with some areas of tropical dry broadleaf forest . The higher mountains are home to montane and subalpine forests, and mangroves are common in coastal areas. According to Conservation International , Wallacea is home to over 10,000 plant species, of which approximately 1,500 (15%) are endemic. [ 1 ]
Endemism is higher among terrestrial vertebrate species; out of 1,142 species described there, almost half (529) were endemic. 45% of the region retains some sort of forest cover, though only 52,017 km 2 (15%) is in a pristine state. Of Wallacea's total 347,000 km 2 -area, about 20,000 km 2 are protected. [ 1 ]
Tropical and subtropical moist broadleaf forests :
Tropical and subtropical dry broadleaf forests :
Australia may be isolated by sea, but technically through Wallacea, it can be zoologically extended. Australian Early-Middle Pliocene rodent fossils have been found in Chinchilla Sands and Bluffs Down in Queensland, but a mix of ancestral and derived traits suggest murid rodents made it to Australia earlier, maybe in the Miocene, over a forested archipelago, i.e. Wallacea, and evolved in Australia in isolation. [ 8 ]
Australia's rodents make up much of the continent's placental mammal fauna and include various species from stick-nest rats to hopping mice . Other mammals invaded from the east. Two species of cuscus , the Sulawesi bear cuscus and the Sulawesi dwarf cuscus , are the westernmost representatives of the Australasian marsupials. [ 9 ]
The tectonic uplift of Wallacea during the collision between Australia and Asia c. 23 million years ago allowed the global dispersal of passerine birds from Australia across the Indonesian islands. [ 10 ] Bustards and megapodes must have somehow colonized Australia. Cockatiels similar to those from Australia inhabit Komodo Island in Wallacea. [ citation needed ]
A few species of Eucalyptus , a predominant genus of trees in Australia, are found in Wallacea: Eucalyptus deglupta on Sulawesi, and E. urophylla and E. alba in East Nusa Tenggara. [ 11 ] For land snails Wallacea and Wallace's Line do not form a barrier for dispersal. [ 12 ]
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The Favorskii rearrangement is principally a rearrangement of cyclopropanones and α-halo ketones that leads to carboxylic acid derivatives. In the case of cyclic α-halo ketones, the Favorskii rearrangement constitutes a ring contraction. This rearrangement takes place in the presence of a base, sometimes hydroxide , to yield a carboxylic acid, but usually either an alkoxide base or an amine to yield an ester or an amide , respectively. α,α'-Dihaloketones eliminate HX under the reaction conditions to give α,β-unsaturated carbonyl compounds. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] Note that trihalomethyl ketone substrates will result in haloform and carboxylate formation via the haloform reaction instead.
The reaction is named for the Russian chemist Alexei Yevgrafovich Favorskii . [ 6 ] [ 7 ] [ 8 ]
The reaction mechanism is thought to involve the formation of an enolate on the side of the ketone away from the chlorine atom. This enolate cyclizes to a cyclopropanone intermediate which is then attacked by the hydroxide nucleophile . Its formation can otherwise be viewed as a 2-electron electrocyclization of a 1,3-dipole , which can be captured in Diels Alder reactions . The cyclopropanone intermediate is opened to yield the more stable carbanion , which is quickly protonated . [ 9 ]
The second step has also been proposed to be stepwise process, with chloride anion leaving first to produce a zwitterionic oxyallyl cation before a disrotatory electrocyclic ring closure takes place to afford the cyclopropanone intermediate. [ 10 ]
Usage of alkoxide anions such as sodium methoxide, instead of sodium hydroxide, yields the ring-contracted ester product.
When enolate formation is impossible, the Favorskii rearrangement takes place by an alternate mechanism, in which addition to hydroxide to the ketone takes place, followed by concerted collapse of the tetrahedral intermediate and migration of the neighboring carbon with displacement of the halide. This is sometimes known as the pseudo-Favorskii rearrangement or quazi-Favorskii rearrangement, although previous to labeling studies, it was thought that all Favorskii rearrangements proceeded through this mechanism.
In the related Wallach degradation ( Otto Wallach , 1918) not one but two halogen atoms flank the ketone resulting in a new contracted ketone after oxidation and decarboxylation [ 11 ] [ 12 ]
The reaction type also exists as a photochemical reaction . The photo-Favorskii reaction has been used in the photochemical unlocking of certain phosphates (for instance those of ATP ) protected by p-hydroxyphenacyl groups. [ 13 ] The deprotection proceeds through a triplet diradical ( 3 ) and a dione spiro intermediate ( 4 ) although the latter has thus far eluded detection. [ 14 ]
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The Wallach rearrangement , also named Wallach transformation , is a name reaction in the organic chemistry . It is named after Otto Wallach , who discovered this reaction in 1880. In general it is a strong acid-promoted conversion of azoxybenzenes into hydroxyazobenzenes. [ 1 ] [ 2 ] [ 3 ]
The Wallach rearrangement is an organic reaction converting an aromatic azoxy compound with sulfuric acid or other strong acids to an azo compound with one arene ring substituted by a hydroxyl group in the aromatic para position . [ 4 ]
Conceptually related reactions are the Fries rearrangement , the Fischer–Hepp rearrangement , the Bamberger rearrangement , the benzidine rearrangement and the Hofmann–Martius rearrangement . In the first part of the reaction, two equivalents of acid tease the oxygen atom away from the azoxy group. The resulting dicationic intermediate with an unusual R–N + =N + –R motif in this scheme has been observed by proton NMR in a system of fluoroantimonic acid and azoxybenzene at −50 °C. [ 5 ] In the second part, the HSO 4 − anion is a nucleophile in a nucleophilic aromatic substitution followed by hydrolysis .
The reaction mechanism for this reaction is not known with great precision despite experimental evidence:
A mechanism not inconsistent with these findings is depicted below: [ 2 ]
First, azoxybenzene undergoes protonation twice to afford a gitionic intermediate. The difficulty of protonating next to an already cationic nitrogen makes this second protonation step rate-determining. Water is eliminated to give the inferred symmetric intermediate, which is again gitionic and superelectrophilic. Water adds at the terminal position to give an intermediate that undergoes two successive deprotonation steps to give the 4-hydroxyazobenzene.
This reaction has a general application in the preparation of hydroxyazobenzenes and hydroxyazonaphthalenes. They are used for coloration of soap , lacquer and resin .
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In geometry , Wallis's conical edge is a ruled surface given by the parametric equations
where a , b and c are constants.
Wallis's conical edge is also a kind of right conoid . It is named after the English mathematician John Wallis , who was one of the first to use Cartesian methods to study conic sections . [ 1 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Wallis's_conical_edge
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The Wallis product is the infinite product representation of π :
It was published in 1656 by John Wallis . [ 1 ]
Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining ∫ 0 π sin n x d x {\displaystyle \int _{0}^{\pi }\sin ^{n}x\,dx} for even and odd values of n {\displaystyle n} , and noting that for large n {\displaystyle n} , increasing n {\displaystyle n} by 1 results in a change that becomes ever smaller as n {\displaystyle n} increases. Let [ 2 ]
(This is a form of Wallis' integrals .) Integrate by parts :
Now, we make two variable substitutions for convenience to obtain:
We obtain values for I ( 0 ) {\displaystyle I(0)} and I ( 1 ) {\displaystyle I(1)} for later use.
Now, we calculate for even values I ( 2 n ) {\displaystyle I(2n)} by repeatedly applying the recurrence relation result from the integration by parts. Eventually, we end get down to I ( 0 ) {\displaystyle I(0)} , which we have calculated.
Repeating the process for odd values I ( 2 n + 1 ) {\displaystyle I(2n+1)} ,
We make the following observation, based on the fact that sin x ≤ 1 {\displaystyle \sin {x}\leq 1}
Dividing by I ( 2 n + 1 ) {\displaystyle I(2n+1)} :
By the squeeze theorem ,
See the main page on Gaussian integral .
While the proof above is typically featured in modern calculus textbooks, the Wallis product is, in retrospect, an easy corollary of the later Euler infinite product for the sine function .
Let x = π 2 {\displaystyle x={\frac {\pi }{2}}} :
Stirling's approximation for the factorial function n ! {\displaystyle n!} asserts that
Consider now the finite approximations to the Wallis product, obtained by taking the first k {\displaystyle k} terms in the product
where p k {\displaystyle p_{k}} can be written as
Substituting Stirling's approximation in this expression (both for k ! {\displaystyle k!} and ( 2 k ) ! {\displaystyle (2k)!} ) one can deduce (after a short calculation) that p k {\displaystyle p_{k}} converges to π 2 {\displaystyle {\frac {\pi }{2}}} as k → ∞ {\displaystyle k\rightarrow \infty } .
The Riemann zeta function and the Dirichlet eta function can be defined: [ 1 ]
Applying an Euler transform to the latter series, the following is obtained:
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https://en.wikipedia.org/wiki/Wallis_product
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A Walloon forge (or Walloon process ) is a type of finery forge that decarbonizes pig iron into wrought iron .
The process was conceived in the Liège region, and from there extended to France, [ 1 ] then England around the end of the 15th century. [ 2 ] [ 3 ] Louis de Geer brought it to Roslagen in Sweden at the beginning of the 17th century, with Walloon blacksmiths. [ 4 ] [ 5 ]
The Walloon process spread to Sweden in the Uppland province north of Stockholm , where it was used to produce a specific kind of wrought iron called oregrounds iron . [ citation needed ]
The source material was pig iron produced by a blast furnace using charcoal and the manganese rich iron ore from the Dannemora mine . A V-shaped hearth using charcoal was used to heat up the pig iron bar that was presented to a tuyere that decarbonized it and made it melt and fall in drops that solidified in a pool of slag where the decarburization continued. [ 6 ] The iron drops were picked up with an iron bar and presented again in front of the tuyere and one by one agglomerated into a ball. That heterogeneous iron was full of slag and the carbon content ranged from pure iron to nearly pig iron. It was therefore reheated in a chafery and hammered and folded using a waterwheel powered trip hammer .
The ore from Dannemora was very low in sulphur and high in manganese. It is possible the manganese bonded with the impurities during the oxidation , creating a pretty pure wrought iron. The use of charcoal prevented the contamination with impurities usually associated with the usage of coal or coke , of which Sweden has very little (although coal was mined in Höganäs , Scania County from 1797). [ 7 ] [ 8 ] In England, the chafery might use coal or coke, as in this stage the iron is solidified and the contamination remain low.
The iron was sold to England, where it was recarbonized into blister steel using the cementation process . This steel still contained some slag, and if the carbon was around 1% at the surface, it was lower in the center. The blister steel was than purchased by Benjamin Huntsman who melted it in crucibles heated in coke-fired ovens and poured it. This modern crucible steel was different from the medieval wootz from India, but was homogeneous and without slag.
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https://en.wikipedia.org/wiki/Walloon_forge
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A wallpaper group (or plane symmetry group or plane crystallographic group ) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art , especially in textiles , tiles , and wallpaper .
The simplest wallpaper group, Group p 1, applies when there is no symmetry beyond simple translation of a pattern in two dimensions. The following patterns have more forms of symmetry, including some rotational and reflectional symmetries:
Examples A and B have the same wallpaper group; it is called p 4 m in the IUCr notation and *442 in the orbifold notation . Example C has a different wallpaper group, called p 4 g or 4*2 . The fact that A and B have the same wallpaper group means that they have the same symmetries, regardless of the designs' superficial details; whereas C has a different set of symmetries.
The number of symmetry groups depends on the number of dimensions in the patterns. Wallpaper groups apply to the two-dimensional case, intermediate in complexity between the simpler frieze groups and the three-dimensional space groups .
A proof that there are only 17 distinct groups of such planar symmetries was first carried out by Evgraf Fedorov in 1891 [ 1 ] and then derived independently by George Pólya in 1924. [ 2 ] The proof that the list of wallpaper groups is complete came only after the much harder case of space groups had been done. The seventeen wallpaper groups are listed below; see § The seventeen groups .
A symmetry of a pattern is, loosely speaking, a way of transforming the pattern so that it looks exactly the same after the transformation. For example, translational symmetry is present when the pattern can be translated (in other words, shifted) some finite distance and appear unchanged. Think of shifting a set of vertical stripes horizontally by one stripe. The pattern is unchanged. Strictly speaking, a true symmetry only exists in patterns that repeat exactly and continue indefinitely. A set of only, say, five stripes does not have translational symmetry—when shifted, the stripe on one end "disappears" and a new stripe is "added" at the other end. In practice, however, classification is applied to finite patterns, and small imperfections may be ignored.
The types of transformations that are relevant here are called Euclidean plane isometries . For example:
However, example C is different . It only has reflections in horizontal and vertical directions, not across diagonal axes. If one flips across a diagonal line, one does not get the same pattern back, but the original pattern shifted across by a certain distance. This is part of the reason that the wallpaper group of A and B is different from the wallpaper group of C .
Another transformation is a glide reflection , a combination of reflection and translation parallel to the line of reflection.
Mathematically, a wallpaper group or plane crystallographic group is a type of topologically discrete group of isometries of the Euclidean plane that contains two linearly independent translations .
Two such isometry groups are of the same type (of the same wallpaper group) if they are the same up to an affine transformation of the plane . Thus e.g. a translation of the plane (hence a translation of the mirrors and centres of rotation) does not affect the wallpaper group. The same applies for a change of angle between translation vectors, provided that it does not add or remove any symmetry (this is only the case if there are no mirrors and no glide reflections , and rotational symmetry is at most of order 2).
Unlike in the three-dimensional case , one can equivalently restrict the affine transformations to those that preserve orientation .
It follows from the Bieberbach conjecture that all wallpaper groups are different even as abstract groups (as opposed to e.g. frieze groups , of which two are isomorphic with Z ).
2D patterns with double translational symmetry can be categorized according to their symmetry group type.
Isometries of the Euclidean plane fall into four categories (see the article Euclidean plane isometry for more information).
The condition on linearly independent translations means that there exist linearly independent vectors v and w (in R 2 ) such that the group contains both T v and T w .
The purpose of this condition is to distinguish wallpaper groups from frieze groups , which possess a translation but not two linearly independent ones, and from two-dimensional discrete point groups , which have no translations at all. In other words, wallpaper groups represent patterns that repeat themselves in two distinct directions, in contrast to frieze groups, which only repeat along a single axis.
(It is possible to generalise this situation. One could for example study discrete groups of isometries of R n with m linearly independent translations, where m is any integer in the range 0 ≤ m ≤ n .)
The discreteness condition means that there is some positive real number ε, such that for every translation T v in the group, the vector v has length at least ε (except of course in the case that v is the zero vector, but the independent translations condition prevents this, since any set that contains the zero vector is linearly dependent by definition and thus disallowed).
The purpose of this condition is to ensure that the group has a compact fundamental domain, or in other words, a "cell" of nonzero, finite area, which is repeated through the plane. Without this condition, one might have for example a group containing the translation T x for every rational number x , which would not correspond to any reasonable wallpaper pattern.
One important and nontrivial consequence of the discreteness condition in combination with the independent translations condition is that the group can only contain rotations of order 2, 3, 4, or 6; that is, every rotation in the group must be a rotation by 180°, 120°, 90°, or 60°. This fact is known as the crystallographic restriction theorem , [ 3 ] and can be generalised to higher-dimensional cases.
Crystallography has 230 space groups to distinguish, far more than the 17 wallpaper groups, but many of the symmetries in the groups are the same. Thus one can use a similar notation for both kinds of groups, that of Carl Hermann and Charles-Victor Mauguin . An example of a full wallpaper name in Hermann-Mauguin style (also called IUCr notation ) is p 31 m , with four letters or digits; more usual is a shortened name like cmm or pg .
For wallpaper groups the full notation begins with either p or c , for a primitive cell or a face-centred cell ; these are explained below. This is followed by a digit, n , indicating the highest order of rotational symmetry: 1-fold (none), 2-fold, 3-fold, 4-fold, or 6-fold. The next two symbols indicate symmetries relative to one translation axis of the pattern, referred to as the "main" one; if there is a mirror perpendicular to a translation axis that is the main one (or if there are two, one of them). The symbols are either m , g , or 1 , for mirror, glide reflection, or none. The axis of the mirror or glide reflection is perpendicular to the main axis for the first letter, and either parallel or tilted 180°/ n (when n > 2) for the second letter. Many groups include other symmetries implied by the given ones. The short notation drops digits or an m that can be deduced, so long as that leaves no confusion with another group.
A primitive cell is a minimal region repeated by lattice translations. All but two wallpaper symmetry groups are described with respect to primitive cell axes, a coordinate basis using the translation vectors of the lattice. In the remaining two cases symmetry description is with respect to centred cells that are larger than the primitive cell, and hence have internal repetition; the directions of their sides is different from those of the translation vectors spanning a primitive cell. Hermann-Mauguin notation for crystal space groups uses additional cell types.
Here are all the names that differ in short and full notation.
The remaining names are p 1 , p 2 , p 3 , p 3 m 1 , p 31 m , p 4 , and p 6 .
Orbifold notation for wallpaper groups, advocated by John Horton Conway (Conway, 1992) (Conway 2008), is based not on crystallography, but on topology. One can fold the infinite periodic tiling of the plane into its essence, an orbifold , then describe that with a few symbols.
