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c_xs5m8eoryomd | Despite this controversy, Maples continued to grow and in the 1883 edition of A Dictionary of Common Wants, the entry for Maple & Co. read:"MESSRS. MAPLE & CO., 145, 146, 147, 148, 149, Tottenham Court Road, W.C., undertake, in both town and country, every description of Artistic Decorations, Parquet Flooring, Solid Oa... | Maple & Co. |
c_bftqu99j15xz | The showrooms cover an area of more than five acres which will give some idea of the extent of the business carried on; but no adequate conception can be formed of the magnitude and variety of the stock without the intending purchaser pays a personal visit to the establishment”. By 1889, Maple & Co. occupied the block ... | Maple & Co. |
c_s56380v8vtv6 | By 1892, Maples held the title of 'Upholsterers by special appointment to her majesty Queen Victoria'. The Royal connection continued and in 1910, when Edward VII died, Maples were appointed 'Upholsters and Decorators to his majesty George V'. Maples used this prestige to their advantage and printed the royal crest in ... | Maple & Co. |
c_nwpz4tk50pjj | In order to cut streamer, fracture or ripple glass, the sheet may be scored on the side without streamers, fractures or ripples with a carbide glass cutter, and broken at the score line with breaker-grozier pliers. In order to cut drapery glass, the sheet may be placed on styrofoam, scored with a carbide glass cutter, ... | Fracture glass |
c_9ugpucy1nbfp | In order to de-risk the programme Atlas and the MOD took an incremental approach to the development and implementation of DII, with a separate contract for each increment. The extended timeline allowed the MOD flexibility in defining its requirements. Increment 1: Contract awarded March 2005. This covered 70,000 user a... | Defence Information Infrastructure |
c_r6j7c7w30r4z | Increment 2a: Contract awarded December 2006. This was for an additional 44,000 UADs and 58,000 user accounts in the Restricted and Secret domains, again in fixed locations. Increment 2b: Contract awarded September 2007: This extended DII(F) into the deployed environment with the provision of UADs to support land and m... | Defence Information Infrastructure |
c_d4esreucid3v | Increment 2c: Signed in January 2009. This extended the DII footprint into the above-Secret domain to support a number of key operations and intelligence initiatives. | Defence Information Infrastructure |
c_pq1xx6ghmsas | Increment 3a: Contract awarded January 2010. Atlas provided 42,000 UADs operating in the Restricted and Secret domains to the remaining MOD fixed sites. This supported some 60,000 personnel, notably within the RAF, at Joint Helicopter Command and other MOD locations. Increment 3a received an MOD Chief of Defence Materi... | Defence Information Infrastructure |
c_k983i9ba3by4 | In order to deal with high data-rates, several architectural paradigms are commonly used: Pipeline of processors - each stage of the pipeline consisting of a processor performing one of the functions listed above. Parallel processing with multiple processors, often including multithreading. Specialized microcoded engin... | Network processor |
c_fyomqrktt3b2 | With the advent of multicore architectures, network processors can be used for higher layer (L4-L7) processing.Additionally, traffic management, which is a critical element in L2-L3 network processing and used to be executed by a variety of co-processors, has become an integral part of the network processor architectur... | Network processor |
c_j9pcs810fb1v | In order to deal with occurrences of the digit zero, the following rule set was introduced (referred to as Basic Pilish): In Basic Pilish, each word of n letters represents (1) The digit n if n < 10 (2) The digit 0 if n = 10Since long runs of small non-zero digits are difficult to deal with naturally (such as 1121 or 1... | Pilish |
c_n31rok3b8u2z | In order to deal with space debris, Busek proposed in 2014 a remotely controlled vehicle to rendezvous with this debris, capture it, and attach a smaller deorbit satellite to the debris. The remotely controlled vehicle would then drag the debris/smallsat-combination, using a tether, to the desired location. The larger ... | ORbital DEbris Remover |
c_kau83ay4sdxd | In order to deal with the mission, the Argotec platform uses an autonomous navigation system, two light solar arrays, an integrated propulsion system with thrusters of 50mN thrust and isp of 40s, two cameras, an X-band communication system, and an advanced on-board computer. | LICIACube |
