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In this paper, we developed the probability distribution for a fingerprint-based biometric identification model for crime prevention and control. We fitted Poisson distribution to the fingerprint data and applied Bayesian statistical model to determine and relate the prior to the posterior probabilities and determine the prior and posterior probabilities of the finger prints. The earlier information about the owner of the fingerprint is represented by the prior probabilities and the information from the individual on the second check of the fingerprint is represented by the posterior probabilities. Using the invariant property of biometric identification and classification, the system sees both probabilities as coming from one individual and hence classifies them as the owner of the finger print. The first person has a prior probability to be 1.54E-34 and the posterior probability to be 1.75E-14, etc.

In this paper, we developed the probability distribution for a fingerprint-based biometric identification model for crime prevention and control. We fitted Poisson distribution to the fingerprint data and applied Bayesian statistical model to determine and relate the prior to the posterior probabilities and determine the prior and posterior probabilities of the finger prints. The earlier information about the owner of the fingerprint is represented by the prior probabilities and the information from the individual on the second check of the fingerprint is represented by the posterior probabilities. Using the invariant property of biometric identification and classification, the system sees both probabilities as coming from one individual and hence classifies them as the owner of the finger print. The first person has a prior probability to be 1.54E-34 and the posterior probability to be 1.75E-14, etc.

We prove that a minimal second countable ample groupoid has dynamical comparison if and only if its type semigroup is almost unperforated. Moreover, we investigate to what extent a not necessarily minimal almost finite groupoid has an almost unperforated type semigroup. Finally, we build a bridge between coarse geometry and topological dynamics by characterizing almost finiteness of the coarse groupoid in terms of a new coarsely invariant property for metric spaces, which might be of independent interest in coarse geometry. As a consequence, we are able to construct new examples of almost finite principal groupoids lacking other desirable properties, such as amenability or even a-T-menability. This behaviour is in stark contrast to the case of principal transformation groupoids associated to group actions., Comment: Revised version. To appear in Ergodic Theory and Dynamical Systems

Steering vector transformation technique for wideband antenna array of point sources is presented. Wideband direction of arrival (DoA) estimation using this technique is illustrated. In the present work, steering vector transformation is applied to the conventional frequency domain beamformer to enhance the frequency invariance of the mainlobe pattern. Several simulation examples are presented to illustrate the advantage of the proposed frequency domain beamformer over the conventional one. As the array size increases or the interelement spacing decreases, the proposed beamformer still has a better frequency invariant property of the mainlobe pattern than the conventional beamformer. Finally, using windows, a better frequency invariant property of the mainlobe patter is obtained by the proposed beamformer than the conventional one.

The purpose of this article is to outline the invariant property of the sentence final particle o in Ikwere. To achieve this aim, I consider how it operates in the various sentences in which it occurs and examine the specific part it plays in the construction of meaning of such sentences while hinging on syntactic, semantic and pragmatic constraints associated with its use in a given situation. This article is realized based on the theory of linguistic markers within the framework of enunciative and predicative operations (in French: TOPE for Théorie des Opérations Prédicatives et Enonciatives) elaborated by Antoine Culioli and his research associates. It turns out that the use of the sentence final particle o constantly involves asserting the p value of a given notional domain while disqualifying the alternative p' value previously introduced. Cet article tente de dégager le mode de fonctionnement spécifique et invariant de la particule énonciative o dans la langue ikwere. On s’intéresse de près au rôle spécifique qu’elle joue dans la construction du sens des énoncés dans lesquels elle apparaît et on prend au sérieux les contraintes syntaxiques, sémantiques et contextuelles. Cet article est réalisé dans le cadre de la théorie des opérations énonciatives et prédicatives élaborée par Antoine Culioli et ses associés de recherche. Il en ressort que l’emploi de cette particule implique constamment l’assertion de la valeur p, d’un domaine notionnel donné, tout en laissant p', la valeur alternative prise en compte et dépassée.

We describe a maximal variety 𝔚 of automorphic Moufang loops such that for every loop A in the variety 𝔚, any loop isotopic to A also lies in 𝔚.

O’Hara introduced several functionals as knot energies. One of them is the Mobius energy. We know its Mobius invariance from Doyle-Schramm’s cosine formula. It is also known that the Mobius energy was decomposed into three components keeping the Mobius invariance. The first component of decomposition represents the extent of bending of the curves or knots, while the second one indicates the extent of twisting. The third one is an absolute constant. In this paper, we show a similar decomposition for generalized O’Hara energies. We also extend the cosine formula for the Mobius energy to generalized O’Hara energies. It gives us a condition for which the right circle minimizes the energy under the length-constraint. Furthermore, it shows us how far the energy is from the Mobius invariant property. Using decomposition, the first and second variation formulae are derived.

