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Abstract: Abstract We give an example of a series of finite \( D_{\pi} \) -groups where for each group \( G \) in the series and its \( \pi \) -Hall subgroup \( H \) , the inequality \( H\cap H^{x}\cap H^{y}\neq 1 \) holds for all \( x,y\in G \) . Thus a negative answer is obtained both to Problem 7.3 by Vdovin and Revin and its analog—Question 18.31 in The Kourovka Notebook. We also describe the subgroups \( \operatorname{Min}_{G}(H,H,H) \) and \( \min_{G}(H,H,H) \) . PubDate: 2022-07-01

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Abstract: Abstract We examine the Dirichlet problem in a bounded plane domain for a strongly elliptic functional-differential equation of the second order containing the argument transformations \( x\mapsto px \) ( \( p>0 \) ) and \( x\mapsto-x \) in higher-order derivatives. The study of solvability of the problem relies on a Gårding-type inequality for which some necessary and sufficient conditions are obtained in algebraic form. PubDate: 2022-07-01

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Abstract: Abstract A subgroup \( A \) of a group \( G \) is \( G \) -permutable in \( G \) if for every subgroup \( B\leq G \) there is \( x\in G \) satisfying \( AB^{x}=B^{x}A \) . A subgroup \( A \) is hereditarily \( G \) -permutable in \( G \) if \( A \) is \( E \) -permutable in every subgroup \( E \) of \( G \) which includes \( A \) . The Kourovka Notebook contains Problem 17.112: Which finite nonabelian simple groups \( G \) possess a proper (hereditarily) \( G \) -permutable subgroup' We answer the question for simple sporadic groups. PubDate: 2022-07-01

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Abstract: Abstract Under study is the temporal multiagent logic with different intervals of lost time which are individual for each of the agents. The logic bases on the frames with principal basic sets on all naturals \( N \) as temporal states, where each agent \( j \) can have their own proper sets \( X_{j} \) of inaccessible (lost, forgotten) temporal states ( \( X_{j}\subset N \) for all \( j\in J \) ). The unification problem and the problem of the algorithmic recognition of admissible inference rules are the main mathematical problems of the paper. The solution of the unification problem consists in finding a finite computable set of formulas which is a complete set of unifiers. The problem is solved by the Ghilardi technique of projective formulas. We prove that every formula unifiable in this logic is projective and provide some algorithm constructing its projective unifier, which solves the unification problem. This makes it possible to solve the open problem of the algorithmic recognition of admissible rules. The article ends with some generalization of the definition of projective formulas—weakly projective formulas—and exhibits an easy example of their application. PubDate: 2022-07-01

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Abstract: Abstract We study the well-posedness of a third boundary value problem for a multidimensional parabolic equation in the case when the coefficient of the conormal derivative vanishes at some points. We show that under some conditions on the sign of this coefficient there exists nonexistence or nonuniqueness of a solution in the conventional anisotropic Sobolev space. Using the regularization method, we prove existence and uniqueness theorems for the regular solution in suitable weighted spaces. PubDate: 2022-07-01

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Abstract: Abstract This paper is concerned with feedback stabilization of linear delay systems of neutral type. When the unstable characteristic roots of the systems are far from the imaginary axis, the discretization of unstable differential equations results in a large error. In this case, it is difficult to seek stabilizing control laws via a direct extension of the algorithm provided in the literature. In order to remedy the difficulty, a modified state equation is constructed through a shifting parameter such that it is asymptotically stable. Then, basing on the modified state equation, we present some numerical algorithms to design the stabilizing controller and the observer of the neutral systems, respectively. Furthermore, we derive a separation property for the observer-based stabilizing controller of the neutral systems which extends the result in the literature. PubDate: 2022-07-01

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Abstract: Abstract We prove that the de Rham \( L^{\phi} \) -cohomology of a Riemannian manifold \( M \) admitting a convenient triangulation \( X \) is isomorphic to the simplicial \( \ell^{\phi} \) -cohomology of \( X \) under some assumptions on the Young function \( \phi \) . This result implies the quasi-isometry invariance of the first cohomology. PubDate: 2022-07-01

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Abstract: Abstract We give a simple explicit formula for an arbitrary \( 3j \) -symbol for the Lie algebra \( {\mathfrak{gl}}_{3} \) . The symbol is expressed as the ratio of values of hypergeometric functions with \( \pm 1 \) substituted for all arguments. Finding a \( 3j \) -symbol is essentially equivalent to the determination of an arbitrary Clebsch–Gordan coefficient for \( {\mathfrak{gl}}_{3} \) . The coefficients are important in the quark theory of quantum mechanics. PubDate: 2022-07-01

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Abstract: Abstract The degree \( d(x) \) of a vertex or face \( x \) in a graph \( G \) on the plane or other orientable surface is the number of incident edges. A face \( f=v_{1}\ldots v_{d(f)} \) is of type \( (k_{1},k_{2},\dots) \) if \( d(v_{i})\leq k_{i} \) whenever \( 1\leq i\leq d(f) \) . We denote the minimum vertex-degree of \( G \) by \( \delta \) . The purpose of our paper is to prove that every triangulation with \( \delta\geq 4 \) of the torus, as well as of large enough such a triangulation of any fixed orientable surface of higher genus has a face of one of the types \( (4,4,\infty) \) , \( (4,6,12) \) , \( (4,8,8) \) , \( (5,5,8) \) , \( (5,6,7) \) , or \( (6,6,6) \) , where all parameters are best possible. PubDate: 2022-07-01