c_5vd09rrvxibr | In order to deal with the problem of increased noise due to imputation, Rubin (1987) developed a method for averaging the outcomes across multiple imputed data sets to account for this. All multiple imputation methods follow three steps. Imputation – Similar to single imputation, missing values are imputed. | Imputation (statistics) |
c_v5jflmxifj21 | However, the imputed values are drawn m times from a distribution rather than just once. At the end of this step, there should be m completed datasets. Analysis – Each of the m datasets is analyzed. | Imputation (statistics) |
c_76fchj1q5ife | At the end of this step there should be m analyses. Pooling – The m results are consolidated into one result by calculating the mean, variance, and confidence interval of the variable of concern or by combining simulations from each separate model.Just as there are multiple methods of single imputation, there are multi... | Imputation (statistics) |
c_ybsydo0ae7qs | Multiple imputation can be used in cases where the data are missing completely at random, missing at random, and even when the data are missing not at random. A popular approach is multiple imputation by chained equations (MICE), also known as "fully conditional specification" and "sequential regression multiple imputa... | Imputation (statistics) |
c_shkkm7521ecl | However, MICE can suffer from performance problems when the number of observation is large and the data have complex features, such as nonlinearities and high dimensionality. More recent approaches to multiple imputation use machine learning techniques to improve its performance. | Imputation (statistics) |
c_gw1u1hlpznjs | MIDAS (Multiple Imputation with Denoising Autoencoders), for instance, uses denoising autoencoders, a type of unsupervised neural network, to learn fine-grained latent representations of the observed data. MIDAS has been shown to provide accuracy and efficiency advantages over traditional multiple imputation strategies... | Imputation (statistics) |
c_uklqhgq3mlys | After imputation, the data is treated as if they were the actual real values in single imputation. The negligence of uncertainty in the imputation can lead to overly precise results and errors in any conclusions drawn. By imputing multiple times, multiple imputation accounts for the uncertainty and range of values that... | Imputation (statistics) |
c_24fmnla36n0p | As expected, the combination of both uncertainty estimation and deep learning for imputation is among the best strategies and has been used to model heterogeneous drug discovery data.Additionally, while single imputation and complete case are easier to implement, multiple imputation is not very difficult to implement. ... | Imputation (statistics) |
c_xyjtwqhd53bk | In order to deceive wary trout, or to reach deep runs where salmon may lie, the fly angler often needs to wade to the right casting position. He therefore requires sure footing and insulation from cold water, both provided by hip boots or chest-high waders. The latter are of two main types, one-piece "boot foot" waders... | Fly fishing |
c_h0139848os3p | In the mid-20th century, American anglers developed felt boot soles for a better grip in rocky rivers: but felt is now prohibited in some US states, as a vector of fish and plant diseases that damage sport fisheries. Manufacturers now offer wading boots with special rubber treads or metal studs. | Fly fishing |
c_8vqhwwwkx58i | Breathable Gore-Tex waders provide ventilation when hiking along the water, but do not provide flotation in the event of slipping or falling into deep water. In deep water streams, an inflatable personal flotation device (PFD), or a Type III Kayak fishing vest, adds a degree of safety. Some "catch and release" anglers ... | Fly fishing |
c_nbixiglcy5od | In order to decide which clusters should be combined (for agglomerative), or where a cluster should be split (for divisive), a measure of dissimilarity between sets of observations is required. In most methods of hierarchical clustering, this is achieved by use of an appropriate distance d, such as the Euclidean distan... | Hierarchical Clustering |
c_xar9c84jujq8 | The linkage criterion determines the distance between sets of observations as a function of the pairwise distances between observations. Some commonly used linkage criteria between two sets of observations A and B and a distance d are: Some of these can only be recomputed recursively (WPGMA, WPGMC), for many a recursiv... | Hierarchical Clustering |