The group denoted in crystallographic notation by cmm will, in Conway's notation, be 2*22 . The 2 before the * says there is a 2-fold rotation centre with no mirror through it. The * itself says there is a mirror. The first 2 after the * says there is a 2-fold rotation centre on a mirror. The final 2 says there is an independent second 2-fold rotation centre on a mirror, one that is not a duplicate of the first one under symmetries.
The group denoted by pgg will be 22× . There are two pure 2-fold rotation centres, and a glide reflection axis. Contrast this with pmg , Conway 22* , where crystallographic notation mentions a glide, but one that is implicit in the other symmetries of the orbifold.
Coxeter 's bracket notation is also included, based on reflectional Coxeter groups , and modified with plus superscripts accounting for rotations, improper rotations and translations.
An orbifold can be viewed as a polygon with face, edges, and vertices which can be unfolded to form a possibly infinite set of polygons which tile either the sphere , the plane or the hyperbolic plane . When it tiles the plane it will give a wallpaper group and when it tiles the sphere or hyperbolic plane it gives either a spherical symmetry group or Hyperbolic symmetry group . The type of space the polygons tile can be found by calculating the Euler characteristic , χ = V − E + F , where V is the number of corners (vertices), E is the number of edges and F is the number of faces. If the Euler characteristic is positive then the orbifold has an elliptic (spherical) structure; if it is zero then it has a parabolic structure, i.e. a wallpaper group; and if it is negative it will have a hyperbolic structure. When the full set of possible orbifolds is enumerated it is found that only 17 have Euler characteristic 0.
When an orbifold replicates by symmetry to fill the plane, its features create a structure of vertices, edges, and polygon faces, which must be consistent with the Euler characteristic. Reversing the process, one can assign numbers to the features of the orbifold, but fractions, rather than whole numbers. Because the orbifold itself is a quotient of the full surface by the symmetry group, the orbifold Euler characteristic is a quotient of the surface Euler characteristic by the order of the symmetry group.
The orbifold Euler characteristic is 2 minus the sum of the feature values, assigned as follows:
For a wallpaper group, the sum for the characteristic must be zero; thus the feature sum must be 2.
Now enumeration of all wallpaper groups becomes a matter of arithmetic, of listing all feature strings with values summing to 2.
Feature strings with other sums are not nonsense; they imply non-planar tilings, not discussed here. (When the orbifold Euler characteristic is negative, the tiling is hyperbolic ; when positive, spherical or bad ).
To work out which wallpaper group corresponds to a given design, one may use the following table. [ 4 ]
See also this overview with diagrams .
Each of the groups in this section has two cell structure diagrams, which are to be interpreted as follows (it is the shape that is significant, not the colour):
On the right-hand side diagrams, different equivalence classes of symmetry elements are colored (and rotated) differently.
The brown or yellow area indicates a fundamental domain , i.e. the smallest part of the pattern that is repeated.
The diagrams on the right show the cell of the lattice corresponding to the smallest translations; those on the left sometimes show a larger area.
The two translations (cell sides) can each have different lengths, and can form any angle.
(The first three have a vertical symmetry axis, and the last two each have a different diagonal one.)
Without the details inside the zigzag bands the mat is pmg ; with the details but without the distinction between brown and black it is pgg .
Ignoring the wavy borders of the tiles, the pavement is pgg .
The rotational symmetry of order 2 with centres of rotation at the centres of the sides of the rhombus is a consequence of the other properties.
The pattern corresponds to each of the following:
A p 4 pattern can be looked upon as a repetition in rows and columns of equal square tiles with 4-fold rotational symmetry. Also it can be looked upon as a checkerboard pattern of two such tiles, a factor √ 2 smaller and rotated 45°.
This corresponds to a straightforward grid of rows and columns of equal squares with the four reflection axes. Also it corresponds to a checkerboard pattern of two of such squares.
Examples displayed with the smallest translations horizontal and vertical (like in the diagram):
Examples displayed with the smallest translations diagonal:
A p 4 g pattern can be looked upon as a checkerboard pattern of copies of a square tile with 4-fold rotational symmetry, and its mirror image. Alternatively it can be looked upon (by shifting half a tile) as a checkerboard pattern of copies of a horizontally and vertically symmetric tile and its 90° rotated version. Note that neither applies for a plain checkerboard pattern of black and white tiles, this is group p 4 m (with diagonal translation cells).
Imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one orientation, and the other half upside down. This wallpaper group corresponds to the case that all triangles of the same orientation are equal, while both types have rotational symmetry of order three, but the two are not equal, not each other's mirror image, and not both symmetric (if the two are equal it is p 6 , if they are each other's mirror image it is p 31 m , if they are both symmetric it is p 3 m 1 ; if two of the three apply then the third also, and it is p 6 m ). For a given image, three of these tessellations are possible, each with rotation centres as vertices, i.e. for any tessellation two shifts are possible. In terms of the image: the vertices can be the red, the blue or the green triangles.
Equivalently, imagine a tessellation of the plane with regular hexagons, with sides equal to the smallest translation distance divided by √ 3 . Then this wallpaper group corresponds to the case that all hexagons are equal (and in the same orientation) and have rotational symmetry of order three, while they have no mirror image symmetry (if they have rotational symmetry of order six it is p 6 , if they are symmetric with respect to the main diagonals it is p 31 m , if they are symmetric with respect to lines perpendicular to the sides it is p 3 m 1 ; if two of the three apply then the third also, it is p 6 m ). For a given image, three of these tessellations are possible, each with one third of the rotation centres as centres of the hexagons. In terms of the image: the centres of the hexagons can be the red, the blue or the green triangles.
Like for p 3 , imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one orientation, and the other half upside down. This wallpaper group corresponds to the case that all triangles of the same orientation are equal, while both types have rotational symmetry of order three, and both are symmetric, but the two are not equal, and not each other's mirror image. For a given image, three of these tessellations are possible, each with rotation centres as vertices. In terms of the image: the vertices can be the red, the blue or the green triangles.
Like for p 3 and p 3 m 1 , imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one orientation, and the other half upside down. This wallpaper group corresponds to the case that all triangles of the same orientation are equal, while both types have rotational symmetry of order three and are each other's mirror image, but not symmetric themselves, and not equal. For a given image, only one such tessellation is possible. In terms of the image: the vertices must be the red triangles, not the blue triangles.
A pattern with this symmetry can be looked upon as a tessellation of the plane with equal triangular tiles with C 3 symmetry, or equivalently, a tessellation of the plane with equal hexagonal tiles with C 6 symmetry (with the edges of the tiles not necessarily part of the pattern).
A pattern with this symmetry can be looked upon as a tessellation of the plane with equal triangular tiles with D 3 symmetry, or equivalently, a tessellation of the plane with equal hexagonal tiles with D 6 symmetry (with the edges of the tiles not necessarily part of the pattern). Thus the simplest examples are a triangular lattice with or without connecting lines, and a hexagonal tiling with one color for outlining the hexagons and one for the background.
There are five lattice types or Bravais lattices , corresponding to the five possible wallpaper groups of the lattice itself. The wallpaper group of a pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself.
The actual symmetry group should be distinguished from the wallpaper group. Wallpaper groups are collections of symmetry groups. There are 17 of these collections, but for each collection there are infinitely many symmetry groups, in the sense of actual groups of isometries. These depend, apart from the wallpaper group, on a number of parameters for the translation vectors, the orientation and position of the reflection axes and rotation centers.
The numbers of degrees of freedom are:
However, within each wallpaper group, all symmetry groups are algebraically isomorphic.
Some symmetry group isomorphisms:
Note that when a transformation decreases symmetry, a transformation of the same kind (the inverse) obviously for some patterns increases the symmetry. Such a special property of a pattern (e.g. expansion in one direction produces a pattern with 4-fold symmetry) is not counted as a form of extra symmetry.
Change of colors does not affect the wallpaper group if any two points that have the same color before the change, also have the same color after the change, and any two points that have different colors before the change, also have different colors after the change.
If the former applies, but not the latter, such as when converting a color image to one in black and white, then symmetries are preserved, but they may increase, so that the wallpaper group can change.
Several software graphic tools will let you create 2D patterns using wallpaper symmetry groups. Usually you can edit the original tile and its copies in the entire pattern are updated automatically.
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https://en.wikipedia.org/wiki/Wallpaper_group
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The Walls of Ston ( Croatian : Stonske zidine ) are a series of defensive stone walls , originally more than 7 kilometres (4.3 mi) long, that surrounded and protected the city of Ston , in Dalmatia , part of the Republic of Ragusa , in what is now southern Croatia . [ 1 ] Their construction was begun in 1358. [ 2 ] On the Field Gate of the Walls ( Poljska vrata ) there is a Latin inscription which dates from 1506. Today, it is among the longest preserved fortification systems in the world. [ 3 ]
The Walls of Ston were known as the "European Great Wall of China ". [ 4 ]
Despite being well protected by massive city walls, the Republic of Ragusa used Pelješac to build another line of defence. [ 5 ] At its narrowest point, just before it joins the mainland, a wall was built from Ston to Mali Ston . [ 5 ] Throughout the era of the Republic, the walls were maintained and renovated once they meant to protect the precious salt pans that contributed to Dubrovnik's wealth, which are still being worked today.
Demolition work began on the walls following the fall of the Republic. Later the Austrian authorities took materials away from the wall to build schools and community buildings, and also for a triumphal arch on the occasion of the visit by the Austrian Emperor in 1884. The wall around Mali Ston was demolished with the excuse that it was damaging the health of the people. The demolition was halted after World War II.
The wall, today 5.5 kilometres long, links Ston to Mali Ston, and is in the shape of an irregular pentangle. It was completed in the 15th century, along with its 40 towers (20 of which have survived) and 5 fortresses. Within, three streets were laid from north to south and three others from east to west. Thus, fifteen equal blocks were formed with 10 houses in each. Residential buildings around the edges. The Gothic Republic Chancellery and the Bishop's Palace are outstanding among the public buildings.
The main streets are 6 m wide (except the southern street which is 8 m wide) and the side streets are two m wide. The town was entered by two city gates: the Field Gate ( Poljska vrata ) has a Latin inscription and dates from 1506. The centres of the system are the fortress Veliki kaštio in Ston, Koruna in Mali Ston and the fortress on Podzvizd hill (224 m). Noted artist who work on the walls project are Michelozzo , Bernardino Gatti of Parma and Giorgio da Sebenico (Juraj Dalmatinac). [ 6 ]
The city plan of Dubrovnik was used as a model for Ston, but since Ston was built on prepared terrain, that model was more closely followed than Dubrovnik itself.
Ian Plummer (USA) currently holds the world record for fastest run over the wall connecting Ston to Mali Ston. The record was set on June 15, 2019. While the female record was set by Cora Taylor (UK) on July 8, 2019.
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https://en.wikipedia.org/wiki/Walls_of_Ston
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Ernst Hjalmar Waloddi Weibull (18 June 1887 – 12 October 1979) was a Swedish civil engineer , materials scientist , and applied mathematician . The Weibull distribution is named after him.
Weibull joined the Swedish Coast Guard in 1905 as a midshipman. He moved up the ranks with promotion to sublieutenant in 1907, Captain in 1916 and Major in 1940. While in the coast guard he took courses at the Royal Institute of Technology . In 1924 he graduated and became a full professor. [ 1 ] He obtained his doctorate from the University of Uppsala in 1932. [ 1 ] He was employed in Swedish and German industry as a consulting engineer.
In 1914, while on expeditions to the Mediterranean , the Caribbean and the Pacific Ocean on the research ship Albatross , Weibull wrote his first paper on the propagation of explosive waves. He developed the technique of using explosive charges to determine the type of ocean bottom sediments and their thickness. [ 3 ] The same technique is still used today in offshore oil exploration .
In 1939 he published his paper on the Weibull distribution in probability theory and statistics. [ 4 ] [ 1 ] In 1941 he received a personal research professorship in Engineering Physics at the Royal Institute of Technology in Stockholm from the arms producer Bofors . [ 1 ]
Weibull published many papers on strength of materials , fatigue , rupture in solids, bearings , and of course, the Weibull distribution , as well as one book on fatigue analysis in 1961. [ 2 ] [ 5 ] 27 of these papers were reports to the US Air Force at Wilbur Wright Field on Weibull analysis.
In 1951 he presented his paper on the Weibull distribution to the American Society of Mechanical Engineers (ASME), using seven case studies.
The American Society of Mechanical Engineers awarded Weibull their gold medal in 1972. The Great Gold Medal from the Royal Swedish Academy of Engineering Sciences was personally presented to him by King Carl XVI Gustaf of Sweden in 1978. [ 1 ]
Weibull came from a family that had strong ties to Scania . He was a cousin of the historian brothers Lauritz , Carl Gustaf and Curt Weibull . Weibull died on 12 October 1979 in Annecy , France. [ 2 ]
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Walsh diagrams , often called angular coordinate diagrams or correlation diagrams , are representations of calculated orbital binding energies of a molecule versus a distortion coordinate (bond angles), used for making quick predictions about the geometries of small molecules. [ 1 ] [ 2 ] By plotting the change in molecular orbital levels of a molecule as a function of geometrical change, Walsh diagrams explain why molecules are more stable in certain spatial configurations (e.g. why water adopts a bent conformation). [ 3 ]
A major application of Walsh diagrams is to explain the regularity in structure observed for related molecules having identical numbers of valence electrons (e.g. why H 2 O and H 2 S look similar), and to account for how molecules alter their geometries as their number of electrons or spin state changes. Additionally, Walsh diagrams can be used to predict distortions of molecular geometry from knowledge of how the LUMO (Lowest Unoccupied Molecular Orbital) affects the HOMO (Highest Occupied Molecular Orbital) when the molecule experiences geometrical perturbation.
Walsh's rule for predicting shapes of molecules states that a molecule will adopt a structure that best provides the most stability for its HOMO. If a particular structural change does not perturb the HOMO, the closest occupied molecular orbital governs the preference for geometrical orientation. [ 4 ]
Walsh diagrams were first introduced by A.D. Walsh , a British chemistry professor at the University of Dundee , in a series of ten papers in one issue of the Journal of the Chemical Society . [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states , by applying theoretical contributions made by Mulliken . Specifically, Walsh calculated and explained the effect of changes in the shape of a molecule on the energy of molecular orbitals. Walsh diagrams are an illustration of such dependency, and his conclusions are what are referred to as the "rules of Walsh." [ 15 ]
In his publications, Walsh showed through multiple examples that the geometry adopted by a molecule in its ground state primarily depends on the number of its valence electrons. [ 16 ] He himself acknowledged that this general concept was not novel, but explained that the new data available to him allowed the previous generalizations to be expanded upon and honed. He also noted that Mulliken had previously attempted to construct a correlation diagram for the possible orbitals of a polyatomic molecule in two different nuclear configurations, and had even tried to use this diagram to explain shapes and spectra of molecules in their ground and excited states. [ 17 ] [ 18 ] However, Mulliken was unable to explain the reasons for the rises and falls of certain curves with increases in angle, thus Walsh claimed "his diagram was either empirical or based upon unpublished computations." [ 5 ]
Walsh originally constructed his diagrams by plotting what he described as "orbital binding energies" versus bond angles . What Walsh was actually describing by this term is unclear; some believe he was in fact referring to ionization potentials , however this remains a topic of debate. [ 19 ] At any rate, the general concept he put forth was that the total energy of a molecule is equal to the sum of all of the "orbital binding energies" in that molecule. Hence, from knowledge of the stabilization or destabilization of each of the orbitals by an alteration of the molecular bond angle, the equilibrium bond angle for a particular state of the molecule can be predicted. Orbitals which interact to stabilize one configuration (ex. Linear) may or may not overlap in another configuration (ex. Bent), thus one geometry will be calculably more stable than the other.
Typically, core orbitals (1s for B, C, N, O, F, and Ne) are excluded from Walsh diagrams because they are so low in energy that they do not experience a significant change by variations in bond angle. Only valence orbitals are considered. However, one should keep in mind that some of the valence orbitals are often unoccupied.
In preparing a Walsh diagram, the geometry of a molecule must first be optimized for example using the Hartree–Fock (HF) method [ 2 ] for approximating the ground-state wave function and ground-state energy of a quantum many-body system. [ 20 ] Next, single-point energies are performed for a series of geometries displaced from the above-determined equilibrium geometry. Single-point energies (SPEs) are calculations of potential energy surfaces of a molecule for a specific arrangement of the atoms in that molecule. In conducting these calculations, bond lengths remain constant (at equilibrium values) and only the bond angle should be altered from its equilibrium value. The single-point computation for each geometry can then be plotted versus bond angle to produce the representative Walsh diagram.
For the simplest AH 2 molecular system, Walsh produced the first angular correlation diagram by plotting the ab initio orbital energy curves for the canonical molecular orbitals while changing the bond angle from 90° to 180°. As the bond angle is distorted, the energy for each of the orbitals can be followed along the lines, allowing a quick approximation of molecular energy as a function of conformation. It is still unclear whether or not the Walsh ordinate considers nuclear repulsion, and this remains a topic of debate. [ 21 ] A typical prediction result for water is a bond angle of 90°, which is not even close to the experimental derived value of 104°. At best the method is able to differentiate between a bent and linear molecule. [ 2 ]
This same concept can be applied to other species including non-hydride AB 2 and BAC molecules, HAB and HAAH molecules, tetraatomic hydride molecules (AH 3 ), tetraatomic nonhydride molecules (AB), H 2 AB molecules, acetaldehyde , pentaatomic molecules (CH3I), hexatomic molecules ( ethylene ), and benzene .