In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the existence of trajectory statistical solutions for autonomous evolution equations. Then we establish that the constructed trajectory statistical solutions possess invariant property and satisfy a Liouville type equation. Moreover, we reveal that the equation describing the invariant property of the trajectory statistical solutions is a particular situation of the Liouville type equation. Finally, we study the equations of three-dimensional incompressible magneto-micropolar fluids in detail and illustrate how to apply our abstract results to some concrete autonomous evolution equations.

The invariant relationship between the sets of load conductivity values and the corresponding values of the input currents of the two or three wire communication lines is shown. This relationship does not depend on parameters of the lines and the accuracy of measuring devices. It allows transmitting signals in the analog form of different physical sensors for monitoring technical or natural objects.

Introduction. In evaluating the space-time structure of the Earth’s surface, the data of remote sensing of the Earth become more important. Increasing the effectiveness of space survey analysis tools is possible through studying the problem of obtaining an integrated space-time characterization of the state of lands. The purpose of this study is to improve the accuracy of the automated analysis of remote sensing data by taking into account the invariant and dynamic descriptors of the vicinity. Materials and Methods. In order to improve the accuracy of the remote sensing data classification, a computation of complex space-time characteristics of the state of the lands was conducted based on the system analysis of data characterizing the dynamic and invariant states of the territory surrounding the geophysical site. The formalization of this process includes methods for calculating a set of numerical descriptors of the neighborhood: local entropy, local range, standard deviation, color moment, histogram of hues, and color cortege. A technique for calculating a complex descriptor based on the Fisher vector is described. To approbate the solution, a plan for the experiment was drawn up and a sample of the initial data was sampled. Results. The approbation of the methodology and the algorithm developed on its basis, implemented as a set of programs, on the test polygon system showed a variation in the classification accuracy in the range of 81–89% (without regard to the neighborhood), and taking into account the neighborhood, it increases to 91–97%. It is revealed that a significant increase in the radius of the analyzed neighborhood leads to a decrease in the classification accuracy. Conclusions. The application of the developed set of programs allows for the rapid implementation of modeling of spatial systems for the purpose of thematic mapping of land use and analyzing the development of emergency situations. The developed methodology for analyzing lands with regard to the descriptors of the neighborhood makes it possible to improve the accuracy of classification.

The invariant properties of input-output of circuits, established in Chap. 4, are generalized for multi-ports. A mutual influence of loads at inputs of passive multi-ports is investigated by affine and projective transformations too. The direct and reverse formulas of recalculation of currents and non-uniform coordinates are obtained in the form of fractionally linear expressions of identical type. The results allow separating or restoring two signals at output via input currents of the four-port circuit or the three-wire line inputs without determination of their transmission parameters.

Stimulated by the study of sufficient matrices in linear complementarity problems, we study column sufficient tensors and tensor complementarity problems. Column sufficient tensors constitute a wide range of tensors that include positive semi-definite tensors as special cases. The inheritance property and invariant property of column sufficient tensors are presented. Then, various spectral properties of symmetric column sufficient tensors are given. It is proved that all H-eigenvalues of an even-order symmetric column sufficient tensor are nonnegative, and all its Z-eigenvalues are nonnegative even in the odd order case. After that, a new subclass of column sufficient tensors and the handicap of tensors are defined. We prove that a tensor belongs to the subclass if and only if its handicap is a finite number. Moreover, several optimization models that are equivalent with the handicap of tensors are presented. Finally, as an application of column sufficient tensors, several results on tensor complementarity problems are established.

We introduce the notion of a t-nilpotent endomorphism of modules and study the modules which are invariant under t-nilpotent endomorphisms of their injective envelope, such as modules are called t-nilpotent invariant. We provide several characterizations and investigate properties of each of these concepts. It is shown that a module M is t-nilpotent invariant if and only if M=Z2(M)⊕M′, Z2(M) is quasi-injective, M′ is nilpotent invariant and Z2(M) is M′-injective. Also, it is proved that, for modules, being t-nilpotent invariant is a Morita invariant property. Moreover, we provide some characterizations of known rings in terms of t-nilpotent invariant modules.

Cutting plane methods are an important component in solving the mixed integer programming (MIP). By carefully studying the coefficient strengthening method, which is originally a presolving method, we are able to generalize this method to generate a family of valid inequalities called generalized coefficient strengthening (GCS) inequalities. The invariant property of the GCS inequalities is established under bound substitutions. Furthermore, we develop a separation algorithm for finding the violated GCS inequalities for a general mixed integer set. The separation algorithm is proved to have the polynomial time complexity. Extensive numerical experiments are made on standard MIP test sets, which demonstrate the usefulness of the resulting GCS separator.

Methods based on Convolutional neural network (CNN) have been effectively applied to object detection. However, the Traditional object detection models face huge obstacles in the field of the aerial scene due to the complexity of the aerial image and the wide degree of freedom of the remote sensing object in density, scale, and orientation. In this article, we applied rotatable bounding boxes (RBox) instead of the traditional bounding box (BBox) and improved the CNN-based network to effectively handle the oriented angle of the detected object so that the rotation invariant property can be achieved. Our model is trained and tested on 3 classes of remote sensing category Airplanes, ships, and Cars. Compared with two of the common benchmarks of the BBox methods Faster R-CNN and SDD, our model outperforms both of them. Where our model efficiently output the orientation angles of the detected objects.