c_do00naft3umb | In order to declare a PHEIC, the WHO Director-General is required to take into account factors that include the risk to human health and international spread as well as advice from an international committee of experts, the IHR Emergency Committee (EC), one of whom should be an expert nominated by the State within whos... | Health emergencies |
c_xcdu4a7n4bjr | The director-general takes the advice of the EC, following their technical assessment of the crisis using legal criteria and a predetermined algorithm after a review of all available data on the event. Upon declaration, the EC then makes recommendations on what actions the director-general and member states should take... | Health emergencies |
c_iew8ffu2uwwt | In order to declare a PHEIC, the WHO Director-General is required to take into account factors which include the risk to human health and international spread as well as advice from an internationally made up committee of experts, the IHR Emergency Committee (EC), one of which should be an expert nominated by the State... | International Health Regulations |
c_pd9mhg573q74 | The Director-General takes the EC's advice following their technical assessment of the crisis using legal criteria and a predetermined algorithm after a review of all available data on the event. Upon declaration of the PHEIC, the EC then makes recommendations on what actions the Director-General and Member States shou... | International Health Regulations |
c_6hcdqe8l2q6d | In order to decouple the real-time operating system platform from the application software, ARINC 653 defines an API called APplication EXecutive (APEX). Each application software is called a partition and has its own memory space. It also has a dedicated time slot allocated by the APEX API. Within each partition, mult... | ARINC 653 |
c_a3646ioe0utp | The APEX API provides services to manage partitions, processes and timing, as well as partition/process communication and error handling. The partitioning environment can be implemented by using a hypervisor to map partitions to virtual machines, but this is not required. The standard is overseen by the AEEC APEX Subco... | ARINC 653 |
c_nvcfx51f18ge | In order to decrease the amounts owed to states under the Medicaid Drug Rebate Program, some companies misrepresented material facts regarding the regulatory origin/status of their brand name drugs, the AMP, and/or the best price. Despite the Government's good faith reliance to charge manufacturers a unit rebate amount... | Pharmaceutical fraud |
c_cx409903nua6 | In order to decrease the risk of a counter party to default, a technique called portfolio margining is applied, which simply means that the assets within a portfolio are clustered and sorted by the descending projected net loss, e.g. calculated by a pricing model. One can then determine for which cluster(s) one wants t... | Margining risk |
c_plajl6jsxvy1 | In order to decrease the time in which an island is detected, rate of change of frequency has been adopted as a detection method. The rate of change of frequency is given by the following expression: d f d t = R O C O F = Δ P f 2 G H {\displaystyle {\frac {\mathrm {d} f}{\mathrm {d} t}}=ROCOF={\frac {\Delta Pf}{2GH}}} ... | Islanding |
c_3hv2hpcd9nyb | In order to decrease the value of the critical radius r c {\displaystyle r_{c}} and promote nucleation, a supercooling or superheating process may be used. Supercooling is a phenomenon in which the system's temperature is lowered under the phase transition temperature without the creation of the new phase. Let Δ T = T ... | Critical radius |
c_evfj4sgta7gh | In order to decrease work wages, reduce operational cost and improve productivity, automated forklifts have also been developed. Automated forklifts are also called forked automated guided vehicles and are already available for sale. | Forklift |
c_bqq8sz06xukt | In order to decrypt, we turn the ciphertext back into a vector, then simply multiply by the inverse matrix of the key matrix (IFK/VIV/VMI in letters). We find that, modulo 26, the inverse of the matrix used in the previous example is: ( 6 24 1 13 16 10 20 17 15 ) − 1 ( mod 26 ) ≡ ( 8 5 10 21 8 21 21 12 8 ) {\displaysty... | Hill cipher |
