Special Basis Research Articles

Local solutions for a hyperbolic equation

Let W be an open bounded set of R n with its boundary G constituted of two disjoint parts and G1 with G0 G1 = ˘. This paper deals with the existence of local solutions to the nonlinear hyperbolic problem u 00 4 u +juj r = f in W (0, T0), u = 0 on (0, T0), ¶u ¶n + h( , u 0 ) = 0 on G1 (0, T0), ( ) where r > 1 is a real number, n(x) is the exterior unit normal at x 2 G1 and h(x, s) (for x2 G1 and s2 R) is a continuous function and strongly monotone in s. We obtain existence results to problem ( ) by applying the Galerkin method with a special basis, Strauss' approximations of continuous functions and trace theorems for non-smooth functions. As usual, restrictions on r are considered in order to have the continuous embedding of Sobolev spaces.

A temperature and emissivity separation algorithm based on maximum entropy estimation of alpha spectrum's scaling and translation

In the thermal infrared (TIR) waveband, solving the target emissivity spectrum and temperature leads to an ill-posed problem in which the number of unknown parameters is larger than that of available measurements. Generally, the approaches developed for solving this kind of problems are called, by a joint name, the TES (temperature and emissivity separation) algorithm. As is shown in the name, the TES algorithm is dedicated to separating the target temperature and emissivity in the calculating procedure. In this paper, a novel method called the new MaxEnt (maximum entropy) TES algorithm is proposed, which is considered as a promotion of the MaxEnt TES algorithm proposed by Barducci. The maximum entropy estimation is utilized as the basic framework in the two preceding algorithms, so that the two algorithms both could make temperature and emissivity separation, independent of experiential information derived by some special data bases. As a result, the two algorithms could be applied to solve the temperature and emissivity spectrum of the targets which are absolutely unknown to us. However, what makes the two algorithms different is that the alpha spectrum derived by the ADE (alpha derived emissivity) method is considered as priori information to be added in the new MaxEnt TES algorithm. Based on the Wien approximation, the ADE method is dedicated to the calculation of the alpha spectrum which has a similar distribution to the true emissivity spectrum. Based on the preceding promotion, the new MaxEnt TES algorithm keeps a simpler mathematical formalism. Without any doubt, the new MaxEnt TES algorithm provides a faster computation for large volumes of data (i.e. hyperspectral images of the Earth). Some numerical simulations have been performed; the data and results show that, the maximum RMSE of emissivity estimation is 0.017, the maximum absolute error of temperature estimation is 0.62 K. Added with Gaussian white noise in which the signal to noise ratio is measured to be 11, the relative RMSE of emissivity estimation is 2.67%, the relative error of temperature estimation is 1.26%. Conclusion shows that the new MaxEnt TES algorithm may achieve high accuracy and fast calculating speed, and also get nice robustness against noise.

Освобождение от уголовной ответственности по делам о преступлениях в сфере экономической деятельности

In recent years in our country the steady tendency to increase of authority of the state in the sphere of business and strengthening of economic security is observed. The state finds new opportunities of effective counteraction of crime in the economic sphere, including by means of liberalization and a humanization of the criminal legislation. Among the main acts aimed at the improvement of criminal law, can be called the Federal law of December 7, 2011 No. 420-FZ “On Amendments to the Criminal Code of the Russian Federation and Certain Legislative Acts of the Russian Federation” which provides the special basis of release from criminal liability for commission of crimes in the sphere of economic activity. The specified basis is fixed in the new Article 761 “Exemption from criminal liability in cases of crimes in the sphere of economic activity” of the Criminal Code of the Russian Federation. In the explanatory note to this document it is noted that “such addition of the criminal law is caused by the necessity of its further humanization and counteraction to abuses in the field of investigation of economic crimes”. In the article mentioned Article 761 thoroughly analyzed in conformity with the requirements of the legal techniques and modern economic realities. The special attention is paid to the conditions of release from criminal responsibility provided for in second part of Article 761, given their critical assessment. It seems to the author that the legislator, providing special possibility of the exemption from criminal liability in cases of crimes in the sphere of economic activity had departed from the constitutional principle of equality of citizens before the law and court, having allowed thereby an inequality between the persons who have committed a crime.

Genomic diversification in strains of Rickettsia felis Isolated from different arthropods.