Walsh diagrams in conjunction with molecular orbital theory can also be used as a tool to predict reactivity. By generating a Walsh Diagram and then determining the HOMO/LUMO of that molecule, it can be determined how the molecule is likely to react. In the following example, the Lewis acidity of AH 3 molecules such as BH 3 and CH 3 + is predicted.
Six electron AH 3 molecules should have a planar conformation. It can be seen that the HOMO, 1e’, of planar AH 3 is destabilized upon bending of the A-H bonds to form a pyramid shape, due to disruption of bonding. The LUMO, which is concentrated on one atomic center, is a good electron acceptor and explains the Lewis acid character of BH 3 and CH 3 + . [ 22 ]
Walsh correlation diagrams can also be used to predict relative molecular orbital energy levels. The distortion of the hydrogen atoms from the planar CH 3 + to the tetrahedral CH 3 -Nu causes a stabilization of the C-Nu bonding orbital, σ. [ 22 ]
Other correlation diagrams are Tanabe-Sugano diagrams and Orgel diagrams .
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Walter Liese (31 January 1926 – 24 February 2023) was a German forestry and wood researcher and wood biologist. [ 1 ] [ 2 ] [ 3 ]
Liese was born in Berlin on 31 January 1926, and grew up in Eberswalde . He studied forestry at the University of Freiburg and the University of Göttingen . He obtained his PhD in 1951 under Prof. Herbert Zycha.
In 1963, Liese became Professor at the University of Hamburg . He searched about the wood and bark anatomy, wood quality, bamboo and many other subjects, having more than 500 publications. In 1991, he became an Emeritus professor. He was also honorary member of the Association of German Wood Scientists ( Bund Deutscher Holzwirte ) and an elected member in the International Academy of Wood Science (IAWS). [ 4 ]
Liese was the co-editor of many scientific journals, e.g.:
Liese died on 24 February 2023, at the age of 97. [ 5 ]
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Walter Cox McCrone Jr. (June 9, 1916 – July 10, 2002) was an American chemist who worked extensively on applications of polarized light microscopy and is sometimes characterized as the "father of modern microscopy ". [ 1 ] [ 2 ] He was also an expert in electron microscopy , crystallography , ultra- microanalysis , and particle identification. In 1960 he founded the McCrone Research Institute , a non-profit educational and research organization for microscopy based in Chicago .
McCrone's crystallographic work on polymorphism and its pharmaceutical applications played a central role in the subsequent development of the field. [ 3 ] To the general public, McCrone was best known for his work in forensic science , especially his analyses of the Vinland Map and the Shroud of Turin . In 2000, he received the American Chemical Society 's National Award in Analytical Chemistry . [ 4 ] [ 5 ]
Walter McCrone was born in Wilmington, Delaware , but he grew up mostly in New York State . [ 2 ] His father was a civil engineer in charge of one of the first DuPont plants to manufacture cellophane . [ 6 ] McCrone received a bachelor's degree in chemistry from Cornell University in 1938 and a Ph.D. in organic chemistry from the same institution in 1942. From 1942 to 1944 he was a post-doctoral researcher at Cornell. In 1944, McCrone published a detailed study on The Microscopic Examination of High Explosives and Boosters . [ 7 ]
In 1944, McCrone began to work as a microscopist and materials scientist at the Armour Research Foundation , now the Illinois Institute of Technology (IIT) Research Institute. [ 2 ] He was also a professor at IIT and served as assistant chairman of its Chemistry and Chemical Engineering Department. [ 8 ] In 1948, McCrone and IIT electron microscopist Charles F. Tufts organized the first of the meetings that are now the International Microscopy Conference (Inter/Micro). Among the speakers at the first conference was Nobel laureate Frits Zernike . [ 9 ]
In 1956, McCrone left IIT and founded an analytical consulting firm, McCrone Associates, which is now located in Westmont, Illinois . In 1960, he established the McCrone Research Institute , a nonprofit organization for teaching and research in microscopy and crystallography, based in Chicago . In 1979, he retired from McCrone Associates in order to dedicate himself to teaching full time. [ 10 ] The proceeds from his work as a consulting chemist allowed McCrone to endow the Émile M. Chamot Professorship of Chemistry at Cornell, named in honor of McCrone's university mentor. [ 2 ] According to chemist and forensic scientist John A. Reffner, "during McCrone's life, he taught microscopy to more students than anyone else in history". [ 11 ]
For more than thirty years McCrone edited and published The Microscope , an international quarterly journal of microscopy that had been established in 1937 by the British microscopist Arthur L. E. Barron. [ 9 ] McCrone also wrote more than 400 technical articles along with sixteen books or chapters. [ 12 ] He is credited with expanding the usefulness of the optical microscopy to chemists, who had previously regarded it as primarily a tool for biologists . [ 5 ] One of his publications was the Particle Atlas , first published in 1967, which provided an exhaustive description of small particles and how to identify them with the aid of a microscope. That work became widely used in forensic laboratories. [ 7 ] The Particle Atlas , which was written in collaboration with other staff members of McCrone Associates, appeared in a six-volume second edition in 1973. In 1992, it became available in CD-ROM . [ 8 ] [ 12 ]
Walter McCrone served on the board of directors and as president of the Ada S. McKinley Community Services, a nonprofit social services agency in Chicago. [ 8 ] He died of congestive heart failure at his home in Chicago, at the age of 86. [ 12 ] From 1957 until his death in 2002, he was married to Lucy B. McCrone, née Beman. The two had met while she was working as an analytical chemist for the management consulting firm Arthur D. Little , in Cambridge, Massachusetts . After their marriage, Lucy McCrone worked as a chemical microanalyst for McCrone Associates in Chicago and was co-founder and director of the McCrone Research Institute until 1984. [ 9 ]
In the 1950s and 1960s, McCrone conducted extensive research on the microscopic characterization of polymorphs , which he defined as materials that are "different in crystal structure but identical in the liquid or vapor states". [ 13 ] He investigated the difference in the properties of polymorphs of medications , co-authoring with John Haleblian a review article on "the pharmaceutical application of polymorphism", published in 1969. [ 14 ] McCrone's work on polymorphism exerted a strong influence upon the scientific career of Joel Bernstein. [ 15 ]
The Vinland Map appears to be a 15th-century mappa mundi showing a landmass in the Atlantic Ocean , directly south-west of Greenland , labelled Vinlanda Insula ("Isle of Vinland "). It first came to light in 1957 and was acquired by Yale University in 1964. The map's authenticity would have demonstrated the awareness of European catographers of a part of the American continent , before the voyages of Christopher Columbus . McCrone, already reputed for his expertise in authenticating ancient documents and works of art, was asked by Yale to analyze the map in 1972. In 1974, he published evidence that the ink of the map contained synthetic anatase (a form of titanium dioxide ), a substance not used as a pigment until the 1920s. McCrone detected the anatase in the yellow ink that the forger used to simulate the natural discoloration that appears over long periods of time around lines drawn on parchment in medieval iron gall ink . [ 16 ] [ 17 ]
McCrone's work on the Vinland Map led to a protracted controversy, with other researchers continuing to argue for the document's authenticity and discounting the presence of anatase as insignificant. In 2021, Raymond Clemens, the curator of early books and manuscripts at Yale's Beinecke Rare Book & Manuscript Library where the map is housed, declared that it had been conclusively shown to be a fake. [ 18 ] That judgment was largely based on the presence of synthetic anatase in the ink, as first identified by McCrone. [ 19 ]
As a result of McCrone's work on the Vinland Map, British author and researcher Ian Wilson approached McCrone in 1974 about the possibility of scientifically analyzing the Shroud of Turin , a length of linen cloth that has been venerated for centuries as the burial shroud of Jesus upon which his image is miraculously imprinted. [ 16 ] This led to McCrone's involvement with the Shroud of Turin Research Project (STURP). In 1977, a team of scientists affiliated with STURP proposed a barrage of tests to be carried out on the Shroud. With permission from the Archbishop of Turin , Cardinal Anastasio Ballestrero , STURP researchers conducted tests over a period of five days in October 1978, also using adhesive tape to obtain samples of the fibers from various parts on the Shroud's surface. [ 10 ]
Based on his microscopic and chemical analysis of the tape samples obtained by STURP, McCrone concluded that the image on the Shroud was painted with a dilute pigment of red ochre in a collagen tempera (i.e., gelatin ) medium, using a technique similar to the grisaille employed in the 14th century by Simone Martini and other European artists. McCrone also found that the "bloodstains" in the image had been highlighted with vermilion (a bright red pigment made from mercury sulfide ), also in a collagen tempera medium. McCrone reported that no actual blood was present in the samples taken from the Shroud. [ 16 ] [ 17 ]
McCrone's results were rejected by other members of STURP and McCrone resigned from STURP in June 1980. Two other members of STURP, John Heller and Alan Adler, published their own analysis concluding that Shroud did show traces of blood. [ 20 ] [ 21 ] Other STURP members also disputed McCrone's conclusion that the Shroud image was painted, finding that physical analyses excluded the presence of pigments in sufficient quantities to account for the visible image. [ 22 ]
McCrone continued to defend his results and to insist that polarized light microscopy , in which he was the only expert among the original members of STURP, was the correct technique to apply to the study of the Shroud. [ 10 ] In 1983, he confidently predicted that radiocarbon dating of the Shroud's linen would show that it had been made shortly before the first historically recorded exhibition of the Shroud in 1356. [ 23 ] [ 24 ] [ 25 ] : 246 The results of the 1988 radiocarbon dating of the Shroud vindicated McCrone's microscopic and chemical analyses. [ 8 ] [ 7 ] [ 17 ]
McCrone re-stated and summarized his evidence that the Shroud was painted in an article published in 1990 in the journal Accounts of Chemical Research . [ 10 ] He later wrote a book on the subject, Judgment Day for the Shroud of Turin , published in 1996 by the McCrone Research Institute's Microscope Publications and re-issued in 1999 by Prometheus Books . [ 25 ] In 2000, the American Chemical Society presented McCrone with its National Award in Analytical Chemistry for his work on the Shroud and for "his enduring patience for the defense of his methodologies". [ 2 ]
McCrone's work as a microscopist first attracted widespread public attention when he helped exonerate Lloyd Eldon Miller, a cabdriver who had been sentenced to death for the 1955 murder of an 8-year-old girl in Canton, Illinois . McCrone was able to show that the stains in a pair of undershorts that the prosecution had presented to the jury as blood were actually red paint. [ 6 ] Miller's conviction was overturned by the US Supreme Court in 1967. In later life, McCrone microscopically examined the physical evidence (hairs, fibers, blood, etc.) that led to the conviction of Wayne Williams as the Atlanta child killer . That work earned him the 1982 Certificate of Merit from the Forensic Sciences Foundation. [ 26 ]
On occasion, McCrone was given hair samples of famous people to analyze. Based on such analysis, he rejected the hypothesis that Napoleon had been poisoned with arsenic , but concluded that Beethoven had suffered from lead poisoning . [ 27 ]
The executive council of the Committee for Skeptical Inquiry (CSI) voted in April 2011 to include Walter McCrone in its "Pantheon of Skeptics". The Pantheon of Skeptics commemorates deceased distinguished fellows of CSI and their exceptional contributions to the cause of scientific skepticism . [ 28 ]
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Walter Sidney Metcalf (18 May 1918 – 25 July 2008) was a New Zealand physical chemist . [ 2 ]
Metcalf was born in Kaitangata on 18 May 1918, the son of George Metcalf, and was educated at Napier Boys' High School . [ 3 ] He earned a bachelor's degree in music in parallel with his first science degree at the University of Otago , [ 4 ] and completed a DPhil degree with E. J. Bowen at England's Oxford University .
Metcalf married Mary Glen Simmers, and the couple went on to have two children. [ 3 ]
Metcalf initially worked at Victoria University College , then moved to Canterbury University College (now the University of Canterbury ) in 1954. He retired as a reader in 1975. He worked mainly on photochemistry and was awarded the T. K. Sidey Medal by the Royal Society of New Zealand for his research in 1966. [ 5 ] Towards the end of his career, he worked on calcium metabolism .
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Walter Rüdorff (October 3, 1909 – April 1, 1989) was a German chemist known for his research on clathrates of graphite [ 1 ] and ternary oxides . [ 2 ] [ 3 ]
Rüdorff was born in Berlin in 1909. He studied chemistry as an undergraduate at Technische Hochschule Berlin (now Technische Universität Berlin ) and graduated in 1925. His graduate study was carried out under the supervision of Ulrich Hofmann at the same university, where he graduated with a PhD thesis titled Über die Kristallstruktur der Hexacarbonyle von Chrom, Molybdän und Wolfram . He then moved to the University of Rostock along with Ulrich Hofmann and achieved his habilitation status with the thesis titled Neuartige Verbindungen mit Graphit in 1941. In 1942, Rüdorff moved to TU Wien following Ulrich Hofmann . He later took up a faculty position at University of Tübingen in 1947. He stayed in Tübingen until his retirement. [ 3 ]
Along with his supervisor Ulrich Hofmann and his father Karl Andreas Hofmann , Rüdorff cowrote the famous textbook on inorganic chemistry [ 4 ] that are referred to as Rüdorff-Hofmann . [ 3 ]
Rüdorff and Ulrich Hofmann 's work on graphite intercalation compound and sulfuric acid [ 5 ] became an ancestor of lithium-ion battery. [ 6 ]
Rüdorff's team discovered the ternary oxide series (including LiVO 2 and NaVO 2 ) in 1954 [ 7 ] with a unique structure. The compounds with the same structural type are called rudorffites for this reason. [ 8 ]
Rüdorff's work in 1965 on hosting lithium in titanium disulfide (TiS 2 ) inspired early efforts into using metal chalcogenides as battery cathode material. [ 9 ]
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Walter Seelmann-Eggebert (17 April 1915 – 19 July 1988) was a German radiochemist. He was son of Erich Eggebert and Edwig Schmidt.
He was a student of Otto Hahn at the Kaiser Wilhelm Institute for Chemistry , where, after 1939, he worked with Fritz Strassmann on nuclear fission .
In 1949, he joined the University of Tucuman in Argentina as a professor of chemistry. Later he created the radiochemistry group at the Buenos Aires University and at the National Atomic Energy Commission , working together with other notable pioneers of radiochemistry, such as Sara Abecasis, Gregorio Baro , Juan Flegenheimer, Jaime Pahissa-Campá, María Cristina Palcos, Enzo Ricci, Renato Radicella, Plinio Rey, Josefina Rodríguez, and Maela Viirsoo, just to mention a few. During his Argentinian years his group discovered 20 new nuclides .
In 1955, Otto Hahn invited him to come back to Germany for the reconstruction of radiochemistry studies in the country. He became professor in Mainz before creating and managing the Radiochemistry Institute from the Karlsruhe Kernforschungszentrum, now the Karlsruhe Institute of Technology (KIT).
In 1958, together with Gerda Pfennig , he edited the first " Karlsruher Nuklidkarte " which has become a basic element both for nuclear scientists and education.
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Walter Thiel (7 March 1949 in Treysa , Hesse – 23 August 2019) [ 2 ] was a German theoretical chemist . [ 1 ] He was the president of the World Association of Theoretical and Computational Chemists (WATOC) from 2011. [ 3 ]
Thiel studied chemistry at the University of Marburg (West Germany) from 1966 to 1971, where he subsequently obtained his doctorate with Armin Schweig in 1973. [ 2 ] [ 1 ] After a post-doctoral stint at the University of Texas at Austin with M. J. S. Dewar (1973–1975), [ 2 ] [ 1 ] he obtained his habilitation from the University of Marburg in 1981. [ 2 ] [ 1 ] He was appointed Professor of Theoretical Chemistry at the University of Wuppertal (West Germany) in 1983 and Professor of Chemistry at the University of Zurich ( Switzerland ) in 1992. [ 2 ] [ 1 ] In 1987 he was a visiting professor at the University of California at Berkeley . [ 2 ] [ 1 ] Since 1999, he was a director at the Max Planck Institute for Coal Research in Mülheim an der Ruhr (Germany) and an honorary professor at the neighboring University of Düsseldorf (Germany) since 2001. [ 2 ] [ 1 ]
Thiel's research interests included the broad areas of theoretical chemistry , in particular quantum chemistry , and computational chemistry , with a focus on large molecules, spectroscopy , and catalysis . [ 1 ] His group was involved in the development of new theoretical methods, in particular for the treatment of large molecules, and applied theoretical calculations to concrete chemical problems, usually in close collaboration with experimentalists. [ 1 ]
Selected methodological contributions
Selected application areas
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Walter John Whiteley is a professor in the department of mathematics and statistics at York University in Canada. [ 1 ] He specializes in geometry and mathematics education , and is known for his expertise in structural rigidity and rigidity matroids .