c_79ncx6q2qugk | The determinant of the encrypting matrix must not have any common factors with the modular base.Thus, if we work modulo 26 as above, the determinant must be nonzero, and must not be divisible by 2 or 13. If the determinant is 0, or has common factors with the modular base, then the matrix cannot be used in the Hill cip... | Hill cipher |
c_45qcomhndc7t | For our example key matrix: | 6 24 1 13 16 10 20 17 15 | = 6 ( 16 ⋅ 15 − 10 ⋅ 17 ) − 24 ( 13 ⋅ 15 − 10 ⋅ 20 ) + 1 ( 13 ⋅ 17 − 16 ⋅ 20 ) = 441 ≡ 25 ( mod 26 ) {\displaystyle {\begin{vmatrix}6&24&1\\13&16&10\\20&17&15\end{vmatrix}}=6(16\cdot 15-10\cdot 17)-24(13\cdot 15-10\cdot 20)+1(13\cdot 17-16\cdot 20)=441\equiv 25{\... | Hill cipher |
c_aftdtxhja2zx | In order to dedicate a person to monitor an aircraft's engines and its other critical flight systems, the position of "flight engineer" (FE) was created. The FE did not actually fly the airplane; instead, the FE's position had a specialized control panel allowing for the monitoring and control of various aircraft syste... | Flight engineer |
c_vhmji26c8su7 | Traditionally, the FE station has been usually placed on the main flight deck just aft of the pilot and copilot, and close to the navigator. Earlier referred to as a "flight mechanic" on the four-engine commercial seaplanes like the Sikorsky S-42, Martin M-130 and the Boeing 314 Clipper, the FE's role was referred to a... | Flight engineer |
c_8zf5duyrw4oy | The FE panel was located in the pylon between the fuselage and the wing. The FE did not have ignition, throttle and propeller controls, thus a person in the cockpit was also required to start the engines.During the war the Avro Lancaster and Handley Page Halifax bombers employed FEs, as these large aircraft employed on... | Flight engineer |
c_4uu0stlmaws0 | In order to define A {\displaystyle A} , we define an objective function describing classification accuracy in the transformed space and try to determine A ∗ {\displaystyle A^{*}} such that this objective function is maximized. A ∗ = argmax A f ( A ) {\displaystyle A^{*}={\mbox{argmax}}_{A}f(A)} | Neighbourhood components analysis |
c_5562vo8gce5p | In order to define K-stability, we need to first exclude certain test configurations. Initially it was presumed one should just ignore trivial test configurations as defined above, whose Donaldson-Futaki invariant always vanishes, but it was observed by Li and Xu that more care is needed in the definition. One elegant ... | K-stability |
c_y144rka7alw4 | Then Tr ( A k ) = w ( k ) {\displaystyle \operatorname {Tr} (A_{k})=w(k)} . Similarly to the polynomials w ( k ) {\displaystyle w(k)} and P ( k ) {\displaystyle {\mathcal {P}}(k)} , the function Tr ( A k 2 ) {\displaystyle \operatorname {Tr} (A_{k}^{2})} is a polynomial for large enough integers k {\displaystyle k}... | K-stability |
c_9drj0wr10ppq | {\displaystyle \operatorname {Tr} (A_{k}^{2})=c_{0}k^{n+2}+O(k^{n+1}).} The norm of a test configuration is defined by the expression ‖ ( X , L ) ‖ 2 = c 0 − b 0 2 a 0 . | K-stability |
c_9qlsy5q8azd9 | {\displaystyle \|({\mathcal {X}},{\mathcal {L}})\|^{2}=c_{0}-{\frac {b_{0}^{2}}{a_{0}}}.} According to the analogy with the Hilbert-Mumford criterion, once one has a notion of deformation (test configuration) and weight on the central fibre (Donaldson-Futaki invariant), one can define a stability condition, called K-st... | K-stability |
c_5ec1y64vfh7k | We say that ( X , L ) {\displaystyle (X,L)} is: K-semistable if μ ( X , L ) ≥ 0 {\displaystyle \operatorname {\mu } ({\mathcal {X}},{\mathcal {L}})\geq 0} for all test configurations ( X , L ) {\displaystyle ({\mathcal {X}},{\mathcal {L}})} for ( X , L ) {\displaystyle (X,L)} . K-stable if μ ( X , L ) ≥ 0 {\display... | K-stability |
c_qwar1ur57hov | In order to define a custom structure type using Oracle Database one could use statements such as these:Such structure type can be then used to create a table that would also hold all columns defined in Person_Type:Custom structure types support inheritance, which means that one can create another type that inherits fr... | Structured type |
c_tl7023ddt7ja | In order to define a good DPN application, it is important to understand what DPN can do that other techniques can't. Direct-write techniques, like contact printing, can pattern multiple biological materials but it cannot create features with subcellular resolution. Many high-resolution lithography methods can pattern ... | Dip-Pen Nanolithography |