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Abstract: Abstract We study the structure of nonsolvable finite groups whose every nonsolvable maximal subgroup is \( \Phi \) -simple. PubDate: 2022-07-01

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Abstract: Abstract Let \( {\mathcal{A}} \) be a unital \( \ast \) -algebra containing a nontrivial projection. Under some mild conditions on \( {\mathcal{A}} \) , it is shown that a map \( \Phi:{\mathcal{A}}\rightarrow{\mathcal{A}} \) is a nonlinear mixed Jordan triple \( * \) -derivation if and only if \( \Phi \) is an additive \( * \) -derivation. In particular, we apply the above result to prime \( \ast \) -algebras, von Neumann algebras with no central summands of type \( I_{1} \) , factor von Neumann algebras, and standard operator algebras. PubDate: 2022-07-01

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Abstract: Abstract Considering the Bingham fluid motion model, we study the approximation problem, prove its unique solvability, and the existence of attractors. We show that the attractors of the approximation problem converge to the attractors of the Bingham model in the sense of the Hausdorff semidistance in the corresponding metric space as the approximation parameter vanishes. PubDate: 2022-07-01

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Abstract: Abstract Considering a nonempty formation \( {\mathfrak{X}} \) of nilpotent groups, we prove that a group \( G \) is an extension of a nilpotent group by an \( {\mathfrak{X}} \) -group if and only if every Sylow normalizer in \( G \) is solvable and its \( {\mathfrak{X}} \) -residual is subnormal in \( G \) . We also show that \( G \) is supersolvable if and only if every Sylow normalizer in \( G \) is supersolvable and its nilpotent residual is subnormal in \( G \) . PubDate: 2022-07-01

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Abstract: Abstract We find the three-dimensional subspaces of four-dimensional Lie algebras which generate the algebras, as well as abnormal extremals on the connected Lie groups determined by these algebras and endowed with the left-invariant sub-Finsler quasimetrics defined by seminorms on the subspaces. Using the structure constants of Lie algebras and dual seminorms, we establish a criterion for the strict abnormality of the extremals. PubDate: 2022-07-01

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Abstract: Abstract We obtain a rather simple characterization of semiexponential distributions. This allows us to relax substantially the conditions for the fulfillment of the moderately large deviation principle for the trajectories of random walks when Cramér’s condition does not hold. Besides, using the previous results, we establish the local large deviation principle (LDP) outside the zone of moderately large deviations for semiexponential random walks. The latter principle differs much from the LDP in the case that Cramér’s condition holds: The deviation function for it is concave but not convex, the deviation functional is finite only on jump trajectories, and so forth. PubDate: 2022-07-01

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Abstract: Abstract We address the unital right alternative bimodules over the matrix algebras \( {\mathrm{M}}_{n}(\Phi) \) of order \( n\geq 3 \) , prove that each of these bimodules is the direct sum of an associative bimodule and a Graves bimodule, and fully describe the structure of twisted Graves bimodules. Also, we construct an irreducible right alternative \( {\mathrm{M}}_{n}(\Phi) \) -bimodule of minimal dimension \( n(n-1) \) . Furthermore, we show that no element \( f(x,y) \) of the free right alternative algebra of rank 3 is its nuclear element. The results of this article are needed for the study of the right alternative superalgebras whose even part includes \( {\mathrm{M}}_{n}(\Phi) \) with \( n\geq 3 \) . PubDate: 2022-07-01

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Abstract: Abstract Under study is the structure of the \( m \) -homomorphic images of \( m \) -subgroups in a Cartesian product of \( m \) -groups which admit a faithful \( m \) -transitive representation. We propose some construction that enables us to produce idempotents in the semigroup of varieties of \( m \) -groups. PubDate: 2022-07-01

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Abstract: Abstract We study the solvability of bi-infinite systems of linear equations whose matrices are diagonally dominant. We prove that the estimates of the norm of the solution in terms of the diagonal dominance value well-known in the case of finite systems of linear equations are also valid for bi-infinite systems of equations. The estimates are used in interpolation by splines on nonuniform meshes on the real line. Using the estimates, we prove the existence and uniqueness of a cubic spline of linear or quadratic growth interpolating data of linear or quadratic growth, without any constraints on node spacing. The familiar estimates of the interpolation error on a segment are carried over to the case of interpolation on the whole real line. PubDate: 2022-07-01

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Abstract: Abstract Up to conjugation by an automorphism, we describe the Rota–Baxter operators of weight zero or nonzero on the simple four-dimensional Jordan superalgebra \( D_{t} \) over an algebraically closed field of characteristic 0. The description includes the classification of all decompositions of \( D_{t} \) into a direct sum of two subalgebras. PubDate: 2022-07-01

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Abstract: Abstract We present an algorithm for constructing a rectangular diagram of a Seifert surface for the link represented by an arbitrary rectangular diagram and estimate the complexity of the resulting surface diagram. PubDate: 2022-05-01 DOI: 10.1134/S003744662203017X