Accurate built-up area (BA) information plays crucial role for many applications. PolSAR imagery can provide important source for BAs information analysis. However, the BAs with large orientation angles are usually misdetected as vegetation, and labeled BA samples with special orientations are diffi-cult to obtain. In this paper, a PolSAR BA extraction method based on eigenvalue statistical information and PU-Learning is proposed to overcome abovementioned problems. Firstly, the roll invariance of coherency-matrix eigenvalues and the building orientations have been analyzed. Then, by adopting eigenvalue-Wishart unsupervised classification, regional statistical information and rotation invariant property are comprehensively utilized. Finally, the BAs are extracted by combining PU-Learning classifier with only positive samples at same distinguishable orientation. Six experiments on PolSAR imageries show the accuracy of proposed method can reach 92-99% with only a few positive samples, 8-20% higher than classical model decomposition-based PU-Learning method, and the requirement for labeled samples is less than 0.65%.

We study $C_0$-semigroups acting on a Banach space which possess an invariant property with respect to an action of the multiplicative group of positive real numbers (scaling). Some properties on the domains or the spectrum of the associated generators are presented.

Conventional Approaches to line segment matching have shown their performances less satisfactory mainly since some of the features used for matching, such as the center and the starting/ending points of line segments, are not invariant. Furthermore, a pair of line segment sets to be matched may not have one to one correspondence, but each can be a subset of the other. This led to multiple solutions or interpretations in matching, where finding out all the possible solutions or interpretations out of an arbitrarily overlapping pair of line segment is of an issue. This paper presents a general method of identifying all the possible solutions or interpretations for an arbitrary pair of line segment sets by using invariant features associated with line segments. The invariant property of line segments comes from the orientation and location contexts of line segments that are defined based on infinite line representation of individual line segments. Simulation and experiment shown the effectiveness of the proposed method compared to conventional methods.

The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory statistical solutions for two-dimensional dissipative Euler equations. Further, it is established that the constructed trajectory statistical solutions possess an invariant property and satisfy a Liouville type equation. National Science Foundation of China European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Ciencia, Innovación y Universidades (MICINN). España

For 1-variable weighted shifts, it is well known that given three positive numbers α 0 α 1 α 2 , we always find Stampfli's subnormal weighted shift whose first three weights are α 0 , α 1 and α 2 (we call it a type-abc completion, or shift.) On the other hand, given four positive numbers α 0 α 1 α 2 α 3 , it is not always possible to find a subnormal weighted shift whose first four weights are α 0 , α 1 , α 2 and α 3 . In this paper, we extend the notion of a type-abc shift to the 2-variable weighted shifts using a localization technique from the theory of truncated moment problems. We next study an inner propagation phenomena of a 2-variable weighted shift whose core is of type-abc. We further establish the necessary and sufficient conditions for the subnormality of one-step extensions of type-abc 2-variable weighted shifts. Finally, we study a certain invariant property under powers for type-abc 2-variable weighted shifts.

In this paper, we give several sufficient conditions ensuringthat any positive radial solution (u,v) of the following γ-Laplacian sys-tems in the whole space R n has the components symmetry property u ≡ vˆ−div(|∇u| γ−2 ∇u) = f(u,v) in R n ,−div(|∇v| γ−2 ∇v) = g(u,v) in R n .Here n > γ, γ > 1.Thus, the systems will be reduced to a single γ-Laplacian equation:−div(|∇u| γ−2 ∇u) = f(u) in R n .Our proofs are based on suitable comparation principle arguments, com-bined with properties of radial solutions. 1. IntroductionIn 2008, Li and Ma [10] studied the stationary Schr¨odinger system(1.1)ˆ−∆u = u p v q in R n ,−∆v = u q v p in R n ,and obtained a components symmetry result:Proposition 1.1. Assume n > γ, 1 ≤ p,q ≤ n+2n−2 and p + q = n−2 . Thenany (L n2−n2 (R n )) 2 -positive solution pair (u,v) to (1.1) is radial symmetric, andhence u ≡ v = a(b 2 +|x −x 0 | 2 ) (2−n)/2 with a,b > 0 and x 0 ∈ R n .The proof was achieved by the classification result in [4] and the methodof moving planes based on the conformal invariant property. Afterwards, Leiand Li ([8]) studied the asymptotic radial symmetry and decay estimates ofpositive integrable solutions of(1.2)ˆ−div(|∇u

We describe recent progress on rationality and stable rationality questions. We discuss the cohomological or Chow decomposition of the diagonal, a very strong stably birationally invariant property which controls many of the previously defined stable birational invariants. On the other hand, it behaves very well under specialization and desingularization of mild singularities.