c_8ztiflgxl7qb | In order to define a model structure on the category of simplicial sets, one has to define fibrations, cofibrations and weak equivalences. One can define fibrations to be Kan fibrations. A map of simplicial sets is defined to be a weak equivalence if its geometric realization is a weak homotopy equivalence of spaces. A... | Simplicial homotopy theory |
c_09vdf4cw7362 | It is a difficult theorem of Daniel Quillen that the category of simplicial sets with these classes of morphisms becomes a model category, and indeed satisfies the axioms for a proper closed simplicial model category. A key turning point of the theory is that the geometric realization of a Kan fibration is a Serre fibr... | Simplicial homotopy theory |
c_8kkzpl92yhby | Furthermore, the geometric realization and singular functors give a Quillen equivalence of closed model categories inducing an equivalence |•|: Ho(sSet) ↔ Ho(Top)between the homotopy category for simplicial sets and the usual homotopy category of CW complexes with homotopy classes of continuous maps between them. It is... | Simplicial homotopy theory |
c_mwbs03s0pazh | In order to define a specific Schröder–Bernstein property one should decide what kind of mathematical objects are X and Y, what is meant by "a part", what is meant by "similar".In the classical (Cantor–)Schröder–Bernstein theorem, objects are sets (maybe infinite), "a part" is interpreted as a subset, "similar" is inte... | Schröder–Bernstein property |
c_zc395olyoj2d | Then a Schröder–Bernstein property takes the following form. If X is embeddable into Y and Y is embeddable into X then X and Y are similar.The same in the language of category theory: If objects X, Y are such that X injects into Y (more formally, there exists a monomorphism from X to Y) and also Y injects into X then X... | Schröder–Bernstein property |
c_xyu1shldfok5 | In order to define a specific proof of knowledge, one need not only define the language, but also the witnesses the verifier should know. In some cases proving membership in a language may be easy, while computing a specific witness may be hard. This is best explained using an example: Let ⟨ g ⟩ {\displaystyle \langle ... | Proof of knowledge |
c_x9mgcjgqwv7m | In order to define an intersection product, cycles must be "movable" so we can intersect them in general position. Choosing a suitable equivalence relation on cycles will guarantee that every pair of cycles has an equivalent pair in general position that we can intersect. The Chow groups are defined using rational equi... | Motivic Galois group |
c_re5h8tspnkei | In order to define and characterize a biosynthetic gene cluster, all the putative genes within said cluster must first be identified and their functions must be characterized. This can be performed by complementation and knock out experiments. In the process of characterizing putative genes, the genome under study beco... | Putative gene |
c_it13x8hwfr3i | Genomic evolution occurs by processes such as duplication of individual genes, genome segments, or entire genomes. These processes can result in loss of function, altered function, or gain of function, and have drastic affects on the phenotype.DNA mutations outside of a putative gene can act by positional effect, in wh... | Putative gene |
c_509ydoi00i5o | In order to define formally the ATE, we define two potential outcomes: y 0 ( i ) {\displaystyle y_{0}(i)} is the value of the outcome variable for individual i {\displaystyle i} if they are not treated, y 1 ( i ) {\displaystyle y_{1}(i)} is the value of the outcome variable for individual i {\displaystyle i} if they ar... | Average treatment effect |
c_52vxma7nb0p2 | The average treatment effect is given by ATE = E {\displaystyle {\text{ATE}}=\mathbb {E} } and can be estimated (if a law of large numbers holds) A T E ^ = 1 N ∑ i ( y 1 ( i ) − y 0 ( i ) ) {\displaystyle {\widehat {ATE}}={\frac {1}{N}}\sum _{i}(y_{1}(i)-y_{0}(i))} where the summation occurs over all N {\displaystyle ... | Average treatment effect |
c_tgn71u3s1j8x | In order to define performatives, Austin refers to those sentences which conform to the old prejudice in that they are used to describe or constate something, and which thus are true or false; and he calls such sentences "constatives". In contrast to them, Austin defines "performatives" as follows: Performative utteran... | Performative utterance |