Rickettsia felis (Alphaproteobacteria: Rickettsiales) is the causative agent of an emerging flea-borne rickettsiosis with worldwide occurrence. Originally described from the cat flea, Ctenocephalides felis, recent reports have identified R. felis from other flea species, as well as other insects and ticks. This diverse host range for R. felis may indicate an underlying genetic variability associated with host-specific strains. Accordingly, to determine a potential genetic basis for host specialization, we sequenced the genome of R. felis str. LSU-Lb, which is an obligate mutualist of the parthenogenic booklouse Liposcelis bostrychophila (Insecta: Psocoptera). We also sequenced the genome of R. felis str. LSU, the second genome sequence for cat flea-associated strains (cf. R. felis str. URRWXCal2), which are presumably facultative parasites of fleas. Phylogenomics analysis revealed R. felis str. LSU-Lb diverged from the flea-associated strains. Unexpectedly, R. felis str. LSU was found to be divergent from R. felis str. URRWXCal2, despite sharing similar hosts. Although all three R. felis genomes contain the pRF plasmid, R. felis str. LSU-Lb carries an additional unique plasmid, pLbaR (plasmid of L. bostrychophila associated Rickettsia), nearly half of which encodes a unique 23-gene integrative conjugative element. Remarkably, pLbaR also encodes a repeats-in-toxin-like type I secretion system and associated toxin, heretofore unknown from other Rickettsiales genomes, which likely originated from lateral gene transfer with another obligate intracellular parasite of arthropods, Cardinium (Bacteroidetes). Collectively, our study reveals unexpected genomic diversity across three R. felis strains and identifies several diversifying factors that differentiate facultative parasites of fleas from obligate mutualists of booklice.

Structures for pairs of mock modular forms with the Zagier duality

Zagier introduced special bases for weakly holomorphic modular forms to give the new proof of Borcherds' theorem on the infinite product expansions of integer weight modular forms on $\SL_2(\ZZ)$ with a Heegner divisor. These good bases appear in pairs, and they satisfy a striking duality, which is now called the Zagier duality. After the result of Zagier, this type duality was studied broadly in various view points including the theory of a mock modular form. In this paper, we consider this problem with the Eichler cohomology theory, especially the supplementary function theory developed by Knopp. Using holomorphic Poincare series and their supplementary functions, we construct a pair of families of vector-valued harmonic weak Maass forms satisfying the Zagier duality with integer weights $-k$ and $k+2$ respectively, $k>0$, for a $H$-group. We also investigate the structures of them such as the images under the differential operators $D^{k+1}$ and $\xi_{-k}$ and quadric relations of the critical values of their $L$-functions.

The method of multipole fields for 3D vector tomography

To investigate the spherical tokamak plasmas the multipole fields method for the inversion of Doppler spectroscopy measurements is proposed. The method is based on the expansion of unknown vector field and ray transform on the special basis vector functions. An analytical expression for the ray transform of basis vector functions and the results of computer simulation are given.

One projection method for linear third order equation

In this paper we study the Galyorkin method with a special basis for a linear operator-differential equation of the third order in a separable Hilbert space. The projection method is based on the eigenvectors of the operator similar to the leading operator of equation. We obtain estimates for the convergence rate of approximate solutions in uniform topology.

Translator associations—from gatekeepers to communities

Analysis of 217 associations for translators and/or interpreters shows that, after the heroic age of the generalist national and international groupings in the 1950s and 1960s, there has been a progressive specialization of associations. In rough chronological order, separate institutions have been created for literary translators, sworn/authorized translators and interpreters, conference interpreters, public-service interpreters and audiovisual translators. This process might be seen as a division of labor, a normal result of increasing memberships. Analysis of the communication strategies employed by the associations nevertheless suggests that there has been a profound shift in their very nature: from a model where the association ideally vouches for the professional trustworthiness of several thousands of members, thus implicitly speaking to clients and other professions, we find a tendency toward communication patterns where the association becomes a place for social, pedagogical and political action between its members. The greater density and plexity of the interactions means that the newer associations involve smaller groups of people, selected on the basis of either professional specialization or geographical proximity. Similar interactive models are found in online marketplaces for translations and in communities of volunteer translators, which prove to be innovative not only in promoting interactive communication but also in inventing new ways of signaling translators’ trustworthiness. A way forward for the traditional associations might be to adapt some of the communication strategies operative in the electronic marketplaces and among volunteers.

Toward a Competitive Pakistan: The Role of Industrial Policy

This paper’s basic premise is that an improvement in Pakistan’s export performance is crucial to raising economic growth. After examining the reasons generally given for Pakistan’s poor export performance, we conclude that the country’s very slow productivity growth was the single most important factor that hurt competitiveness. We argue that a coherent and articulated industrial policy is required to overcome this disadvantage. While the experience of the East Asian economies offers useful lessons, Pakistan’s policy must accord with its own conditions, which are, in many ways, different. The formulation of industrial policy should involve key stakeholders, particularly the private sector. The paper identifies certain factors that should underpin the new industrial policy, notably the changed basis of international specialization and rules governing world trade.