Whiteley graduated from Queen's University in 1966. [ 2 ] [ 3 ] He earned his Ph.D. in 1971 from the Massachusetts Institute of Technology , with a dissertation titled Logic and Invariant Theory supervised by Gian-Carlo Rota . [ 4 ] He worked as an instructor at Champlain College Saint-Lambert , with a joint appointment in mathematics and humanities, from 1972 until he joined the York University faculty in 1992. [ 2 ] [ 3 ]
In 2009, Whiteley won the Adrien Pouliot Award of the Canadian Mathematical Society for his contributions to mathematics education. [ 3 ] In August 2014, the Fields Institute at the University of Toronto hosted a workshop on rigidity theory and spatial reasoning, "inspired by the distinguished career of Professor Walter Whiteley". [ 5 ]
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Wanda Szmielew née Montlak (5 April 1918 – 27 August 1976) [ 1 ] was a Polish mathematical logician who first proved the decidability of the first-order theory of abelian groups . [ 1 ]
Wanda Montlak was born on 5 April 1918 in Warsaw . She completed high school in 1935 and married, taking the name Szmielew. In the same year she entered the University of Warsaw , where she studied logic under Adolf Lindenbaum , Jan Łukasiewicz , Kazimierz Kuratowski , and Alfred Tarski . Her research at this time included work on the axiom of choice , but it was interrupted by the 1939 Invasion of Poland . [ 1 ]
Szmielew became a surveyor during World War II , during which time she continued her research on her own, developing a decision procedure based on quantifier elimination for the theory of abelian groups. She also taught for the Polish underground. After the liberation of Poland, Szmielew took a position at the University of Łódź , which was founded in May 1945. In 1947, she published her paper on the axiom of choice, earned a master's degree from the University of Warsaw, and moved to Warsaw as a senior assistant. [ 1 ] [ 2 ]
In 1949 and 1950, Szmielew visited the University of California, Berkeley , where Tarski had found a permanent position after being exiled from Poland for the war. She
lived in the home of Tarski and his wife as Tarski's mistress, leaving her husband behind in Poland, [ 3 ] and completed a Ph.D. at Berkeley in 1950 under Tarski's supervision, with her dissertation consisting of her work on abelian groups. [ 1 ] [ 2 ] [ 4 ] For the 1955 journal publication of these results, Tarski convinced Szmielew to rephrase her work in terms of his theory of arithmetical functions, a decision that caused this work to be described by Solomon Feferman as "unreadable". [ 5 ] Later work by Eklof & Fischer (1972) re-proved Szmielew's result using more standard model-theoretic techniques. [ 5 ] [ 6 ]
Returning to Warsaw as an assistant professor, her interests shifted to the foundations of geometry . With Karol Borsuk , she published a text on the subject in 1955 (translated into English in 1960), and another monograph, published posthumously in 1981 and (in English translation) 1983. [ 1 ] [ 2 ]
She died of cancer on 27 August 1976 in Warsaw. [ 1 ]
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In dynamical systems and ergodic theory , the concept of a wandering set formalizes a certain idea of movement and mixing . When a dynamical system has a wandering set of non-zero measure, then the system is a dissipative system . This is the opposite of a conservative system , to which the Poincaré recurrence theorem applies. Intuitively, the connection between wandering sets and dissipation is easily understood: if a portion of the phase space "wanders away" during normal time-evolution of the system, and is never visited again, then the system is dissipative. The language of wandering sets can be used to give a precise, mathematical definition to the concept of a dissipative system. The notion of wandering sets in phase space was introduced by Birkhoff in 1927. [ citation needed ]
A common, discrete-time definition of wandering sets starts with a map f : X → X {\displaystyle f:X\to X} of a topological space X . A point x ∈ X {\displaystyle x\in X} is said to be a wandering point if there is a neighbourhood U of x and a positive integer N such that for all n > N {\displaystyle n>N} , the iterated map is non-intersecting:
A handier definition requires only that the intersection have measure zero . To be precise, the definition requires that X be a measure space , i.e. part of a triple ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} of Borel sets Σ {\displaystyle \Sigma } and a measure μ {\displaystyle \mu } such that
for all n > N {\displaystyle n>N} . Similarly, a continuous-time system will have a map φ t : X → X {\displaystyle \varphi _{t}:X\to X} defining the time evolution or flow of the system, with the time-evolution operator φ {\displaystyle \varphi } being a one-parameter continuous abelian group action on X :
In such a case, a wandering point x ∈ X {\displaystyle x\in X} will have a neighbourhood U of x and a time T such that for all times t > T {\displaystyle t>T} , the time-evolved map is of measure zero:
These simpler definitions may be fully generalized to the group action of a topological group . Let Ω = ( X , Σ , μ ) {\displaystyle \Omega =(X,\Sigma ,\mu )} be a measure space, that is, a set with a measure defined on its Borel subsets . Let Γ {\displaystyle \Gamma } be a group acting on that set. Given a point x ∈ Ω {\displaystyle x\in \Omega } , the set
is called the trajectory or orbit of the point x .
An element x ∈ Ω {\displaystyle x\in \Omega } is called a wandering point if there exists a neighborhood U of x and a neighborhood V of the identity in Γ {\displaystyle \Gamma } such that
for all γ ∈ Γ − V {\displaystyle \gamma \in \Gamma -V} .
A non-wandering point is the opposite. In the discrete case, x ∈ X {\displaystyle x\in X} is non-wandering if, for every open set U containing x and every N > 0, there is some n > N such that
Similar definitions follow for the continuous-time and discrete and continuous group actions.
A wandering set is a collection of wandering points. More precisely, a subset W of Ω {\displaystyle \Omega } is a wandering set under the action of a discrete group Γ {\displaystyle \Gamma } if W is measurable and if, for any γ ∈ Γ − { e } {\displaystyle \gamma \in \Gamma -\{e\}} the intersection
is a set of measure zero.
The concept of a wandering set is in a sense dual to the ideas expressed in the Poincaré recurrence theorem. If there exists a wandering set of positive measure, then the action of Γ {\displaystyle \Gamma } is said to be dissipative , and the dynamical system ( Ω , Γ ) {\displaystyle (\Omega ,\Gamma )} is said to be a dissipative system . If there is no such wandering set, the action is said to be conservative , and the system is a conservative system . For example, any system for which the Poincaré recurrence theorem holds cannot have, by definition, a wandering set of positive measure; and is thus an example of a conservative system.
Define the trajectory of a wandering set W as
The action of Γ {\displaystyle \Gamma } is said to be completely dissipative if there exists a wandering set W of positive measure, such that the orbit W ∗ {\displaystyle W^{*}} is almost-everywhere equal to Ω {\displaystyle \Omega } , that is, if
is a set of measure zero.
The Hopf decomposition states that every measure space with a non-singular transformation can be decomposed into an invariant conservative set and an invariant wandering set.
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The Wang 3300 was an minicomputer released by Wang Laboratories in 1971.
Model with machine time sharing created between Wang 4000 and Wang 2200 . [ 1 ] Wang's first computer, the Wang 3300, was an 8-bit integrated circuit general-purpose minicomputer designed to be the central processor for a multi-terminal time-sharing system . Byte-oriented, it also provided a number of double-byte operand memory commands. Core memory ranged from 4,096 to 65,536 bytes in 4,096-byte increments. [ 2 ] Up to 16 teletype terminals could be connect to one 3300. Wang claimed at the time that it was "the most easily operated minicomputer time-sharing system available" but it has become to be seen as a "false start" since programs, stored on paper tape, took up to 40 minutes to load and it only used the physical teletype terminals instead of CRTs . [ 3 ]
Development began after hiring Rick Bensene in June 1968. [ 4 ] The software was developed by PHI Computer Services, which Wang had purchased in 1968, on an IBM 360/65 emulating the 3300. [ 5 ] The product was announced in February 1969 [ 6 ] and shipped to its first customer on March 29, 1971. [ 7 ]
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The Wang 4000 was the first programmable computer system from Wang Laboratories , released in 1967. [ 1 ]
However, already in the spring of 1968, An Wang , seeing that he was not able to compete with the PDP-8 , focused on a new computer — model 3300 . [ 2 ] Allowed the use of peripheral devices, in particular printers . [ 3 ]
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Wang Yung-ching ( Chinese : 王永慶 ; pinyin : Wáng Yǒngqìng ; Pe̍h-ōe-jī : Ông Éng-khèng ; 18 January 1917 – 15 October 2008), also called YC Wang , was a Taiwanese businessman. He was best known for being the chairman of Formosa Plastics Corporation , one of Taiwan's foremost plastic manufacturing establishments until his retirement in June 2006, where he stepped down at the age of 89. [ 1 ]
In 2008, Forbes ranked him as the 178th richest person in the world with an estimated net worth of US$5.5 billion. [ 2 ]
Despite lacking any formal schooling beyond elementary school, [ 3 ] he was ranked 2nd in the Forbes list of Taiwan's Richest in 2008. [ 4 ]
Wang was born in Chyokutan jō, Shinden ku, Shinden shichō, Taihoku Chō (modern-day Chitan Village, Xindian District , New Taipei City ) in then-Japan-ruled-Taiwan . [ citation needed ]
In 1995, Wang signed a contract with Marco Terragni (chairman of Italproducts ) to create Inteplast, the biggest company in the world for the production of Cartonplast . [ citation needed ]
Wang served as the chairman of the board of Formosa Plastics Corporation , one of the largest plastic manufacturers in the world, until June 2006, when he stepped down at the age of 89. [ 5 ] He remained chairman of the boards of Nan Ya Plastics Corporation, Formosa Chemistry & Fibre Corporation, and Cyma Plywood & Lumber Co. Ltd, but indicated his intention to gradually resign from these positions to focus on his retirement. He was chairman of Ming-chi Institute of Technology, and Chang Gung Medical Foundation . After his death, Wang's position at Chang Gung was taken over by his younger brother Wang Yung-tsai , and then third wife Lee Pao-chu. [ 6 ] He had been a vocal supporter of the Three Links between Taiwan and Mainland China . [ 7 ]
Wang's first marriage was to Wang (née Guo) Yueh-lan, with whom he had no children. [ 8 ] His second marriage to Yang Chiao produced Wang's first child, making a total of five. [ 9 ] Wang later married a third time in 1935 to Lee Pao-chu. [ 10 ] Wang and Lee had another five children; Wang fathered a total of ten. [ 11 ] His eldest son from his second marriage with Yang Chiao, Winston Wang , founded Grace Semiconductor Manufacturing with Jiang Mianheng , the son of former Chinese Communist Party General Secretary Jiang Zemin in 2000. A daughter from his second marriage, Charlene Wang founded Taiwan-based First International Computer , Inc. Another daughter, Cher Wang , founded High Tech Computer (HTC) and VIA Technologies . Among the Wang siblings, Cher has come closest to rivaling her father's wealth. [ 12 ] In 2011, Forbes estimated Cher Wang's personal fortune at $8.8 billion, making her the wealthiest individual in Taiwan at the time. [ 13 ]
Wang passed away in his sleep on October 15, 2008 at his home in Short Hills, New Jersey . [ 14 ] He was 91 years old. [ 15 ]
The family struggles which followed his death led to the discovery that he had engaged in extensive tax evasion and had stashed billions of dollars offshore. [ 16 ]
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Wang Yung-tsai ( Chinese : 王永在 ; pinyin : Wáng Yǒngzài ; 24 January 1921 – 27 November 2014) was the younger brother of Wang Yung-ching , founder of Formosa Plastics Group . [ 1 ]
He was born in Chyokutan, Shinden Town, Bunsan District, Taihoku Prefecture , Japanese Taiwan (modern-day Xindian District , New Taipei ). [ 2 ]
Wang began his business career by founding a lumber company in 1948, which he closed ten years later to help run Formosa Plastics. [ 2 ]
In 1993, Wang was named director of Formosa Plastics' naphtha cracker, the sixth processing plant of its kind in Taiwan. [ 1 ] In 2002, Wang Yung-ching went into retirement, leaving Wang Yung-tsai in control of Formosa Plastics. [ 3 ] Both officially retired as chairmen in 2006, handing the conglomerate over to their children. [ 4 ]
In 2010, Wang Yung-tsai was named #10 wealthiest person in Taiwan by Forbes. [ 5 ] By 2014, Wang had dropped two spots to #12. [ 6 ]
Wang Yung-tsai had three children and a granddaughter named Megan Chen who now goes to TES, and one wife. [ 7 ] He was a fan of golf and would often wake up at 5 A.M to play. [ 8 ] He died on 27 November 2014 at the age of 93. [ 9 ] Wang's funeral was held on 14 December 2014. [ 10 ]
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In algebra and network theory , a Wang algebra is a commutative algebra A {\displaystyle A} , over a field or (more generally) a commutative unital ring , in which A {\displaystyle A} has two additional properties: (Rule i) For all elements x of A {\displaystyle A} , x + x = 0 (universal additive nilpotency of degree 1). (Rule ii) For all elements x of A {\displaystyle A} , x ⋅ x = 0 (universal multiplicative nilpotency of degree 1). [ 1 ] [ 2 ]
Rules (i) and (ii) were originally published by K. T. Wang (Wang Ki-Tung, 王 季同) in 1934 as part of a method for analyzing electrical networks. [ 3 ] From 1935 to 1940, several Chinese electrical engineering researchers published papers on the method. The original Wang algebra is the Grassman algebra over the finite field mod 2 . [ 1 ] At the 57th annual meeting of the American Mathematical Society , held on December 27–29, 1950, Raoul Bott and Richard Duffin introduced the concept of a Wang algebra in their abstract (number 144 t ) The Wang algebra of networks . They gave an interpretation of the Wang algebra as a particular type of Grassman algebra mod 2. [ 4 ] In 1969 Wai-Kai Chen used the Wang algebra formulation to give a unification of several different techniques for generating the trees of a graph . [ 5 ] The Wang algebra formulation has been used to systematically generate King-Altman directed graph patterns. Such patterns are useful in deriving rate equations in the theory of enzyme kinetics. [ 6 ]
According to Guo Jinhai, professor in the Institute for the History of Natural Sciences of the Chinese Academy of Sciences , Wang Ki Tung's pioneering method of analyzing electrical networks significantly promoted electrical engineering not only in China but in the rest of the world; the Wang algebra formulation is useful in electrical networks for solving problems involving topological methods, graph theory, and Hamiltonian cycles. [ 7 ]
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The Wang and Landau algorithm , proposed by Fugao Wang and David P. Landau , [ 1 ] is a Monte Carlo method designed to estimate the density of states of a system. The method performs a non-Markovian random walk to build the density of states by quickly visiting all the available energy spectrum. The Wang and Landau algorithm is an important method to obtain the density of states required to perform a multicanonical simulation .
The Wang–Landau algorithm can be applied to any system which is characterized by a cost (or energy) function. For instance,
it has been applied to the solution of numerical integrals [ 2 ] and the folding of proteins. [ 3 ] [ 4 ] The Wang–Landau sampling is related to the metadynamics algorithm. [ 5 ]
The Wang and Landau algorithm is used to obtain an estimate for the density of states of a system characterized by a cost function. It uses a non-Markovian stochastic process which asymptotically converges to a multicanonical ensemble . [ 1 ] (I.e. to a Metropolis–Hastings algorithm with sampling distribution inverse to the density of states) The major consequence is that this sampling distribution leads to a simulation where the energy barriers are invisible. This means that the algorithm visits all the accessible states (favorable and less favorable) much faster than a Metropolis algorithm. [ 6 ]
Consider a system defined on a phase space Ω {\displaystyle \Omega } , and a cost function, E, (e.g. the energy), bounded on a spectrum E ∈ Γ = [ E min , E max ] {\displaystyle E\in \Gamma =[E_{\min },E_{\max }]} , which has an associated density of states ρ ( E ) {\displaystyle \rho (E)} , which is to be estimated. The estimator is ρ ^ ( E ) ≡ exp ( S ( E ) ) {\displaystyle {\hat {\rho }}(E)\equiv \exp(S(E))} . Because Wang and Landau algorithm works in discrete spectra, [ 1 ] the spectrum Γ {\displaystyle \Gamma } is divided in N discrete values with a difference between them of Δ {\displaystyle \Delta } , such that
Given this discrete spectrum, the algorithm is initialized by:
The algorithm then performs a multicanonical ensemble simulation: [ 1 ] a Metropolis–Hastings random walk in the phase space of the system with a probability distribution given by P ( r ) = 1 / ρ ^ ( E ( r ) ) = exp ( − S ( E ( r ) ) ) {\displaystyle P({\boldsymbol {r}})=1/{\hat {\rho }}(E({\boldsymbol {r}}))=\exp(-S(E({\boldsymbol {r}})))} and a probability of proposing a new state given by a probability distribution g ( r → r ′ ) {\displaystyle g({\boldsymbol {r}}\rightarrow {\boldsymbol {r}}')} . A histogram H ( E ) {\displaystyle H(E)} of visited energies is stored. Like in the Metropolis–Hastings algorithm, a proposal-acceptance step is performed, and consists in (see Metropolis–Hastings algorithm overview ):
After each proposal-acceptance step, the system transits to some value E i {\displaystyle E_{i}} , H ( E i ) {\displaystyle H(E_{i})} is incremented by one and the following update is performed:
This is the crucial step of the algorithm, and it is what makes the Wang and Landau algorithm non-Markovian: the stochastic process now depends on the history of the process. Hence the next time there is a proposal to a state with that particular energy E i {\displaystyle E_{i}} , that proposal is now more likely refused; in this sense, the algorithm forces the system to visit all of the spectrum equally. [ 1 ] The consequence is that the histogram H ( E ) {\displaystyle H(E)} is more and more flat. However, this flatness depends on how well-approximated the calculated entropy is to the exact entropy, which naturally depends on the value of f. [ 7 ] To better and better approximate the exact entropy (and thus histogram's flatness), f is decreased after M proposal-acceptance steps:
It was later shown that updating the f by constantly dividing by two can lead to saturation errors. [ 7 ] A small modification to the Wang and Landau method to avoid this problem is to use the f factor proportional to 1 / t {\displaystyle 1/t} , where t {\displaystyle t} is proportional to the number of steps of the simulation. [ 7 ]
We want to obtain the DOS for the harmonic oscillator potential.