c_40hauka6wqge | "I name this ship the 'Queen Elizabeth'" "I give and bequeath my watch to my brother" – as occurring in a will "I bet you sixpence it will rain tomorrow" (Austin 1962, 5)As Austin later notices himself, these examples belong (more or less strikingly) to what Austin calls, explicit performatives; to utter an "explicit" ... | Performative utterance |
c_c2otvgw89kzh | in order to command someone to leave the room then this utterance is part of the performance of a command; and the sentence, according to Austin, is neither true nor false; hence the sentence is a performative; – still, it is not an explicit performative, for it does not make explicit that the act the speaker is perfor... | Performative utterance |
c_3oic4oh9wz8f | Every performative utterance has its own procedure and risks of failure that Austin calls 'infelicities'. : 14 He sees a sharp distinction between the individual text and the 'total speech act situation' surrounding it. According to Austin, in order to successfully perform an illocutionary act, certain conditions have ... | Performative utterance |
c_cigss3nvgse2 | In order to define quantum stochastic integration, it is important to define a quantum Wiener process:: 155: 3765 B ( t , t 0 ) = ∫ t 0 t b i n ( t ′ ) d t ′ . {\displaystyle B(t,t_{0})=\int _{t_{0}}^{t}b_{\mathrm {in} }(t^{\prime })\mathrm {d} t^{\prime }\,.} This definition gives the quantum Wiener process the commut... | Quantum stochastic calculus |
c_fj1yhcqjwbum | {\displaystyle \langle B^{\dagger }(t,t_{0})B(t,t_{0})\rangle _{\rho (t,t_{0})}=N(t-t_{0})\,.} The quantum Wiener processes are also specified such that their quasiprobability distributions are Gaussian by defining the density operator: ρ ( t , t 0 ) = ( 1 − e − κ ) exp , {\displaystyle \rho (t,t_{0})=(1-e^{-\kappa ... | Quantum stochastic calculus |
c_myy3ilejpgsa | In order to define the Itô QSDE, it is necessary to know something about the bath statistics. : 159 In the context of the white noise formalism described earlier, the Itô QSDE can be defined as:: 156 ( I ) d a = − i ℏ d t + γ ( ( N + 1 ) D a + N D a ) d t − γ ( d B ( t ) − d B † ( t ) ) , {\displaystyle (\mathbf {... | Quantum stochastic calculus |
c_j7bhns21wkvn | In order to define the Jacobian, we first need the notion of a divisor. Consider a hyperelliptic curve C {\displaystyle C} over some field K {\displaystyle K} . Then we define a divisor D {\displaystyle D} to be a formal sum of points in C {\displaystyle C} , i.e. D = ∑ P ∈ C c P {\textstyle D=\sum _{P\in C}{c_{P}}} w... | Imaginary hyperelliptic curve |
c_wrt30a7y5x40 | This means that a divisor is a finite formal sum of scalar multiples of points. Note that there is no simplification of c P {\displaystyle c_{P}} given by a single point (as one might expect from the analogy with elliptic curves). Furthermore, we define the degree of D {\displaystyle D} as deg ( D ) = ∑ P ∈ C c P ∈ ... | Imaginary hyperelliptic curve |
c_1ra0f4bbhy5f | The set of all divisors D i v ( C ) {\displaystyle \mathrm {Div} (C)} of the curve C {\displaystyle C} forms an Abelian group where the addition is defined pointwise as follows ∑ P ∈ C c P + ∑ P ∈ C d P = ∑ P ∈ C ( c P + d P ) {\textstyle \sum _{P\in C}{c_{P}}+\sum _{P\in C}{d_{P}}=\sum _{P\in C}{(c_{P}+d_{P})}} . I... | Imaginary hyperelliptic curve |
c_w7npm5umdljc | Consider the map φ: D i v ( C ) → Z {\displaystyle \varphi :\mathrm {Div} (C)\rightarrow \mathbb {Z} } defined by φ ( D ) = deg ( D ) {\displaystyle \varphi (D)=\deg(D)} , note that Z {\displaystyle \mathbb {Z} } forms a group under the usual addition. Then φ ( ∑ P ∈ C c P + ∑ P ∈ C d P ) = φ ( ∑ P ∈ C ( c P + d P ... | Imaginary hyperelliptic curve |
c_b21t22r5zx3o | Consider a function f ∈ K ¯ ( C ) ∗ {\displaystyle f\in {\overline {K}}(C)^{*}} , then we can look at the formal sum div ( f ) = ∑ P ∈ C o r d P ( f ) {\textstyle (f)=\sum _{P\in C}{\mathrm {ord} _{P}(f)}} . Here o r d P ( f ) {\displaystyle \mathrm {ord} _{P}(f)} denotes the order of f {\displaystyle f} at P {\displa... | Imaginary hyperelliptic curve |
c_vnshqx7nfwmh | It can be shown that f {\displaystyle f} has only a finite number of zeroes and poles, and thus only finitely many of the ord P ( f ) {\displaystyle _{P}(f)} are non-zero. This implies that div ( f ) {\displaystyle (f)} is a divisor. Moreover, as ∑ P ∈ C o r d P ( f ) = 0 {\textstyle \sum _{P\in C}{\mathrm {ord} _{P}(f... | Imaginary hyperelliptic curve |