특수한 정규기저를 이용한 유한체위에서의 역원 계산 알고리즘에 관한 연구

유한체 연산에서 MONB를 사용하면 곱셈 역원 계산시에 대량의 제곱계산이 필요하므로 역원을 계산하는 데에 긴 시간이 필요하게 된다. 이에 본 논문에서는 바탕체 <TEX>$GF(2^{2n})$</TEX> 위의 확대체 <TEX>$GF(2^{2^nm})^*$</TEX>에서 특수한 정규기저를 사용하여 역원을 구하는 저 비용의 알고리즘을 제안한다. 제안하는 알고리즘을 사용하면 곱셈 역원 계산에는 <TEX>$nb(2^nm-1)+w(2^nm-1)-2$</TEX>번의 곱셈과 <TEX>$2^n-1$</TEX>번의 제곱연산이 소요되며, H/W에서 구현한 결과 Itoh 등의 방법 보다 곱셈역원 계산속도가 빠르게 나타났다. Since the computation of a multiplicative inverse using MONB includes many squarings and thus calculating inverse is expensive, we, in this paper, propose a low cost inverse algorithm requiring <TEX>$nb(2^nm-1)+w(2^nm-1)-2$</TEX> multiplications and <TEX>$2^n-1$</TEX> squarings to compute an inverse in <TEX>$GF(2^{2^nm})^*$</TEX> using special normal basis over <TEX>$GF(2^{2^n})$</TEX>, and give some implementation results using the algorithm and, show that the timing results of our implementation is faster than that of Itoh et al.'s method.

Universal behavior of the Shannon and Rényi mutual information of quantum critical chains

We study the Shannon and R\'enyi mutual information (MI) in the ground state (GS) of different critical quantum spin chains. Despite the apparent basis dependence of these quantities we show the existence of some particular basis (we will call them conformal basis) whose finite-size scaling function is related to the central charge $c$ of the underlying conformal field theory of the model. In particular, we verified that for large index $n$, the MI of a subsystem of size $\ensuremath{\ell}$ in a periodic chain with $L$ sites behaves as $\frac{c}{4}\frac{n}{n\ensuremath{-}1}ln[\frac{L}{\ensuremath{\pi}}sin(\frac{\ensuremath{\pi}\ensuremath{\ell}}{L})]$, when the ground-state wave function is expressed in these special conformal basis. This is in agreement with recent predictions. For generic local basis, we will show that, although in some cases ${b}_{n}ln[\frac{L}{\ensuremath{\pi}}sin(\frac{\ensuremath{\pi}\ensuremath{\ell}}{L})]$ is a good fit to our numerical data, in general, there is no direct relation between ${b}_{n}$ and the central charge of the system. We will support our findings with detailed numerical calculations for the transverse field Ising model, $Q=3,4$ quantum Potts chain, quantum Ashkin-Teller chain, and the XXZ quantum chain. We will also present some additional results of the Shannon mutual information ($n=1$), for the parafermionic ${Z}_{Q}$ quantum chains with $Q=5,6,7$, and 8.

TheSU(3)algebra in a cyclic basis

With the couplings between the eight gluons constrained by the structure constants of the su(3) algebra in QCD, one would expect that there should exist a special basis (or set of bases) for the algebra wherein, unlike in a Cartan-Weyl basis, {\em all} gluons interact identically (cyclically) with each other, explicitly on an equal footing. We report here particular such bases, which we have found in a computer search, and we indicate associated $3 \times 3$ representations. We conjecture that essentially all cyclic bases for su(3) may be obtained from these making appropriate circulant transformations,and that cyclic bases may also exist for other su(n), n>3.

Conformal blocks of W N $$ {\mathcal{W}}_N $$ minimal models and AGT correspondence

We study the AGT correspondence between four-dimensional supersymmetric gauge field theory and two-dimensional conformal field theories in the context of W_N minimal models. The origin of the AGT correspondence is in a special integrable structure which appears in the properly extended conformal theory. One of the basic manifestations of this integrability is the special orthogonal basis which arises in the extended theory. We propose modification of the AGT representation for the W_N conformal blocks in the minimal models. The necessary modification is related to the reduction of the orthogonal basis. This leads to the explicit combinatorial representation for the conformal blocks of minimal models and employs the sum over N-tupels of Young diagrams with additional restrictions.

