Large language model (LLM) embeddings offer a promising new avenue for database query optimization. In this paper, we explore how pre-trained execution plan embeddings can guide SQL query execution without the need for additional model training. We introduce LLM-based Plan Mapping (LLM-PM), a framework that embeds the default execution plan of a query, finds its k nearest neighbors among previously executed plans, and recommends database hintsets based on neighborhood voting. A lightweight consistency check validates the selected hint, while a fallback mechanism searches the full hint space when needed. Evaluated on the JOB-CEB benchmark using openGauss, LLM-PM achieves an average 21% reduction in query latency. This work highlights the potential of LLM-powered embeddings to deliver practical improvements in query performance and opens new directions for training-free, embedding-based optimizer guidance systems.
This paper is devoted to research in the theory of blurry models, which serves as a methodology for the logical formalization of subject domains under conditions of imprecision and incompleteness of knowledge about these domains. The article introduces the concept of a submodel of a blurry model as an extension of the notion of a submodel of a classical model, and also defines pairwise independence of submodels: submodels are independent if the events described by the signature of one model are independent from the events described by the signature of another model. The independence of submodels can be interpreted as the mutual independence of groups of objects within the subject domain, i.e., their autonomy and lack of influence on each other. A theorem is proven that formalizes the criterion (i.e., necessary and sufficient condition) for pairwise independence of submodels. Based on the property of submodel independence, blurry models are divided into separable models and entangled models. Each separable model decomposes into a separable union of its submodels. There may be several such decompositions for a given model, among which a “minimal” decomposition, called normal, is selected; a theorem on the uniqueness of the normal decomposition is proven. An algorithm for finding the normal decomposition of a blurry model into a separable union of submodels is presented, and the correctness of this algorithm is proven.
A non-local search method for extremum in nonlinear optimal control problems is developed, based on the use of the property of hidden convexity of the set of admissible velocities of controlled dynamic systems. Extended optimal control problems are formed, which in some cases can be characterized by convex reachable sets. Five variants of the convexification method of the initial optimal control problem are proposed, depending on the way of accounting for the constraints on auxiliary controls. The results of computational experiments on a test collection of nonlinear optimal control problems with geometric constraints are presented. Conclusions are formulated based on the obtained experimental experience and the use of the expansion correctness criterion. The proposed approach allows for the convexification of the velocity set and expands the applicability of numerical optimization methods in the study of non-convex optimal control problems.
This paper addresses a scheduling problem where each job is characterized by its processing requirements and machine needs. The optimization criterion minimizes maximum lateness relative to given job deadlines, with job durations following a convex resource consumption function under limited total resource availability. We analyze the problem’s computational complexity, develop approximation methods for special cases, and construct mathematical programming models that yield new schedule properties.
In this paper, we establish a new fixed point theorem for multi-valued almost pseudo-contractive mappings in quasimetric spaces, extending and improving several known results in the literature. Our approach generalizes earlier works by allowing the contractive constant to the whole interval [0, 1), rather than being subject to more restrictive bounds. As an application, we derive new data dependence results for the fixed point sets of such mappings in quasimetric spaces.
This paper investigates a class of nonlinear multidimensional integral equations on Rn with non-compact Hammerstein operator. These equations arise in various fields of mathematical physics and mathematical epidemiology. A distinguishing feature of the studied equations is the lack of complete continuity of the associated nonlinear operator in the space of bounded functions on Rn, the presence of a trivial (zero) solution, and the non-reflexivity of the corresponding function space, within which the existence of a nontrivial fixed point is considered. Under appropriate conditions on the kernel and the nonlinear term, a constructive theorem is established for the existence of a positive, bounded, and continuous solution. Moreover, the method of successive approximations is shown to converge uniformly to the solution at a rate an infinitely decreasing geometric progression. Within a sufficiently broad subclass of nonnegative, bounded functions on Rn, the uniqueness of the solution is also proven. The integral asymptotic behavior of the constructed solution is examined under additional constraints on the kernel and nonlinearity. Finally, explicit examples of kernels and nonlinearities satisfying all the assumptions of the theorems are provided.
The problem under consideration involves constructing solutions within a parallelepiped for a system of linear equations that depends on a parameter defined within a rectangle. First, it is determined whether the system of linear equations has a solution in the parallelepiped for some value of the parameter within the rectangle. If such a parameter value is found, a linear programming problem is solved for that parameter. Using the basis that identifies this solution, the region of parameter values for which the system of linear equations has solutions in the parallelepiped is determined. The neighboring regions along the boundaries of this region (a polygon) are then identified, where the system also has solutions within the parallelepiped. By repeating this process a finite number of times, the problem under consideration is solved.