c_vd33juilgud5 | Such divisors, i.e. divisors coming from some rational function f {\displaystyle f} , are called principal divisors and the set of all principal divisors P r i n c ( C ) {\displaystyle \mathrm {Princ} (C)} is a subgroup of D i v 0 ( C ) {\displaystyle \mathrm {Div} ^{0}(C)} .Proof. The identity element 0 = ∑ P ∈ C 0 {... | Imaginary hyperelliptic curve |
c_zccobaobdikv | Then D 1 − D 2 = ∑ P ∈ C ( o r d P ( f ) − o r d P ( g ) ) {\textstyle D_{1}-D_{2}=\sum _{P\in C}{(\mathrm {ord} _{P}(f)-\mathrm {ord} _{P}(g))}} comes from the function f / g {\displaystyle f/g} , and thus D 1 − D 2 {\displaystyle D_{1}-D_{2}} is a principal divisor, too. We conclude that P r i n c ( C ) {\displaysty... | Imaginary hyperelliptic curve |
c_iu21xtk5l4jl | Two divisors D 1 , D 2 ∈ D i v 0 ( C ) {\displaystyle D_{1},D_{2}\in \mathrm {Div} ^{0}(C)} are called equivalent if they belong to the same element of J ( C ) {\displaystyle J(C)} , this is the case if and only if D 1 − D 2 {\displaystyle D_{1}-D_{2}} is a principal divisor. Consider for example a hyperelliptic curve ... | Imaginary hyperelliptic curve |
c_fdf2704rrzpm | In order to define the Polyakov action, the world-sheet is equipped with a world-sheet metric g {\displaystyle \mathbf {g} } , which also has signature ( − , + ) {\displaystyle (-,+)} but is independent of the induced metric. Since Weyl transformations are considered a redundancy of the metric structure, the world-shee... | Worldsheet |
c_pb5tfjv89pb0 | In order to define the Pontryagin product we first need a map which sends the direct product of the m-th and n-th homology group to the (m+n)-th homology group of a space. We therefore define the cross product, starting on the level of singular chains. Given two topological spaces X and Y and two singular simplices f: ... | Pontryagin product |
c_3qk9i1g513w5 | In order to define the category Exal _ {\displaystyle {\underline {\text{Exal}}}} we need to define what a square-zero extension actually is. Given a surjective morphism of A {\displaystyle A} -algebras p: E → B {\displaystyle p:E\to B} it is called a square-zero extension if the kernel I {\displaystyle I} of p {\displ... | Exalcomm |
c_83qc2s496b2r | In order to define the data structure difference bound matrix, it is first required to give a data structure to encode atomic constraints. Furthermore, we introduce an algebra for atomic constraints. This algebra is similar to the tropical semiring, with two modifications: An arbitrary ordered monoid may be used instea... | Difference bound matrix |
c_6grsp84ucg20 | In order to define the fundamental group, one needs the notion of homotopy relative to a subspace. These are homotopies which keep the elements of the subspace fixed. Formally: if f and g are continuous maps from X to Y and K is a subset of X, then we say that f and g are homotopic relative to K if there exists a homot... | Homotopy equivalent |
c_jfkgnqo2esec | In order to define the notion of "white noise" in the theory of continuous-time signals, one must replace the concept of a "random vector" by a continuous-time random signal; that is, a random process that generates a function w {\displaystyle w} of a real-valued parameter t {\displaystyle t} . Such a process is said t... | White Gaussian noise |
c_8upm8zo754yw | As in the discrete case, some authors adopt the weaker definition for "white noise", and use the qualifier independent to refer to either of the stronger definitions. Others use weakly white and strongly white to distinguish between them. However, a precise definition of these concepts is not trivial, because some quan... | White Gaussian noise |
c_4zdd0mui6m1j | Indeed, the set of all possible instances of a signal w {\displaystyle w} is no longer a finite-dimensional space R n {\displaystyle \mathbb {R} ^{n}} , but an infinite-dimensional function space. Moreover, by any definition a white noise signal w {\displaystyle w} would have to be essentially discontinuous at every po... | White Gaussian noise |
c_vt0jn5orhghl | Then the covariance E ( w ( t 1 ) ⋅ w ( t 2 ) ) {\displaystyle \mathrm {E} (w(t_{1})\cdot w(t_{2}))} between the values at two times t 1 {\displaystyle t_{1}} and t 2 {\displaystyle t_{2}} is well-defined: it is zero if the times are distinct, and σ 2 {\displaystyle \sigma ^{2}} if they are equal. However, by this defi... | White Gaussian noise |
c_61z0jwoe6674 | Therefore, most authors define the signal w {\displaystyle w} indirectly by specifying non-zero values for the integrals of w ( t ) {\displaystyle w(t)} and | w ( t ) | 2 {\displaystyle |w(t)|^{2}} over any interval {\displaystyle } , as a function of its width r {\displaystyle r} . In this approach, however, the valu... | White Gaussian noise |