More on the Wilson $W_{tk}(v)$ Matrices

For integers $0\leq t\leq k\leq v-t$, let $X$ be a $v$-set, and let $W_{tk}(v)$ be a ${v \choose t}\times{v \choose k}$ inclusion matrix where rows and columns are indexed by $t$-subsets and $k$-subsets of $X$, respectively, and for row $T$ and column $K$, $W_{tk}(v)(T,K)=1$ if $T\subseteq K$ and zero otherwise. Since $W_{tk}(v)$ is a full rank matrix, by reordering the columns of $W_{tk}(v)$ we can write $W_{tk}(v) = (S|N)$, where $N$ denotes a set of independent columns of $W_{tk}(v)$. In this paper, first by classifying $t$-subsets and $k$-subsets, we present a new decomposition of $W_{tk}(v)$. Then by employing this decomposition, the Leibniz Triangle, and a known right inverse of $W_{tk}(v)$, we construct the inverse of $N$ and consequently special basis for the null space (known as the standard basis) of $W_{tk}(v)$.

Cycle construction and geodesic cycles with application to the hypercube

Construction of cycles in a graph is investigated, where cycles from particular subsets (such as bases) are added together so that each partial sum is also a cycle or each new cycle intersects the sum of the preceding terms in a nontrivial path. Starting with the geodesic cycles, a hierarchical construction is given. For the hypercube graph, geodesic cycles are characterized, and it is shown how hypercube geodesic cycles can be constructed in two steps from a special basis. Applications are given to inferring commutativity of a diagram in a groupoid from commutativity of some of its cycles.

Ordered vector spaces

This work was motivated by Problem 49-4 from “IMAGE” Issue Number 49, p. 52, Fall 2012 which was proposed by Rajesh Pereira. Seeking the solution to the problem led to the discovery of some interesting results on ordered vector spaces.It is shown that up to an isomorphism, there is only one order on a finite dimensional real vector space of dimension greater than or equal to 2, namely a lexicographic order on the coefficient vectors with respect to certain special bases. These special bases are called non-Archimedean bases. By examining linear preservers on an ordered vector space a solution to problem 49-4 is found as a by-product.

On -adic logarithms of Gauss sums

For the Gauss sum corresponding to a character of order of the multiplicative group of a finite field of characteristic , we obtain an approximate formula for the -adic logarithm of . We construct a special basis in the group of logarithms and define modulo the coefficients of relative to this basis (modulo if ). These coefficients are defined in terms of power residues of some cyclotomic numbers at the places over .

Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning

We propose a modification of the adaptive approach to time series forecasting. On the first stage, the original signal is decomposed with respect to a special empirical adaptive orthogonal basis, and the Hilbert's integral transform is applied. On the second stage, the resulting orthogonal functions and their instantaneous amplitudes are used as input variables for the machine learning unit that employs a hybrid genetic algorithm to train an artificial neural network and a regressive model based on support vector machines. The efficiency of the proposed approach is demonstrated on real data coming from Nord Pool Spot and Australian National Energy Market.

On symmetric polynomials with only real zeros and nonnegative γ-vectors

We present a family of polynomials with nonnegative coefficients that are symmetric and have only real nonpositive zeros. Therefore, they are also log-concave, unimodal and have nonnegative γ-vectors. This family of polynomials arises by applying the operator (ZrDs)n to the rational function 11−z. Two distinguished examples are the classical Eulerian polynomials and the Narayana polynomials. We use two special linear bases, besides the standard basis, to provide various characterizations for these polynomials and their coefficients, in terms of generalized Stirling numbers of the second kind. The type of generalized Stirling numbers we deal with, emerge from the normal ordering of (ZrDs)n. We generalize several formulas known for Eulerian and Narayana polynomials. Likewise, we provide an explicit formula to compute the so-called γ-vector of any symmetric polynomial of the type consider in this paper. Further related polynomials are obtained by applying the operator (ZrDs)n to a general Möbius transformation. Along the way, associated families of novel nonnegative integer sequences are put in evidence as a byproduct of our polynomial characterizations. We provide explicit formulas for some of these integral sequences.

Research on agricultural information recommendation models based on content filtering

The adaptive recommendation models in the agriculture information service platform are very important, which provides personalized recommendation information to farmers. Aiming at the special agricultural knowledge bases, by using the recommended methods based on content filtering, we have established the farmer interest model and the document feature model. In the two models, taking account of the influence of distribution of features in the different table space and the effect of HTML document structure on the feature weights, we have improved the accuracy of recommendation model by improving the traditional feature extraction algorithm. The experimental results show that with the increasing number of users of agricultural information recommendation models, the precision and recall rate of them are also increasing, the accuracy of them are also rising.