The paper is devoted to the study of the number of real roots of general systems of transcendental equations with real Taylor coefficients in some domain D of multidimensional real space. For a given entire function ' we introduce the notion of a resultant R-phi constructed by the power sums of the roots of the system in the negative degree and the Taylor coefficients of the function phi. For such power sums we obtain formulas for their computation by means of residue integrals. It is shown that if the resultant R-phi has simple roots, then the number of real roots of the system in D coincides with the number of real roots of the resultant R-phi in some interval.
We consider a class of problems in which it is required to determine unknown constant coefficients appearing in the free terms of non-autonomous systems of ordinary differential equations. The basic and additional (overdetermining) conditions are, in the general case, of a nonlocal nature: they involve cumulative characteristics of the unknown state functions – both their values at selected points and their integral values over specified sub-intervals. Depending on the relation between the number of unknown coefficients and the number of additional conditions, several problem settings and corresponding solution methods are discussed. Results of computer experiments are presented, together with an analysis of how errors in the prescribed conditions affect the accuracy of the solutions for test problems.
It was proved by I. Dolguntseva (St. Peterburg Math. J., 2010) that second Hochschild cohomology groups for the associative conformal algebra 𝐶𝑒𝑛𝑑𝑘 with coefficients in an arbitrary conformal bimodule are trivial. In this work, we prove the same for all higher Hochschild cohomologies of 𝐶𝑒𝑛𝑑𝑘 by means of algebraic discrete Morse theory applied to the bar complex of the 1st Weyl algebra.
In 1959, D.R. Hughes conjecture that the full collineation group of any finite non-Desarguesian semifield projective plane is solvable (see also the question 11.76 by N.D. Podufalov in Kourovka notebook). The spread set method is useful to exclude some simple non-Abelian groups from the list of possible autotopism subgroups (collineations fixing a triangle) or for constructing the examples of semifield planes with certain autotopism subgroup. The present paper continues the series of results on 2-subgroups and 2-elements in an autotopism group. The natural restrictions from previous papers allow us to complete the description of dihedral and quaternion autotopism subgroup of order 8, together with their geometrical sense. For a semifield projective plane of odd order and 4-dimensional over the center, the matrix representation of the spread set is determined, depending on the characteristic of prime field. It is proven that the dihedral autotopism group of order 8 necessarily contains the perspectivities and therefore cannot be a subgroup of any simple non-Abelian group. For the case of a quaternion subgroup without perspectivities, examples of semifield projective planes of order 81 and 2401 are constructed, up to isomorphism. The list of exceptions complements the classical results of H. Lu & uml;neburg etc. on projective special linear collineation groups. The method used and the described algorithms allow for generalization to the case of a different dimension or a different order.
Given a finite group L, let N(L) denote the set of its conjugacy class sizes. Let X and Y be sets of natural numbers, G be a finite group such that N(G) = X & times; Y. In the article [16] the question is formulated: for which sets X and Y is it true that G <^> A & times; B, where N(A) = X and N(B) = Y? More than 30 years ago, J. Thompson formulated a conjecture that any finite simple group is uniquely determined by its set of sizes of conjugacy classes in the class of finite groups with trivial center. In 2019, the validity of this conjecture was proven. In 2020, it was noted that in addition to simple groups, some direct products of simple groups are also determined by this set. We prove that if N(G) = N(Alt(p) & times; Alt(5)), where p is a prime greater than 1361 and the group G has a trivial center, then G <^> Alt(5)& times; Alt(p) .
Within the framework of the theory of microstructural deformation, a new approach is proposed for constructing a solution to the bending equation of a long rectangular nanoplate that is under the influence of a transverse load. The proposed approach is based on the collocation method using a system of orthogonal Chebyshev polynomials of the first kind. The bending function is represented as a partial sum of a series of these polynomials. The roots of Chebyshev polynomials of the first kind are chosen as the collocation points. By sequentially multiplying the left and right sides of the resulting matrix equation by the inverse matrix to the matrix with the values of Chebyshev polynomials at the collocation points and by the generalized inverse matrix to the degenerate matrix of differentiation of these polynomials, the equation of the bending surface, taking into account boundary conditions, is reduced to a system of linear algebraic equations with respect to unknown coefficients in the representation of the solution. In this case, the elements of each of these matrices are presented explicitly. An estimate of the error of the constructed solution based on an infinite norm is obtained. The results of the conducted computational experiments are presented, which demonstrate the effectiveness of the proposed approach.
The paper is devoted to the study of the solvability of boundary value problems for fourth-order linear composite-type differential equations. A distinctive feature of the considered equations is that the operator coefficient at the highest derivative with respect to the time (distinguished) variable may be non-invertible. For the problems under study, theorems on the existence and uniqueness of regular solutions are proved—solutions that possess all generalized derivatives in the sense of S.L. Sobolev entering the corresponding equation.