The analytical DOS is given by,
by performing the last integral we obtain
In general, the DOS for a multidimensional harmonic oscillator will be given by some power of E , the exponent will be a function of the dimension of the system.
Hence, we can use a simple harmonic oscillator potential to test the accuracy of Wang–Landau algorithm because we know already the analytic form of the density of states. Therefore, we compare the estimated density of states ρ ^ ( E ) {\displaystyle {\hat {\rho }}(E)} obtained by the Wang–Landau algorithm with ρ ( E ) {\displaystyle \rho (E)} .
The following is a sample code of the Wang–Landau algorithm in Python , where we assume that a symmetric proposal distribution g is used:
The code considers a "system" which is the underlying system being studied.
Molecular dynamics (MD) is usually preferable to Monte Carlo (MC), so it is desirable to have a MD algorithm incorporating the basic WL idea for flat energy sampling. That algorithm is Statistical Temperature Molecular Dynamics (STMD), developed [ 8 ] by Jaegil Kim et al at Boston University.
An essential first step was made with the Statistical Temperature Monte Carlo (STMC) algorithm. WLMC requires an extensive increase in the number of energy bins with system size, caused by working directly with the density of states. STMC is centered on an intensive quantity, the statistical temperature, T ( E ) = 1 / ( d S ( E ) / d E ) {\displaystyle T(E)=1/(dS(E)/dE)} , where E is the potential energy. When combined with the relation, Ω ( E ) = e S ( E ) {\displaystyle \Omega (E)=e^{S(E)}} , where we set k B = 1 {\displaystyle k_{B}=1} , the WL rule for updating the density of states gives the rule for updating the discretized statistical temperature,
where α j ± 1 = 1 / ( 1 ∓ δ f T ~ j ± 1 ) , δ f = ( l n f / 2 Δ E ) , Δ E {\displaystyle \alpha _{j\pm 1}=1/(1\mp \delta f{\tilde {T}}_{j\pm 1}),\delta f=(lnf/2\Delta E),\Delta E} is the energy bin size, and T ~ {\displaystyle {\tilde {T}}} denotes the running estimate. We define f as in, [ 1 ] a factor >1 that multiplies the estimate of the DOS for the i'th energy bin when the system visits an energy in that bin.
The details are given in Ref. [ 8 ] With an initial guess for T ( E ) {\displaystyle T(E)} and the range restricted to lie between T L {\displaystyle T_{L}} and T U {\displaystyle T_{U}} , the simulation proceeds as in WLMC, with significant numerical differences. An interpolation of T ~ ( E ) {\displaystyle {\tilde {T}}(E)} gives a continuum expression of the estimated S ( E ) {\displaystyle S(E)} upon integration of its inverse, allowing the use of larger energy bins than in WL. Different values of S ( E ) {\displaystyle S(E)} are available within the same energy bin when evaluating the acceptance probability. When histogram fluctuations are less than 20% of the mean, f {\displaystyle f} is reduced according to f → f {\displaystyle f\rightarrow {\sqrt {f}}} .
STMC was compared with WL for the Ising model and the Lennard-Jones liquid. Upon increasing energy bin size, STMC gets the same results over a considerable range, while the performance of WL deteriorates rapidly. STMD can use smaller initial values of f d = f − 1 {\displaystyle f_{d}=f-1} for more rapid convergence. In sum, STMC needs fewer steps to obtain the same quality of results.
Now consider the main result, STMD. It is based on the observation that in a standard MD simulation at temperature T 0 {\displaystyle T_{0}} with forces derived from the potential energy E ( [ x ] ) {\displaystyle E([x])} , where [ x ] {\displaystyle [x]} denotes all the positions, the sampling weight for a configuration is e − E ( [ x ] ) / T 0 {\displaystyle e^{-E([x])/T_{0}}} . Furthermore, if the forces are derived from a function W ( E ) {\displaystyle W(E)} , the sampling weight is e − W ( E ( [ x ] ) ) / T 0 {\displaystyle e^{-W(E([x]))/T_{0}}} .
For flat energy sampling, let the effective potential be T 0 S ( E ) {\displaystyle T_{0}S(E)} - entropic molecular dynamics. Then the weight is e − S ( E ) {\displaystyle e^{-S(E)}} . Since the density of states is e + S ( E ) {\displaystyle e^{+S(E)}} , their product gives flat energy sampling.
The forces are calculated as
where F 0 {\displaystyle F^{0}} denotes the usual force derived from the potential energy. Scaling the usual forces by the factor ( T 0 / T ( E ) ) {\displaystyle (T_{0}/T(E))} produces flat energy sampling.
STMD starts with an ordinary MD algorithm at constant T 0 {\displaystyle T_{0}} and V. The forces are scaled as indicated, and the statistical temperature is updated every time step, using the same procedure as in STMC. As the simulation converges to flat energy sampling, the running estimate T ~ ( E ) {\displaystyle {\tilde {T}}(E)} converges to the true T ( E ) {\displaystyle T(E)} . Technical details including steps to speed convergence are described in [ 8 ] and. [ 9 ]
In STMD T 0 {\displaystyle T_{0}} is called the kinetic temperature as it controls the velocities as usual, but does not enter the configurational sampling, which is unusual. Thus STMD can probe low energies with fast particles. Any canonical average can be calculated with reweighting, but the statistical temperature, T ( E ) {\displaystyle T(E)} , is immediately available with no additional analysis. It is extremely valuable for studying phase transitions. In finite nanosystems T ( E ) {\displaystyle T(E)} has a feature corresponding to every “subphase transition”. For a sufficiently strong transition, an equal-area construction on an S-loop in 1 / T ( E ) {\displaystyle 1/T(E)} gives the transition temperature.
STMD has been refined by the BU group, [ 9 ] and applied to several systems by them and others. It was recognized by D. Stelter that despite our emphasis on working with intensive quantities, l n ( f ) {\displaystyle ln(f)} is extensive. However δ f = ( l n ( f ) / 2 Δ E ) {\displaystyle \delta f=(ln(f)/2\Delta E)} is intensive, and the procedure f → f {\displaystyle f\rightarrow {\sqrt {f}}} based on histogram flatness is replaced by cutting δ f {\displaystyle \delta f} in half every fixed number of time steps. This simple change makes STMD entirely intensive and substantially improves performance for large systems. [ 9 ] Furthermore, the final value of the intensive δ f {\displaystyle \delta f} is a constant that determines the magnitude of error in the converged T ( E ) {\displaystyle T(E)} , and is independent of system size. STMD is implemented in LAMMPS as fix stmd.
STMD is particularly useful for phase transitions. Equilibrium information is impossible to obtain with a canonical simulation, as supercooling or superheating is necessary to cause the transition. However an STMD run obtains flat energy sampling with a natural progression of heating and cooling, without getting trapped in the low energy or high energy state. Most recently it has been applied to the fluid/gel transition [ 9 ] in lipid-wrapped nanoparticles.
Replica exchange STMD [ 10 ] has also been presented by the BU group.
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Short names:
The WannaCry ransomware attack was a worldwide cyberattack in May 2017 by the WannaCry ransomware cryptoworm , which targeted computers running the Microsoft Windows operating system by encrypting data and demanding ransom payments in the form of Bitcoin cryptocurrency . [ 4 ] It was propagated using EternalBlue , an exploit developed by the United States National Security Agency (NSA) for Microsoft Windows systems. EternalBlue was stolen and leaked by a group called The Shadow Brokers (TSB) a month prior to the attack. While Microsoft had released patches previously to close the exploit, much of WannaCry's spread was from organizations that had not applied these patches, or were using older Windows systems that were past their end of life . These patches were imperative to cyber security, but many organizations did not apply them, citing a need for 24/7 operation, the risk of formerly working applications breaking because of the changes, lack of personnel or time to install them, or other reasons.
The attack began at 07:44 UTC on 12 May 2017 and was halted a few hours later at 15:03 UTC by the registration of a kill switch discovered by Marcus Hutchins . The kill switch prevented already infected computers from being encrypted or further spreading WannaCry. [ 5 ] The attack was estimated to have affected more than 300,000 computers [ 6 ] across 150 countries, [ 6 ] with total damages ranging from hundreds of millions to billions of dollars . At the time, security experts believed from preliminary evaluation of the worm that the attack originated from North Korea or agencies working for the country. In December 2017, the United States and United Kingdom formally asserted that North Korea was behind the attack, although North Korea has denied any involvement with the attack. [ 7 ]
A new variant of WannaCry forced Taiwan Semiconductor Manufacturing Company (TSMC) to temporarily shut down several of its chip-fabrication factories in August 2018. The worm spread onto 10,000 machines in TSMC's most advanced facilities. [ 8 ]
WannaCry is a ransomware crypto worm , which targets computers running the Microsoft Windows operating system by encrypting (locking) data and demanding ransom payments in the Bitcoin cryptocurrency . The worm is also known as WannaCrypt, [ 9 ] Wana Decrypt0r 2.0, [ 10 ] WanaCrypt0r 2.0, [ 11 ] and Wanna Decryptor. [ 12 ] It is considered a network worm because it also includes a transport mechanism to automatically spread itself. This transport code scans for vulnerable systems, then uses the EternalBlue exploit to gain access, and the DoublePulsar tool to install and execute a copy of itself. [ 13 ] WannaCry versions 0, 1 and 2 were created using Microsoft Visual C++ 6.0 . [ 14 ]
EternalBlue is an exploit of Microsoft's implementation of their Server Message Block (SMB) protocol released by The Shadow Brokers . Much of the attention and comment around the event was occasioned by the fact that the U.S. National Security Agency (NSA) (from whom the exploit was likely stolen) had already discovered the vulnerability, but used it to create an exploit for its own offensive work , rather than report it to Microsoft. [ 15 ] [ 16 ] Microsoft eventually discovered the vulnerability, and on Tuesday , 14 March 2017, they issued security bulletin MS17-010, which detailed the flaw and announced that patches had been released for all Windows versions that were currently supported at that time, these being Windows Vista , Windows 7 , Windows 8.1 , Windows 10 , Windows Server 2008 , Windows Server 2008 R2 , Windows Server 2012 , and Windows Server 2016 . [ 17 ]
DoublePulsar is a backdoor tool, also released by The Shadow Brokers on 14 April 2017. Starting from 21 April 2017, security researchers reported that there were tens of thousands of computers with the DoublePulsar backdoor installed. [ 18 ] By 25 April, reports estimated that the number of infected computers could be up to several hundred thousand, with numbers increasing every day. [ 19 ] [ 20 ] The WannaCry code can take advantage of any existing DoublePulsar infection, or installs it itself. [ 13 ] [ 21 ] [ 22 ] On 9 May 2017, private cybersecurity company RiskSense released code on GitHub with the stated purpose of allowing legal white hat penetration testers to test the CVE-2017-0144 exploit on unpatched systems. [ 23 ]
When executed, the WannaCry malware first checks the kill switch domain name (iuqerfsodp9ifjaposdfjhgosurijfaewrwergwea.com); if it is not found, then the ransomware encrypts the computer's data, [ 24 ] [ 25 ] [ 26 ] then attempts to exploit the SMB vulnerability to spread out to random computers on the Internet, [ 27 ] and laterally to computers on the same network. [ 28 ] On the local system, the WannaCry executable file extracts and installs binary and configuration files from its resource section. It also hides the extracted directory, modifies security descriptors, creates an encryption key, deletes shadow copies, and so on. As with other modern ransomware, the payload displays a message informing the user that their files have been encrypted, and demands a payment of around US$300 in bitcoin within three days, or US$600 within seven days, [ 25 ] [ 29 ] warning that "you have not so enough time. [ sic ]" Three hardcoded bitcoin addresses, or wallets, are used to receive the payments of victims. As with all such wallets, their transactions and balances are publicly accessible even though the cryptocurrency wallet owners remain unknown. [ 30 ]
Several organizations released detailed technical write-ups of the malware, including a senior security analyst at RiskSense, [ 31 ] [ 32 ] Microsoft , [ 33 ] Cisco , [ 13 ] Malwarebytes , [ 27 ] Symantec , and McAfee . [ 28 ]
The attack began on Friday, 12 May 2017, [ 34 ] [ 35 ] with evidence pointing to an initial infection in Asia at 07:44 UTC. [ 34 ] [ 36 ] The initial infection was likely through an exposed vulnerable SMB port, [ 37 ] rather than email phishing as initially assumed. [ 34 ] Within a day the code was reported to have infected more than 230,000 computers in over 150 countries. [ 38 ] [ 39 ]
Organizations that had not installed Microsoft's security update from March were affected by the attack. [ 40 ] Those still running unsupported versions of Microsoft Windows , such as Windows XP and Windows Server 2003 [ 41 ] [ 42 ] were at particularly high risk because no security patches had been released since April 2014 for Windows XP and July 2015 for Windows Server 2003. [ 9 ] A Kaspersky Lab study reported, however, that less than 0.1 percent of the affected computers were running Windows XP, and that 98 percent of the affected computers were running Windows 7. [ 9 ] [ 43 ] In a controlled testing environment, the cybersecurity firm Kryptos Logic found that it was unable to infect a Windows XP system with WannaCry using just the exploits, as the payload failed to load, or caused the operating system to crash rather than actually execute and encrypt files. However, when executed manually, WannaCry could still operate on Windows XP. [ 44 ] [ 45 ] [ 46 ]
Experts quickly advised affected users against paying the ransom due to no reports of people getting their data back after payment and as high revenues would encourage more of such campaigns. [ 47 ] [ 48 ] [ 49 ] As of 14 June 2017, after the attack had subsided, a total of 327 payments totaling US$130,634.77 (51.62396539 BTC) had been transferred (worth approximately US$5,390,000 as of 23 January 2025). [ 50 ]
The day after the initial attack in May, Microsoft released out-of-band security updates for end-of-life products Windows XP , Windows Server 2003 and Windows 8 ; these patches had been created in February, but were previously only available to those who paid for a custom support plan. [ 42 ] [ 51 ] Organizations were advised to patch Windows and plug the vulnerability in order to protect themselves from the cyber attack. [ citation needed ] The head of Microsoft's Cyber Defense Operations Center, Adrienne Hall, said that "Due to the elevated risk for destructive cyber-attacks at this time, we made the decision to take this action because applying these updates provides further protection against potential attacks with characteristics similar to WannaCrypt [alternative name to WannaCry]". [ 52 ] [ 53 ]
Researcher Marcus Hutchins [ 54 ] [ 55 ] discovered the kill switch domain hardcoded in the malware. [ 56 ] [ 57 ] [ 58 ] Registering a domain name for a DNS sinkhole stopped the attack spreading as a worm, because the ransomware only encrypted the computer's files if it was unable to connect to that domain, which all computers infected with WannaCry before the website's registration had been unable to do. While this did not help already infected systems, it severely slowed the spread of the initial infection and gave time for defensive measures to be deployed worldwide, particularly in North America and Asia, which had not been attacked to the same extent as elsewhere. [ 59 ] [ 60 ] [ 61 ] [ 62 ] [ 63 ] On 14 May, a first variant of WannaCry appeared with a new and second [ 64 ] kill-switch registered by Matt Suiche on the same day. This was followed by a second variant with the third and last kill-switch on 15 May, which was registered by Check Point threat intelligence analysts. [ 65 ] [ 66 ] A few days later, a new version of WannaCry was detected that lacked the kill switch altogether. [ 67 ] [ 68 ] [ 69 ] [ 70 ]
On 19 May, it was reported that hackers were trying to use a Mirai botnet variant to effect a distributed denial-of-service attack on WannaCry's kill-switch domain with the intention of knocking it offline. [ 71 ] On 22 May, Hutchins protected the domain by switching to a cached version of the site, capable of dealing with much higher traffic loads than the live site. [ 72 ]
Separately, researchers from University College London and Boston University reported that their PayBreak system could defeat WannaCry and several other families of ransomware by recovering the keys used to encrypt the user's data. [ 73 ] [ 74 ]
It was discovered that Windows encryption APIs used by WannaCry may not completely clear the prime numbers used to generate the payload's private keys from the memory, making it potentially possible to retrieve the required key if they had not yet been overwritten or cleared from resident memory. The key is kept in the memory if the WannaCry process has not been killed and the computer has not been rebooted after being infected. [ 75 ] This behaviour was used by a French researcher to develop a tool known as WannaKey, which automates this process on Windows XP systems. [ 76 ] [ 77 ] [ 78 ] This approach was iterated upon by a second tool known as Wanakiwi, which was tested to work on Windows 7 and Server 2008 R2 as well. [ 79 ]
Within four days of the initial outbreak, new infections had slowed to a trickle due to these responses. [ 80 ]
Linguistic analysis of the ransom notes suggested the authors were likely fluent in Chinese and proficient in English, as the versions of the notes in those languages appeared to be human-written while the rest seemed to be machine-translated . [ 81 ] [ 82 ] According to an analysis by the FBI's Cyber Behavioral Analysis Center, the computer that created the ransomware language files had Hangul language fonts installed, as indicated by the presence of the "\fcharset129" Rich Text Format tag. [ 14 ] Metadata in the language files also showed that the computers used to create the ransomware were set to UTC+09:00 , a time zone used in Korea . [ 14 ]