c_7yqfb0sqpdec | In order to define the twist of a rigid body, we must consider its movement defined by the parameterized set of spatial displacements, D(t)=(,d(t)), where is a rotation matrix and d is a translation vector. This causes a point p that is fixed in moving body coordinates to trace a curve P(t) in the fixed frame given by... | Screw theory |
c_ztevya9xvzab | Now substitute p = (P − d) into this equation to obtain, V P ( t ) = P + v − d or V P ( t ) = ω × P + v + d × ω , {\displaystyle \mathbf {V} _{P}(t)=\mathbf {P} +\mathbf {v} -\mathbf {d} \quad {\text{or}}\quad \mathbf {V} _{P}(t)=\mathbf {\omega } \times \mathbf {P} +\mathbf {v} +\mathbf {d} \times \mathbf {\omega } ... | Screw theory |
c_3wvcrtqzt1j1 | The vector V = v + d × ω is the velocity of the point in the body that corresponds with the origin of the fixed frame. There are two important special cases: (i) when d is constant, that is v = 0, then the twist is a pure rotation about a line, then the twist is L = ( ω , d × ω ) , {\displaystyle {\mathsf {L}}=(\omega ... | Screw theory |
c_qoik89yviyr9 | In order to define these formulas, the movement of a component B of a mechanical system is defined by the set of rotations and translations d(t) assembled into the homogeneous transformation =. If p is the coordinates of a point P in B measured in the moving reference frame M, then the trajectory of this point traced ... | Kinematics |
c_b1uoii5q091z | In order to demonstrate that IP ⊆ PSPACE, we present a simulation of an interactive proof system by a polynomial space machine. Now, we can define: Pr = max P Pr {\displaystyle \Pr=\max \nolimits _{P}\Pr \left} and for every 0 ≤ j ≤ p and every message history Mj, we inductively define the function NMj: N M j = { 0 j... | IP (complexity) |
c_f9h89gsknkuy | In order to demonstrate the quantum mechanical behaviour, the team first needed to cool the mechanical resonator until it was in its quantum ground state (the state with the lowest possible energy). Specifically, a temperature T ≪ h f k {\displaystyle T\ll {\frac {hf}{k}}} was required, where h {\displaystyle h} is the... | Quantum machine |
c_8qlodtloq1hj | In order to demonstrate the use of some of the indicative verb tenses in Louisiana French, take the example of manger, meaning "to eat": Some minor simplification of tenses is exhibited in the conjugation of the verb manger, namely of the plural first and second person conjugations which are inflected identically to th... | Cajun French Language |
c_1fnoucush55x | In order to demonstrate the usefulness of the partition function, let us calculate the thermodynamic value of the total energy. This is simply the expected value, or ensemble average for the energy, which is the sum of the microstate energies weighted by their probabilities: or, equivalently, Incidentally, one should n... | Canonical partition function |
c_ykapjja7fhec | In order to demonstrate their new Jupiter engine in an inexpensive yet relatively high performance aircraft, the Bristol Aeroplane Company authorised the conversion of three war-surplus F.2 airframes to use the Jupiter, to create the Type 76 Jupiter Fighter, which it was also hoped to sell as a fighter to foreign air f... | Bristol Jupiter Fighter |
c_uo4j9ynxaw62 | In order to derive properties of a regular curve it is advantageous to use the arc length s {\displaystyle s} of the given curve as its parameter, because of | c → ′ | = 1 {\textstyle \left|{\vec {c}}'\right|=1} and n → ′ = − c → ′ / ρ {\textstyle {\vec {n}}'=-{\vec {c}}'/\rho } (see Frenet–Serret formulas). Hence the ... | Evolute |
c_sg6ueilyyusf | (See the diagrams of the evolutes of the parabola, the ellipse, the cycloid and the nephroid.) For any arc of the evolute that does not include a cusp, the length of the arc equals the difference between the radii of curvature at its endpoints. This fact leads to an easy proof of the Tait–Kneser theorem on nesting of o... | Evolute |
c_ahb3bdg9bb2o | The normals of the given curve at points of nonzero curvature are tangents to the evolute, and the normals of the curve at points of zero curvature are asymptotes to the evolute. Hence: the evolute is the envelope of the normals of the given curve. At sections of the curve with ρ ′ > 0 {\displaystyle \rho '>0} or ρ ′ <... | Evolute |
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