Closed classes under superposition are examined in k-valued logic. E. Post established that the lattice (on inclusion) of all closed classes in two-valued logic is countable. Besides, each closed class has a finite basis in two-valued logic. Yu. I. Yanov and A. A. Muchnick proved that the lattice of all closed classes in k-valued logic is continuous at each k >= 3. Besides, there are closed classes without a basis and closes classes of a countable basis in k-valued logic at k >= 3. Because of the continuity on the lattice of all closed classes at k >= 3, its sub-lattices are examined. In particular, the closed class of all functions, that are represented by polynomials modulo k, is considered in k-valued logic. This closed class contains all functions of k-valued logic, if and only if k is a prime number. If k is a composite number, then this closed class is not even pre-complete. In works of A. N. Cherepov, A. B. Remizov, A. A. Krokhin, K. L. Safin, E. V. Sukhanov, D. G. Meschaninov and of others the structure of sub-lattices and of over-lattices is examined for the closed class of all polynomial functions at composites k. In this work at each composite number k the continuity of the sub-lattice is established for the closed class of all polynomial functions in k-valued logic.
The main object of our study is the Dirichlet kernel. The properties of this trigonometric polynomial — the sum of cosines of multiple arcs — are of undoubted interest in the theory of trigonometric series. For example, the results on the asymptotic behavior of the Lebesgue constants, which are the integral norms of the Dirichlet kernels, are well known. These results are constantly being developed and generalized as applied to various systems of functions in both one-dimensional and multidimensional situations. In this paper, we find the leading term of the asymptotics for the value of the global minimum of the Dirichlet kernel as its number tends to infinity. The leading term is the product of the said number by a negative constant, which coincides with the value of the global minimum of the sinc-function (cardinal sine). The proof uses the connection between Dirichlet kernels and Chebyshev polynomials of the second kind. As can be seen from the authors’ previous works, the result undergoes quantitative changes in the transition to lacunary sums of cosines. Our interest in such constructions is caused by the problem posed several years ago by L. E. Rossovskii and A. A. Tovsultanov on calculating the spectral radius for a special one-parameter family of functional operators. The question reduces to studying the behavior of “long” products of sines with lacunae in the arguments. It is shown that the revealed asymptotic property of Dirichlet kernels turns out to be useful in a similar “non-lacunary” problem.
This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. We consider the binary level of these structures forming algebras of binary isolating formulas, which are based on families of labels and compositions of related formulas. These algebras are studied for 0-categorical 1-transitive non-primitive weakly circularly minimal theories of convexity rank greater than 1 with a trivial definable closure having a non-trivial monotonic-to-right function to the definable completion of a structure. On the basis of the study, the authors present description of these algebras. It is shown that for this case there exist only commutative algebras. A strict s-deterministicity of such algebras for some natural number s is also established.
In this paper, Shunkov groups are studied in the context of the well-known question of B. Amberg and L. S. Kazarin about the structure of groups containing direct products of a finite number of dihedral groups. To do this, two additional finiteness conditions are imposed on the Shunkov group: it is required that the Shunkov group be periodic and also be saturated with direct products of a finite number of finite dihedral groups.
In this paper, a system of nonlinear Kaup equations with a loaded additional term in the class of periodic functions with respect to the spatial variable is considered. The invariance of the spectrum is proved and an analog of the Dubrovin system is derived for the evolution of the spectral parameters of a quadratic pencil of Sturm-Liouville operators on the entire line, the periodic coefficients of which are the solution of the Cauchy problem posed for the loaded system of nonlinear Kaup equations. Using trace formulas and an analog of the Dubrovin system, it is shown that the loaded system of nonlinear Kaup equations can be integrated by the inverse spectral problem method. An algorithm for solving the Cauchy problem for the loaded nonlinear Kaup's system in the class of periodic functions with respect to the spatial variable is obtained. It is shown that if the initial functions are real analytic functions, then the solution will also be an analytic function with respect to the spatial variable. The pi/2-periodicity of the solution with respect to the spatial variable is revealed for the pi/2-periodicity of the initial functions.
We continue to explore the multi-agent logic of computational trees relative to the relational Kripke semantics of possible worlds: we investigate the question of logical solvability, the complexity of model construction, feasibility testing, and correctness. For the semantics introduced earlier, we proved a strong finite model property, and obtained polynomial estimates of the dimension of minimal models for an arbitrary formulas. We proved the recursive enumerability of finite frames of logic and proposed an effective algorithm for checking the feasibility of formulas, which makes it possible to conclude the solvability of logic. The obtained polynomial estimates are within the framework of theoretical expectations, which makes it possible to perceive the logic under study as an effective tool for analyzing multi-agent distributed systems and practical model-checking, and to count on a positive resolution of issues of unification and description of the admissibility for inference rules.