A security researcher [ 83 ] [ 84 ] initially posted a tweet [ 85 ] referencing code similarities between WannaCry and previous malware. The cybersecurity companies [ 86 ] Kaspersky Lab and Symantec stated that the code shares some similarities with malware previously used by the Lazarus Group , [ 87 ] which has been linked to North Korea and is believed to have carried out the cyberattack on Sony Pictures in 2014 and a Bangladesh bank heist in 2016. [ 87 ] However, these similarities could result from either code reuse by another group [ 88 ] or an attempt to misattribute responsibility—as in a cyber false flag operation. [ 87 ] A leaked internal NSA memo is also alleged to have linked the creation of the worm to North Korea. [ 89 ] Brad Smith , the president of Microsoft, stated he believed North Korea was behind the WannaCry attack, [ 90 ] and the UK's National Cyber Security Centre reached the same conclusion. [ 91 ]
On 18 December 2017, the United States Government formally announced that it considers North Korea to be the main culprit behind the WannaCry attack. [ 92 ] President Donald Trump 's Homeland Security Advisor , Tom Bossert , wrote an op-ed in The Wall Street Journal stating, "We do not make this allegation lightly. It is based on evidence." [ 93 ] In a press conference the following day, Bossert stated that the evidence indicated that Kim Jong-un had given the order to launch the malware attack. [ 94 ] Bossert stated that Canada, New Zealand, and Japan agreed with the United States' assessment of the evidence linking the attack to North Korea, [ 95 ] while the United Kingdom's Foreign and Commonwealth Office expressed support for the United States' assertion. [ 96 ]
North Korea denied responsibility for the cyberattack. [ 97 ] [ 98 ]
On 6 September 2018, the U.S. Department of Justice (DoJ) announced formal charges against Park Jin-hyok for his alleged involvement in the Sony Pictures hack of 2014. The DoJ stated that Park was a North Korean hacker working as part of a team affiliated with the North Korean Reconnaissance General Bureau . The Department of Justice further claimed this team was also involved in the WannaCry attack, among other activities. [ 99 ] [ 100 ]
The ransomware campaign was unprecedented in scale according to Europol , [ 38 ] which estimates that around 200,000 computers were infected across 150 countries. According to Kaspersky Lab , the four most affected countries were Russia , Ukraine , India and Taiwan . [ 102 ]
One of the largest agencies struck by the attack was the National Health Service hospitals in England and Scotland, [ 103 ] [ 104 ] and up to 70,000 devices—including computers, MRI scanners , blood-storage refrigerators and theatre equipment—may have been affected. [ 105 ] On 12 May, some NHS services had to turn away non-critical emergencies, and some ambulances were diverted. [ 106 ] [ 107 ] In 2016, thousands of computers in 42 separate NHS trusts in England were reported to be still running Windows XP. [ 41 ] In 2018 a report by Members of Parliament concluded that all 200 NHS hospitals or other organisations checked in the wake of the WannaCry attack still failed cybersecurity checks. [ 108 ] [ 109 ] NHS hospitals in Wales and Northern Ireland were unaffected by the attack. [ 106 ] [ 110 ]
Nissan Motor Manufacturing UK in Tyne and Wear , England, halted production after the ransomware infected some of their systems. Renault also stopped production at several sites in an attempt to stop the spread of the ransomware. [ 111 ] [ 112 ] Spain's Telefónica , FedEx and Deutsche Bahn were hit, along with many other countries and companies worldwide. [ 113 ] [ 114 ] [ 115 ]
The attack's impact is said to be relatively low compared to other potential attacks of the same type and could have been much worse had Hutchins not discovered that a kill switch had been built in by its creators [ 116 ] [ 117 ] or if it had been specifically targeted on highly critical infrastructure , like nuclear power plants , dams or railway systems. [ 118 ] [ 119 ]
According to cyber-risk-modeling firm Cyence, economic losses from the cyber attack could reach up to US$4 billion, with other groups estimating the losses to be in the hundreds of millions. [ 120 ]
The following is an alphabetical list of organisations confirmed to have been affected:
A number of experts highlighted the NSA 's non-disclosure of the underlying vulnerability, and their loss of control over the EternalBlue attack tool that exploited it. Edward Snowden said that if the NSA had " privately disclosed the flaw used to attack hospitals when they found it, not when they lost it, the attack may not have happened". [ 107 ] British cybersecurity expert Graham Cluley also sees "some culpability on the part of the U.S. intelligence services". According to him and others "they could have done something ages ago to get this problem fixed, and they didn't do it". He also said that despite obvious uses for such tools to spy on people of interest , they have a duty to protect their countries' citizens. [ 163 ] Others have also commented that this attack shows that the practice of intelligence agencies to stockpile exploits for offensive purposes rather than disclosing them for defensive purposes may be problematic. [ 117 ] Microsoft president and chief legal officer Brad Smith wrote, "Repeatedly, exploits in the hands of governments have leaked into the public domain and caused widespread damage. An equivalent scenario with conventional weapons would be the U.S. military having some of its Tomahawk missiles stolen." [ 164 ] [ 165 ] [ 166 ] Russian President Vladimir Putin placed the responsibility of the attack on U.S. intelligence services for having created EternalBlue. [ 152 ]
On 17 May 2017, United States bipartisan lawmakers introduced the PATCH Act [ 167 ] that aims to have exploits reviewed by an independent board to "balance the need to disclose vulnerabilities with other national security interests while increasing transparency and accountability to maintain public trust in the process". [ 168 ]
On 15 June 2017, the United States Congress was to hold a hearing on the attack. [ 169 ] Two subpanels of the House Science Committee were to hear the testimonies from various individuals working in the government and non-governmental sector about how the U.S. can improve its protection mechanisms for its systems against similar attacks in the future. [ 169 ]
Marcus Hutchins , a cybersecurity researcher, working in loose collaboration with UK's National Cyber Security Centre , [ 170 ] [ 171 ] researched the malware and discovered a "kill switch". [ 55 ] Later globally dispersed security researchers collaborated online to develop open-source tools [ 172 ] [ 173 ] that allow for decryption without payment under some circumstances. [ 174 ] Snowden states that when " NSA -enabled ransomware eats the Internet, help comes from researchers, not spy agencies" and asks why this is the case. [ 171 ] [ 175 ] [ 176 ]
Adam Segal , director of the digital and cyberspace policy program at the Council on Foreign Relations , stated that "the patching and updating systems are broken, basically, in the private sector and in government agencies". [ 117 ] In addition, Segal said that governments' apparent inability to secure vulnerabilities "opens a lot of questions about backdoors and access to encryption that the government argues it needs from the private sector for security". [ 117 ] Arne Schönbohm , president of Germany's Federal Office for Information Security (BSI), stated that "the current attacks show how vulnerable our digital society is. It's a wake-up call for companies to finally take IT security [seriously]". [ 177 ]
The effects of the attack also had political implications; in the United Kingdom , the impact on the National Health Service quickly became political, with claims that the effects were exacerbated by government underfunding of the NHS; in particular, the NHS ceased its paid Custom Support arrangement to continue receiving support for unsupported Microsoft software used within the organization, including Windows XP. [ 178 ] Home Secretary Amber Rudd refused to say whether patient data had been backed up , and Shadow Health Secretary Jon Ashworth accused Health Secretary Jeremy Hunt of refusing to act on a critical note from Microsoft, the National Cyber Security Centre (NCSC) and the National Crime Agency that had been received two months previously. [ 179 ]
Others argued that hardware and software vendors often fail to account for future security flaws, selling systems that—due to their technical design and market incentives—eventually won't be able to properly receive and apply patches. [ 180 ]
The NHS denied that it was still using XP, claiming only 4.7% of devices within the organization ran Windows XP. [ 44 ] [ 181 ] The cost of the attack to the NHS was estimated as £92 million in disruption to services and IT upgrades. [ 182 ]
After the attack, NHS Digital refused to finance the estimated £1 billion to meet the Cyber Essentials Plus standard, an information security certification organized by the UK NCSC, saying this would not constitute "value for money", and that it had invested over £60 million and planned "to spend a further £150 [million] over the next two years" to address key cyber security weaknesses. [ 183 ]
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The Wannier equation describes a quantum mechanical eigenvalue problem in solids where an electron in a conduction band and an electronic vacancy (i.e. hole) within a valence band attract each other via the Coulomb interaction . For one electron and one hole, this problem is analogous to the Schrödinger equation of the hydrogen atom ; and the bound-state solutions are called excitons . When an exciton's radius extends over several unit cells , it is referred to as a Wannier exciton in contrast to Frenkel excitons whose size is comparable with the unit cell. An excited solid typically contains many electrons and holes; this modifies the Wannier equation considerably. The resulting generalized Wannier equation can be determined from the homogeneous part of the semiconductor Bloch equations or the semiconductor luminescence equations .
The equation is named after Gregory Wannier .
Since an electron and a hole have opposite charges their mutual Coulomb interaction is attractive. The corresponding Schrödinger equation , in relative coordinate r {\displaystyle \mathbf {r} } , has the same form as the hydrogen atom:
with the potential given by
Here, ℏ {\displaystyle \hbar } is the reduced Planck constant , ∇ {\displaystyle \nabla } is the nabla operator, μ {\displaystyle \mu } is the reduced mass , − | e | {\displaystyle -|e|} ( + | e | {\displaystyle +|e|} ) is the elementary charge related to an electron (hole), ε r {\displaystyle \varepsilon _{r}} is the relative permittivity , and ε 0 {\displaystyle \varepsilon _{0}} is the vacuum permittivity . The solutions of the hydrogen atom are described by eigenfunction ϕ λ ( r ) {\displaystyle \phi _{\lambda }(\mathbf {r} )} and eigenenergy E λ {\displaystyle E_{\lambda }} where λ {\displaystyle \lambda } is a quantum number labeling the different states.
In a solid, the scaling of E λ {\displaystyle E_{\lambda }} and the wavefunction size are orders of magnitude different from the hydrogen problem because the relative permittivity ε r {\displaystyle \varepsilon _{r}} is roughly ten and the reduced mass in a solid is much smaller than the electron rest mass m e {\displaystyle m_{e}} , i.e., μ ≪ m e {\displaystyle \mu \ll m_{e}} . As a result, the exciton radius can be large while the exciton binding energy is small, typically few to hundreds of meV , depending on material, compared to eV for the hydrogen problem. [ 1 ] [ 2 ]
The Fourier transformed version of the presented Hamiltonian can be written as
where k {\displaystyle \mathbf {k} } is the electronic wave vector , E k {\displaystyle E_{\mathbf {k} }} is the kinetic energy and V k {\displaystyle V_{\mathbf {k} }} , ϕ λ ( k ) {\displaystyle \phi _{\lambda }(\mathbf {k} )} are the Fourier transforms of V ( r ) {\displaystyle V(\mathbf {r} )} , ϕ λ ( r ) {\displaystyle \phi _{\lambda }(\mathbf {r} )} , respectively. The Coulomb sums follows from the convolution theorem and the k {\displaystyle \mathbf {k} } -representation is useful when introducing the generalized Wannier equation.
The Wannier equation can be generalized by including the presence of many electrons and holes in the excited system. One can start from the general theory of either optical excitations or light emission in semiconductors that can be systematically described using the semiconductor Bloch equations (SBE) or the semiconductor luminescence equations (SLE), respectively. [ 1 ] [ 3 ] [ 4 ] The homogeneous parts of these equations produce the Wannier equation at the low-density limit. Therefore, the homogeneous parts of the SBE and SLE provide a physically meaningful way to identify excitons at arbitrary excitation levels. The resulting generalized Wannier equation is
where the kinetic energy becomes renormalized
by the electron and hole occupations f k e {\displaystyle f_{\mathbf {k} }^{e}} and f k h {\displaystyle f_{\mathbf {k} }^{h}} , respectively. These also modify the Coulomb interaction into
where ( 1 − f k e − f k h ) {\displaystyle (1-f_{\mathbf {k} }^{\mathrm {e} }-f_{\mathbf {k} }^{\mathrm {h} })} weakens the Coulomb interaction via the so-called phase-space filling factor that stems from the Pauli exclusion principle preventing multiple excitations of fermions. Due to the phase-space filling factor, the Coulomb attraction becomes repulsive for excitations levels f k e + f k h > 1 {\displaystyle f_{\mathbf {k} }^{\mathrm {e} }+f_{\mathbf {k} }^{\mathrm {h} }>1} . At this regime, the generalized Wannier equation produces only unbound solutions which follow from the excitonic Mott transition from bound to ionized electron–hole pairs.
Once electron–hole densities exist, the generalized Wannier equation is not Hermitian anymore. As a result, the eigenvalue problem has both left- and right-handed eigenstates ϕ λ L ( k ) {\displaystyle \phi _{\lambda }^{\mathrm {L} }(\mathbf {k} )} and ϕ λ R ( k ) {\displaystyle \phi _{\lambda }^{\mathrm {R} }(\mathbf {k} )} , respectively. They are connected via the phase-space filling factor, i.e. ϕ λ L ( k ) = ϕ λ R ( k ) / ( 1 − f k e − f k h ) {\displaystyle \phi _{\lambda }^{\mathrm {L} }(\mathbf {k} )=\phi _{\lambda }^{\mathrm {R} }(\mathbf {k} )/(1-f_{\mathbf {k} }^{\mathrm {e} }-f_{\mathbf {k} }^{\mathrm {h} })} . The left- and right-handed eigenstates have the same eigen value E λ {\displaystyle E_{\lambda }} (that is real valued for the form shown) and they form a complete set of orthogonal solutions since
The Wannier equations can also be generalized to include scattering and screening effects that appear due to two-particle correlations within the SBE. This extension also produces left- and right-handed eigenstate, but their connection is more complicated [ 4 ] than presented above. Additionally, E λ {\displaystyle E_{\lambda }} becomes complex valued and the imaginary part of E λ {\displaystyle E_{\lambda }} defines the lifetime of the resonance λ {\displaystyle \lambda } .
Physically, the generalized Wannier equation describes how the presence of other electron–hole pairs modifies the binding of one effective pair. As main consequences, an excitation tends to weaken the Coulomb interaction and renormalize the single-particle energies in the simplest form. Once also correlation effects are included, one additionally observes the screening of the Coulomb interaction, excitation-induced dephasing , and excitation-induced energy shifts. All these aspects are important when semiconductor experiments are explained in detail.
Due to the analogy with the hydrogen problem, the zero-density eigenstates are known analytically for any bulk semiconductor when excitations close to the bottom of the electronic bands are studied. [ 5 ] In nanostructured [ 6 ] materials, such as quantum wells , quantum wires , and quantum dots , the Coulomb-matrix element V k {\displaystyle V_{\mathbf {k} }} strongly deviates from the ideal two- and three-dimensional systems due to finite quantum confinement of electronic states. Hence, one cannot solve the zero-density Wannier equation analytically for those situations, but needs to resort to numerical eigenvalue solvers. In general, only numerical solutions are possible for all semiconductor cases when exciton states are solved within an excited matter. Further examples are shown in the context of the Elliott formula .
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The Wannier functions are a complete set of orthogonal functions used in solid-state physics . They were introduced by Gregory Wannier in 1937. [ 1 ] [ 2 ] Wannier functions are the localized molecular orbitals of crystalline systems.
The Wannier functions for different lattice sites in a crystal are orthogonal, allowing a convenient basis for the expansion of electron states in certain regimes. Wannier functions have found widespread use, for example, in the analysis of binding forces acting on electrons.
Although, like localized molecular orbitals , Wannier functions can be chosen in many different ways, [ 3 ] the original, [ 1 ] simplest, and most common definition in solid-state physics is as follows. Choose a single band in a perfect crystal, and denote its Bloch states by
where u k ( r ) has the same periodicity as the crystal. Then the Wannier functions are defined by
where
where "BZ" denotes the Brillouin zone , which has volume Ω.
On the basis of this definition, the following properties can be proven to hold: [ 4 ]
In other words, a Wannier function only depends on the quantity ( r − R ). As a result, these functions are often written in the alternative notation
where the sum is over each lattice vector R in the crystal.
Wannier functions have been extended to nearly periodic potentials as well. [ 5 ]
The Bloch states ψ k ( r ) are defined as the eigenfunctions of a particular Hamiltonian, and are therefore defined only up to an overall phase. By applying a phase transformation e iθ ( k ) to the functions ψ k ( r ), for any (real) function θ ( k ), one arrives at an equally valid choice. While the change has no consequences for the properties of the Bloch states, the corresponding Wannier functions are significantly changed by this transformation.
One therefore uses the freedom to choose the phases of the Bloch states in order to give the most convenient set of Wannier functions. In practice, this is usually the maximally-localized set, in which the Wannier function ϕ R is localized around the point R and rapidly goes to zero away from R . For the one-dimensional case, it has been proved by Kohn [ 6 ] that there is always a unique choice that gives these properties (subject to certain symmetries). This consequently applies to any separable potential in higher dimensions; the general conditions are not established, and are the subject of ongoing research. [ 7 ]
A Pipek-Mezey style localization scheme has also been recently proposed for obtaining Wannier functions. [ 8 ] Contrary to the maximally localized Wannier functions (which are an application of the Foster-Boys scheme to crystalline systems), the Pipek-Mezey Wannier functions do not mix σ and π orbitals.
The existence of exponentially localized Wannier functions in insulators was proved mathematically in 2006. [ 7 ]
Wannier functions have recently found application in describing the polarization in crystals, for example, ferroelectrics . The modern theory of polarization is pioneered by Raffaele Resta and David Vanderbilt. See for example, Berghold, [ 9 ] and Nakhmanson, [ 10 ] and a power-point introduction by Vanderbilt. [ 11 ] The polarization per unit cell in a solid can be defined as the dipole moment of the Wannier charge density:
where the summation is over the occupied bands, and W n is the Wannier function localized in the cell for band n . The change in polarization during a continuous physical process is the time derivative of the polarization and also can be formulated in terms of the Berry phase of the occupied Bloch states. [ 4 ] [ 12 ]
Wannier functions are often used to interpolate bandstructures calculated ab initio on a coarse grid of k -points to any arbitrary k -point. This is particularly useful for evaluation of Brillouin-zone integrals on dense grids and searching of Weyl points, and also taking derivatives in the k -space. This approach is similar in spirit to the tight binding approximation, but in contrast allows for an exact description of bands in a certain energy range. Wannier interpolation schemes have been derived for spectral properties, [ 13 ] anomalous Hall conductivity , [ 14 ] orbital magnetization , [ 15 ] thermoelectric and electronic transport properties, [ 16 ] gyrotropic effects , [ 17 ] shift current , [ 18 ] spin Hall conductivity [ 19 ] [ 20 ] and other effects.
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The War Bureau of Consultants (WBC) was a committee of 12 prominent scientists and several government consultants put together in November 1941 to investigate the feasibility of a U.S. bio-weapons program. [ 1 ] The bureau's recommendations led to the creation of an official U.S. biological weapons program during World War II .
Despite World War I-era interest in ricin , [ 2 ] as World War II erupted the United States Army still maintained the position that biological warfare (BW) was, for the most part, impractical. [ 3 ] Secretary of War Henry Stimson was mindful of Imperial Germany 's BW attack on the Romanian Cavalry using glanders during World War I and of its saboteurs introducing the disease into the United States among the military horses and mules being shipped to Europe (see Anton Dilger ). It was also understood that intelligence reports (erroneous as it later turned out) clearly stated that Nazi Germany had a BW capability. [ 4 ] Other nations, notably France, Japan and the United Kingdom, had also begun their own BW programs. [ 3 ] However, by the outbreak of World War II the U.S. still had no biological weapons capabilities.
The WBC was formed in 1941. The Bureau was formed after a July 1941 meeting of representatives from the Office of Scientific Research and Development , the Chemical Warfare Service , the Surgeon General , and U.S. Army Intelligence . [ 5 ] That meeting recommended that the U.S. further study the threat of bio-weapons and the feasibility of a U.S. biological weapons program . [ 5 ] Secretary of War Henry L. Stimson requested that Frank B. Jewett , head of the National Academy of Sciences , issue a report on the topic. [ 5 ] Jewett passed the task on to Edwin Broun Fred , a University of Wisconsin bacteriologist. [ 6 ]
Fred formed the WBC which consisted of himself and 12 prominent scientists. [ 6 ] In addition the WBC included liaisons from the Chemical Warfare Service, U.S. Army Ordnance Corps , the U.S. Navy Bureau of Medicine and Surgery , the U.S. Army Surgeon's General Office , the U.S. Department of Agriculture and the U.S. Public Health Service . [ 5 ] [ 6 ] The War Bureau of Consultants' work was to be conducted in extreme secrecy. [ 6 ]
The WBC met for the first time on November 18, 1941, at the National Academy of Sciences in Washington, D.C. [ 7 ] At that meeting it was decided that the WBC would perform a literature search building up to their report. [ 7 ] Between the WBC's first meeting and its first report Pearl Harbor was bombed and reports began trickling in about the Japanese biological attack on the Chinese village of Changteh . [ 7 ]
On February 17, 1942, the WBC produced and released its first formal report. [ 7 ] The document was over 200 pages long, included 13 appendices, and an 89-page annotated bibliography . [ 7 ] The report laid out the results of the WBC's literature search, which showed that there was relatively widespread interest in proposals geared toward BW. [ 7 ]
The report also made some key recommendations. The WBC recommended that the United States take seriously the threat of biological warfare and take steps to defend itself. [ 8 ] Among those steps were the development of vaccines , and protection of the water supplies. [ 8 ] The consultants reported that a U.S. bio-weapons program was a feasible goal. [ 9 ] Their report also concluded that the United States should take steps to develop its own offensive biological warfare capability. [ 8 ]
Stimson forwarded the report, and his summary of its contents, to U.S. President Franklin Roosevelt on April 29, 1942. [ 5 ] His summary emphasized the danger of biological weapons as well as the U.S. need for offensive and defensive biological capabilities. [ 5 ]
The value of biological warfare [wrote Stimson] will be a debatable question until it has been clearly proven or disproved by experiences. The wide assumption is that any method which appears to offer advantages to a nation at war will be vigorously employed by that nation. There is but one logical course to pursue, namely, to study the possibilities of such warfare from every angle, make every preparation for reducing its effectiveness, and thereby reduce the likelihood of its use. [ 10 ]
As a result of the recommendations made by the WBC, Roosevelt ordered Stimson to create the War Research Service to oversee the official, and secret, U.S. biological weapons program. [ 6 ] [ 8 ] [ 9 ]
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The War Research Service (WRS) was a civilian agency of the United States government established during World War II to pursue research relating to biological warfare . Established in May 1942 by Secretary of War Henry L. Stimson , the WRS was embedded in the Federal Security Agency , the federal agency that administered Social Security and other New Deal programs in the administration of President Franklin D. Roosevelt . Headed by George W. Merck , president of the Merck & Co. pharmaceutical firm , the WRS was headquartered at Fort Detrick, Maryland .
Being a civilian agency, the WRS was initially tasked to supervise the military Chemical Warfare Service 's biological program.
However, the WRS was disbanded in 1944, and the weapons research was continued under the exclusive oversight of the CWS. [ 1 ]
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Wars or conflicts can break out between different groups in some ant species for a variety of reasons. These violent confrontations typically involve entire colonies , sometimes allied with each other, and can end in a stalemate, the complete destruction of one of the belligerents, the migration of one of the groups, or, in some cases, the establishment of cordial relations between the different combatants or the adoption of members of the losing group. For some species of ants, this is even a deliberately undertaken strategy, as they require capturing pupae from other species to ensure the continuity of their colony. Thus, there are specific biological evolutions in certain species intended to give them an advantage in such conflicts. In some of these confrontations, ants can adopt ritualized behavior , even governed by certain implicit rules, [ 1 ] for example by organizing duels between the most important ants of each colony or choosing a specific location for a battle. They should not be confused with social conflicts inside the same colony or supercolony of ants .
These conflicts are not simply internal to ants, which can fight each other even within the same species, but also involve other animals, particularly other eusocial insects like termites or wasps . In the early 21st century, with the rapid spread of many species into new habitats facilitated by human colonization, significant wars are being waged between different supercolonies .
The use of the term "war", found in scientific literature, [ 2 ] [ 3 ] [ 4 ] is an anthropocentric analogy, derived from human wars .
The reasons that can lead ant colonies to clash are varied and depend on the species, locations, and contexts. For a number of them, such as leafcutter ants Atta laevigata , wood ants of the genus Formica , certain species of the genus Carebara , or giant ants Dinomyrmex gigas , it is a matter of territory covered and thus the available food for the different colonies. [ 3 ] [ 4 ] [ 5 ] [ 6 ] It can also be related to issues of overpopulation of the same species in the same area at certain times of the year. [ 4 ] In other cases, some species aim to capture the pupae of an opposing group to use them in their own colony later. [ 2 ]
It is difficult to assess the prevalence of this type of behavior in ants, given the significant diversity of species, behaviors, and different situations. Some species undergo specific evolutions with the sole purpose of engaging in these conflicts, such as Polyergus rufescens , which have sickle-shaped mandibles . [ 7 ] The emergence of supercolonies from the 19th century, facilitated by human movements, has certainly reinforced these behaviors in the affected ants. [ 8 ] It also seems to depend on the context in which the ants find themselves. [ 8 ] For instance, within the same species, a colony facing external threats from another ant colony can produce up to twice as many soldier larvae as a colony not experiencing the same pressures. [ 8 ] Some species are almost exclusively on defensive strategies, such as Camponotus ligniperdus , which are peaceful and occupy a small territory but defend it fiercely against any incursion, even against more dangerous or deadly species. [ 9 ]
In general, there are two main ways ants conduct these conflicts. [ 10 ] On the one hand, some species use specific ants that are more powerful and whose primary function is to fight. [ 10 ] On the other hand, colonies increase the number of available fighters and send large numbers of individuals into battle. [ 10 ] [ 11 ] In some species, conflict is ritualized, for example through limited duels undertaken by the individuals most capable of combat, [ 3 ] but phenomena of battles are also common. [ 4 ] [ 11 ] In the genus Formica , such battles are commonplace and can involve tens of thousands of individuals, and they are sometimes ritualized , with the respective groups withdrawing at nightfall only to return the next day to the same locations to resume the battle. [ 4 ] The bodies of dead or injured ants are then brought back to the colony, where they are eaten. [ 4 ] In other species, such as within the genus Carebara , ants arrange themselves in specific formations before the battle, like phalanxes , and advance against each other. [ 6 ] They also regularly sacrifice workers, whose role is to try to hinder, injure, and attack enemy majors, before their own majors join the battlefield and can intervene. [ 6 ]
In other cases, particularly among ants that aim to capture larvae or pupae , colonies use chemical weapons , such as olfactory propaganda, to try to enter the targeted colonies as discreetly as possible. [ 6 ]
Generally, wars between ants are costly for the groups, which must allocate a significant portion of their production to the war effort , to the detriment of forming workers, for example. [ 8 ] These wars can result in the death of tens of thousands of individuals within a few hours; for wood ants of the genus Formica , there are regularly 10,000 casualties per day during the spring. [ 4 ] For these ants, the war ends either when the opposing colony is destroyed or when the available prey is sufficient again for the needs of the colonies, which have then lost thousands of members. [ 4 ] Estimates from 2016 on certain ant species show a loss of about a third of the total colony population in case of victory. [ 12 ]
For some species, such as Crematogaster mimosae , victory over an opposing colony usually results in the flight or death of the opposing queen , but the victorious colony often adopts the surviving ants of the losing colony, likely a way to avoid and mitigate the significant resource loss due to the war effort. [ 12 ] In a few rare cases, the queen of the losing colony is herself adopted by the victorious colony, and the two merge. [ 12 ]
With the development of ant supercolonies , which follows human expansion into new areas, groups of dozens, hundreds, or even thousands of colonies [ 13 ] engage in large-scale conflicts against other species. [ 8 ] For example, around San Diego in the 2010s, millions of ants died each month in significant battles between the supercolony formed by Argentine ants and three other supercolonies present in the area. [ 6 ]
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War sand is sand contaminated by remains of projectiles used in war. This kind of sand has been found in Normandy , since its invasion , among other places. [ 1 ] In 1988, the sand on Omaha Beach was discovered to contain man-made metal and glass particles deriving from shrapnel ; 4% of the sand in the sample was composed of shrapnel particles ranging in size between 0.06 millimetres (0.0024 in) and 1 mm (0.039 in). [ 2 ] Researchers also discovered trace amounts of iron and glass beads in the sand, originating from the intense heat unleashed by munitions explosions in the air and sand. [ 2 ] [ 3 ]
In 2013, Dr. Earle McBride, a researcher studying sandstone diagenesis and the textual and compositional maturation of sand during transportation , [ 4 ] mixed samples collected from Omaha Beach in 1988 with a blue epoxy, creating an "artificial sandstone", before slicing it into thin sections. [ 3 ] Utilising an optical microscope and an external light source, shiny, opaque grains could be identified. Although wave action had elicited rounding on the edges of some coarser grains, the shard-like angularity and corrosion of both coarse and fine grains suggested these grains were man-made. [ 3 ] [ 2 ] It is believed that the roughness of said grains was imparted by microporous surfaces produced during production and corrosion products post-explosion. [ 2 ]
This inspection, alongside tests revealing that the grains were magnetic, led McBride to conclude these grains were pieces of shrapnel. [ 3 ] [ 2 ]
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In mathematics , Waraszkiewicz spirals are subsets of the plane introduced by Waraszkiewicz ( 1932 ). Waraszkiewicz spirals give an example of an uncountable family of pairwise incomparable continua, meaning that there is no continuous map from one onto another.
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Warazan ( 藁算 ) was a system of record-keeping using knotted straw at the time of the Ryūkyū Kingdom . [ 3 ] [ 4 ] In the Southern Ryukyuan languages of the Sakishima Islands it was known as barazan and on Okinawa Island as warazani or warazai . [ 5 ] Formerly used in particular in relation to the "head tax", it is still to be found in connection with the annual Itoman Giant Tug-of-War ( 糸満大綱引 ) , to record the amount of miki or sacred sake dedicated. [ 1 ]
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The Warburg coefficient (or Warburg constant ; denoted A W or σ ) is the diffusion coefficient of ions in solution , associated to the Warburg element , Z W . The Warburg coefficient has units of Ω / seconds = Ω s − 1 / 2 {\displaystyle {\Omega }/{\sqrt {\text{seconds}}}={\Omega }s^{-1/2}}
The value of A W can be obtained by the gradient of the Warburg plot, a linear plot of the real impedance ( R ) against the reciprocal of the square root of the frequency ( 1 / ω {\displaystyle {1}/{\sqrt {\omega }}} ). This relation should always yield a straight line, as it is unique for a Warburg.
Alternatively, the value of A W can be found by:
A W = R T A n 2 F 2 2 ( 1 C O b D O + 1 C R b D R ) = R T A n 2 F 2 Θ C 2 D {\displaystyle A_{W}={\frac {RT}{An^{2}F^{2}{\sqrt {2}}}}{\left({\frac {1}{C_{\mathrm {O} }^{b}{\sqrt {D_{\mathrm {O} }}}}}+{\frac {1}{C_{\mathrm {R} }^{b}{\sqrt {D_{\mathrm {R} }}}}}\right)}={\frac {RT}{An^{2}F^{2}\Theta C{\sqrt {2D}}}}}
where
The equation for A W applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble.
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In plant physiology , the Warburg effect is the decrease in the rate of photosynthesis due to high oxygen concentrations. [ 1 ] [ 2 ] Oxygen is a competitive inhibitor of carbon dioxide fixation by RuBisCO which initiates photosynthesis. Furthermore, oxygen stimulates photorespiration which reduces photosynthetic output. These two mechanisms working together are responsible for the Warburg effect. [ 3 ]
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The Warburg diffusion element is an equivalent electrical circuit component that models the diffusion process in dielectric spectroscopy . That element is named after German physicist Emil Warburg .
A Warburg impedance element can be difficult to recognize because it is nearly always associated with a charge-transfer resistance (see charge transfer complex ) and a double-layer capacitance , but is common in many systems. The presence of the Warburg element can be recognised if a linear relationship on the log of a Bode plot ( log | Z | vs. log ω ) exists with a slope of value –1/2.
The Warburg diffusion element ( Z W ) is a constant phase element (CPE), with a constant phase of 45° (phase independent of frequency) and with a magnitude inversely proportional to the square root of the frequency by:
where
This equation assumes semi-infinite linear diffusion, [ 1 ] that is, unrestricted diffusion to a large planar electrode .
If the thickness of the diffusion layer is known, the finite-length Warburg element [ 2 ] is defined as:
where B = δ D , {\displaystyle B={\tfrac {\delta }{\sqrt {D}}},}
where δ {\displaystyle \delta } is the thickness of the diffusion layer and D is the diffusion coefficient.
There are two special conditions of finite-length Warburg elements: the Warburg Short ( W S ) for a transmissive boundary, and the Warburg Open ( W O ) for a reflective boundary.
This element describes the impedance of a finite-length diffusion with transmissive boundary. [ 3 ] It is described by the following equation:
This element describes the impedance of a finite-length diffusion with reflective boundary. [ 4 ] It is described by the following equation:
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The Warburg hypothesis ( / ˈ v ɑːr b ʊər ɡ / , [ˈvaːɐ̯bʊʁk] ), sometimes known as the Warburg theory of cancer , postulates that the driver of carcinogenesis (cancer formation) is insufficient cellular respiration caused by insult (damage) to mitochondria . [ 1 ] The Warburg effect , on the other hand, describes the observation that cancer cells , and many cells grown in vitro , exhibit glucose fermentation even when enough oxygen is present to properly respire. [ 2 ] In other words, instead of fully respiring in the presence of adequate oxygen, cancer cells ferment. The Warburg hypothesis is that the Warburg effect is the root cause of cancer.
The hypothesis was postulated by the Nobel laureate Otto Heinrich Warburg in 1924. [ 3 ] He hypothesized that cancer , malignant growth, and tumor growth are caused by the fact that tumor cells mainly generate energy (as e.g., adenosine triphosphate / ATP) by non-oxidative breakdown of glucose (a process called glycolysis ). This is in contrast to healthy cells which mainly generate energy from oxidative breakdown of pyruvate . Pyruvate is an end-product of glycolysis , and is oxidized within the mitochondria . Hence, according to Warburg, carcinogenesis stems from the lowering of mitochondrial respiration. Warburg regarded the fundamental difference between normal and cancerous cells to be the ratio of glycolysis to respiration; this observation is also known as the Warburg effect.
In the somatic mutation theory of cancer, malignant proliferation is caused by mutations and altered gene expression, in a process called malignant transformation , resulting in an uncontrolled growth of cells. [ 4 ] [ 5 ] The metabolic difference observed by Warburg adapts cancer cells to the hypoxic (oxygen-deficient) conditions inside solid tumors, and results largely from the same mutations in oncogenes and tumor suppressor genes that cause the other abnormal characteristics of cancer cells. [ 6 ] Therefore, the metabolic change observed by Warburg is not so much the cause of cancer, as he claimed, but rather, it is one of the characteristic effects of cancer-causing mutations.
Warburg articulated his hypothesis in a paper entitled The Prime Cause and Prevention of Cancer which he presented in lecture at the meeting of the Nobel-Laureates on June 30, 1966 at Lindau , Lake Constance , Germany. In this speech, Warburg presented additional evidence supporting his theory that the elevated anaerobiosis seen in cancer cells was a consequence of damaged or insufficient respiration. Put in his own words, "the prime cause of cancer is the replacement of the respiration of oxygen in normal body cells by a fermentation of sugar." [ 7 ]
The body often kills damaged cells by apoptosis , a mechanism of self-destruction that involves mitochondria, but this mechanism fails in cancer cells where the mitochondria are shut down. The reactivation of mitochondria in cancer cells restarts their apoptosis program. [ 8 ]
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The Warburg–Christian method is an ultraviolet spectroscopic protein and nucleic acid assay method based on the absorbance of UV light at 260 nm and 280 nm wavelengths. Proteins generally absorb light at 280 nanometers due to the presence of tryptophan and tyrosine . Nucleic acids absorb more at 260 nm, primarily due to purine and pyrimidine bases. The Warburg–Christian method combines measurements at these wavelengths to estimate the amounts of protein and nucleic acid present. [ 1 ] Original description of the method appeared in 1941. [ 2 ]
The method is named for its creators, the German cancer researcher Otto Heinrich Warburg , Nobel Prize winner, and his employee Walter Christian of the Kaiser Wilhelm Institute for Biology in Berlin.
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Warchalking is the drawing of symbols in public places to advertise an open Wi-Fi network .
Inspired by hobo symbols , the warchalking marks were conceived by a group of friends in June 2002 and published by Matt Jones who designed the set of icons and produced a downloadable document containing them. [ 1 ] [ 2 ] Within days of Jones publishing a blog entry about warchalking, articles appeared in dozens of publications and stories appeared on several major television news programs around the world. [ 2 ]
The word is formed by analogy to wardriving , the practice of driving around an area in a car to detect open Wi-Fi nodes . That term in turn is based on wardialing , the practice of dialing many phone numbers hoping to find a modem . [ 3 ]
Having found a Wi-Fi node, the warchalker draws a special symbol on a nearby object, such as a wall, the pavement, or a lamp post. [ 2 ] Those offering Wi-Fi service might also draw such a symbol to advertise the availability of their Wi-Fi location, whether commercial or personal. [ 4 ]
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Ward-Beck Systems commonly referred to as Ward-Beck or simply WBS , is a Canadian manufacturer of broadcast audio and video equipment. It was founded in a garage in April 1967 by Ron W. Ward and director of engineering, Rodger K. Beck. [ 1 ]
On January 26, 2021, Ward-Beck announced that it would "cease manufacturing operations" effective January 31, 2021, and that the company's intellectual property is available for sale. [ 2 ]
The first two digits of the module or console's serial number dictate the year of manufacturing.
The Ward-Beck Systems Preservation Society was founded in 2005 by Tony Kuzub . The goal and objective of the WBSPS is to keep vintage Ward-Beck equipment running and working by supplying a database of documentation, knowledge, and support. There are only a handful of consoles still in existence and use, and the WBSPS is dedicated to keeping these consoles in use and maintained. Many manuals have been scanned in their entirety and posted for all to learn from. The WBSPS was given permission by Eugene Johnson of Ward-Beck to publish information regarding vintage WBS equipment. [ 6 ] The WBSPS is not directly or in-directly associated with Ward-Beck Systems Incorporated. A Letter of permission from Ward-Beck Systems
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Wardialing (or war dialing ) is a technique to automatically scan a list of telephone numbers, usually dialing every number in a local area code to search for modems, computers, bulletin board systems ( computer servers ) and fax machines . Hackers use the resulting lists for various purposes: hobbyists for exploration, and crackers —malicious hackers who specialize in breaching computer security—for guessing user accounts (by capturing voicemail greetings), or locating modems that might provide an entry-point into computer or other electronic systems. It may also be used by security personnel, for example, to detect unauthorized devices, such as modems or faxes, on a company's telephone network.
A single wardialing call would involve calling an unknown number, and waiting for one or two rings, since answering computers usually pick up on the first ring. If the phone rings twice, the modem hangs up and tries the next number. If a modem or fax machine answers, the wardialer program makes a note of the number. If a human or answering machine answers, the wardialer program hangs up. Depending on the time of day, wardialing 10,000 numbers in a given area code might annoy dozens or hundreds of people, some who attempt and fail to answer a phone in two rings, and some who succeed, only to hear the wardialing modem's carrier tone and hang up. The repeated incoming calls are especially annoying to businesses that have many consecutively numbered lines in the exchange, such as used with a Centrex telephone system.
Some newer wardialing software, such as WarVOX , does not require a modem to conduct wardialing. [ 1 ] Rather, such programs can use VOIP connections, which can speed up the number of calls that a wardialer can make. Sandstorm Enterprises has a patent U.S. patent 6,490,349 on a multi-line war dialer. ("System and Method for Scan-Dialing Telephone Numbers and Classifying Equipment Connected to Telephone Lines Associated therewith.") The patented technology is implemented in Sandstorm's PhoneSweep war dialer.
The popular name for this technique originated in the 1983 film WarGames . [ 2 ] In the film, the protagonist programmed his computer to dial every telephone number in Sunnyvale, California to find other computer systems. Prior to the movie's release, this technique was known as "hammer dialing" or " demon dialing ", [ citation needed ] but the film introduced the method to many, such as the members of The 414s . [ 3 ] By 1985 at least one company advertised a "War Games Autodialer" for Commodore computers . [ 4 ] Such programs became common on bulletin board systems of the time, with file names often truncated to wardial.exe and the like due to length restrictions of 8 characters on such systems. Eventually, the etymology of the name fell behind as "war dialing" gained its own currency within computing culture. [ 2 ]
The popularity of wardialing in 1980s and 1990s prompted some states to enact legislation prohibiting the use of a device to dial telephone numbers without the intent of communicating with a person.
A more recent phenomenon is wardriving , the searching for wireless networks ( Wi-Fi ) from a moving vehicle. Wardriving was named after wardialing, since both techniques involve actively scanning to find computer networks. The aim of wardriving is to collect information about wireless access points (not to be confused with piggybacking ).
Similar to war dialing is a port scan under TCP/IP, which "dials" every TCP port of every IP address to find out what services are available. Unlike wardialing, however, a port scan will generally not disturb a human being when it tries an IP address, regardless of whether there is a computer responding on that address or not. Related to wardriving is warchalking , the practice of drawing chalk symbols in public places to advertise the availability of wireless networks.
The term is also used today by analogy for various sorts of exhaustive brute force attack against an authentication mechanism, such as a password. While a dictionary attack might involve trying each word in a dictionary as the password, "wardialing the password" would involve trying every possible password. Password protection systems are usually designed to make this impractical, by making the process slow and/or locking out an account for minutes or hours after some low number of wrong password entries.
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https://en.wikipedia.org/wiki/Wardialing
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Wardriving is the act of searching for Wi-Fi wireless networks as well as cell towers, usually from a moving vehicle, using a laptop or smartphone . Software for wardriving is freely available on the internet .
Warbiking , warcycling , warwalking and similar use the same approach but with other modes of transportation.
War driving originated from wardialing , a method popularized by a character played by Matthew Broderick in the film WarGames , and named after that film. War dialing consists of dialing every phone number in a specific sequence in search of modems. [ 1 ]
Warbiking or warcycling is similar to wardriving, but is done from a moving bicycle or motorcycle . This practice is sometimes facilitated by mounting a Wi-Fi enabled device on the vehicle.
Warwalking , or warjogging , is similar to wardriving, but is done on foot rather than from a moving vehicle. The disadvantages of this method are a slower speed of travel (leading to the discovery of more infrequently discovered networks) and the absence of a convenient computing environment. Consequently, handheld devices such as pocket computers , which can perform such tasks while users are walking or standing, have dominated this practice. Technology advances and developments in the early 2000s expanded the extent of this practice. Advances include computers with integrated Wi-Fi, rather than CompactFlash (CF) or PC Card (PCMCIA) add-in cards in computers such as Dell Axim , Compaq iPAQ and Toshiba pocket computers starting in 2002. Later, the active Nintendo DS and Sony PSP enthusiast communities gained Wi-Fi abilities on these devices. Further, nearly all modern smartphones integrate Wi-Fi and Global Positioning System (GPS).
Warrailing , or Wartraining , is similar to wardriving, but is done on a train or tram rather than from a slower more controllable vehicle. The disadvantages of this method are higher speed of travel (resulting in less discovery of more infrequently discovered networks) and often limited to major roads with higher traffic.
Warkitting is a combination of wardriving and rootkitting . [ 2 ] In a warkitting attack, a hacker replaces the firmware of an attacked router. This allows them to control all traffic for the victim, and could even permit them to disable TLS by replacing HTML content as it is being downloaded. [ 3 ] Warkitting was identified by Tsow, Jakobsson, Yang, and Wetzel.
Warflying is a variant utilizing aircraft flying around and locating nodes. It was first performed in Perth with a Grumman Tiger in August 2002, [ 4 ] and a week later in San Diego in August 2002 in a Cessna 182 . [ 5 ] [ 6 ]
Wardrivers use a Wi-Fi-equipped device together with a GPS device to record the location of wireless networks. The results can then be uploaded to websites like WiGLE , openBmap or Geomena where the data is processed to form maps of the network neighborhood. There are also clients available for smartphones running Android that can upload data directly. For better range and sensitivity, antennas are built or bought, and vary from omnidirectional to highly directional.
The maps of known network IDs can then be used as a geolocation system—an alternative to GPS —by triangulating the current position from the signal strengths of known network IDs. Examples include Place Lab by Intel , Skyhook , Navizon [ 7 ] by Cyril Houri , SeekerLocate from Seeker Wireless , openBmap and Geomena. Navizon and openBmap combines information from Wi-Fi and cell phone tower maps contributed by users from Wi-Fi-equipped cell phones . [ 8 ] [ 9 ] In addition to location finding, this provides navigation information, and allows for the tracking of the position of friends, and geotagging .
In December 2004, a class of 100 undergraduates worked to map the city of Seattle, Washington over several weeks. They found 5,225 access points; 44% were secured with WEP encryption, 52% were open, and 3% were pay-for-access. They noticed trends in the frequency and security of the networks depending on location. Many of the open networks were clearly intended to be used by the general public, with network names like "Open to share, no porn please" or "Free access, be nice." The information was collected into high-resolution maps, which were published online. [ 10 ] [ 11 ] Previous efforts had mapped cities such as Dublin. [ 12 ]
Some portray wardriving as a questionable practice (typically from its association with piggybacking ), though, from a technical viewpoint, everything is working as designed: many access points broadcast identifying data accessible to anyone with a suitable receiver. It could be compared to making a map of a neighborhood's house numbers and mail box labels. [ 13 ]
While some may claim that wardriving is illegal, there are no laws that specifically prohibit or allow wardriving, though many localities have laws forbidding unauthorized access of computer networks and protecting personal privacy. Google created a privacy storm in some countries after it eventually admitted systematically but surreptitiously gathering Wi-Fi data while capturing video footage and mapping data for its Street View service. [ 14 ] It has since been using Android -based mobile devices to gather this data. [ 15 ]
Passive, listen-only wardriving (with programs like Kismet or KisMAC ) does not communicate at all with the networks, merely logging broadcast addresses. This can be likened to listening to a radio station that happens to be broadcasting in the area or with other forms of DXing .
With other types of software, such as NetStumbler , the wardriver actively sends probe messages, and the access point responds per design. The legality of active wardriving is less certain, since the wardriver temporarily becomes "associated" with the network, even though no data is transferred. Most access points, when using default "out of the box" security settings, are intended to provide wireless access to all who request it. The war driver's liability may be reduced by setting the computer to a static IP, instead of using DHCP , preventing the network from granting the computer an IP address or logging the connection. [ 16 ]
In the United States, the case that is usually referenced in determining whether a network has been "accessed" is State v. Allen . In this case, Allen had been wardialing in an attempt to get free long-distance calling through Southwestern Bell 's computer systems. When presented with a password protection screen, however, he did not attempt to bypass it. The court ruled that although he had "contacted" or "approached" the computer system, this did not constitute "access" of the company's network. [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ]
There are also homebrew wardriving applications for handheld game consoles that support Wi-Fi , such as sniff jazzbox/wardive for the Nintendo DS/Android, Road Dog for the Sony PSP , WiFi-Where for the iPhone , G-MoN, Wardrive, [ 24 ] Wigle Wifi for Android , and WlanPollution [ 25 ] for Symbian NokiaS60 devices. There also exists a mode within Metal Gear Solid: Portable Ops for the Sony PSP (wherein the player is able to find new comrades by searching for wireless access points) which can be used to wardrive. Treasure World for the DS is a commercial game in which gameplay wholly revolves around wardriving.
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https://en.wikipedia.org/wiki/Wardriving
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A warehouse control system (WCS) is a software application that directs the real-time activities within warehouses and distribution centers (DC). As the “traffic cop” for the warehouse/distribution center, the WCS is responsible for keeping everything running smoothly, maximizing the efficiency of the material handling subsystems and often, the activities of the warehouse associates themselves. It provides a uniform interface to a broad range of material handling equipment such as AS/RS , carousels, conveyor systems , sorters, palletizers, etc. The primary functions of a WCS include:
Each major function is designed to work as part of an integrated process to effectively link the host systems with the lower level control system, while relieving the Host from the real-time requirements such as operator screens and lower level equipment control interfaces.
The typical warehouse/distribution center consists of a multi-tier control architecture in which each level in the control hierarchy has a defined role.
The upper most level of the control hierarchy is the warehouse management system (WMS), or host. This system handles the business aspects of the system such as receiving customer orders, allocating inventory, and generating shipping manifests or bills of lading ) and invoices based on order fulfillment information and shipping information received from the material handling control system (WCS). It typically interacts with the material handling system on a non-real-time basis.
Coordinating the activities of the various material handling sub-systems is the role of the warehouse control system (WCS). The WCS directs the "real-time" data management and interface responsibilities of the material handling system as well as provides common user interface screens for monitoring, control, and diagnostics. As the focal point for managing the operational aspects of the material handling system, the WCS provides the critical link between the non-real time based host and the real-time MHE control system. It receives information from the upper level Host and coordinates the various real-time control devices (conveyors, print and apply applicators, etc.) to accomplish the daily workload. At each decision point, the WCS determines the most efficient routing of the product and transmits directives to the equipment controllers to achieve the desired result.
At the lowest level, closest to the physical equipment, are the equipment controller(s). These controllers are typically some form of a programmable logic controller (PLC) or a dedicated, real-time PC control system. They interface to peripheral Input/Output (I/O) devices such as photo-eyes scanners, motors, etc. as well as data collection devices such as bar code scanners ( barcode reader ) and weigh scales and are responsible for the physical operation of the material handling equipment. The equipment controllers are also responsible for the physical handling of product and tracking it from point-to-point based on the direction from the upper level control systems. Typically a single controller is only concerned with the operations of a defined area or sub-system of the overall material handling system.
Ultimately, the control hierarchy within the distribution center reflects the organizational structure of their human counterparts. The management staff (or the WMS) determines the workload to be accomplished for the day while the supervisory staff (WCS) oversees the real-time activities of the warehouse associates (equipment controllers) to complete the daily activities. Each warehouse associate is assigned a specific task based on their area of expertise (order selection – carousel/Pick To Light, transportation - conveyors, etc.). As each operator completes their individual assignment, the supervisor (WCS) assigns the next task based on the current workload. As orders are completed, the (WCS) supervisor reports back to (WMS) management the status of the orders along with any pertinent order information.
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https://en.wikipedia.org/wiki/Warehouse_control_system
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