math
math
11-25 00:00
arXiv:2511.17503v1 Announce Type: new Abstract: In this paper, we show how to expand Euclidean/Hermitian self-orthogonal code preserving their orthogonal property. Our results show that every $k$-dimension Hermitian self-orthogonal code is contained in a $(k+1)$-dimensional Hermitian self-orthogonal code. Also, for $k< n/2-1$, every $[n,k]$ Euclidean self-orthogonal code is contained in an $[n,k+1]$ Euclidean self-orthogonal code. Moreover, for $k=n/2-1$ and $p=2$, we can also fulfill the expanding process. But for $k=n/2-1$ and $p$ odd prime, the expanding process can be fulfilled if and only if an extra condition must be satisfied. We also propose two feasible algorithms on these expanding procedures.
cs.itmath.comath.it
math
math
11-25 00:00
arXiv:2511.17504v1 Announce Type: new Abstract: We study covert communication and covert secret key generation with positive rates over quantum state-dependent channels. Specifically, we consider fully quantum state-dependent channels when the transmitter shares an entangled state with the channel. We study this problem setting under two security metrics. For the first security metric, the transmitter aims to communicate covertly with the receiver while simultaneously generating a covert secret key, and for the second security metric, the transmitter aims to transmit a secure message covertly and generate a covert secret key with the receiver simultaneously. Our main results include one-shot and asymptotic achievable positive covert-secret key rate pairs for both security metrics. Our results recover as a special case the best-known results for covert communication over state-dependent classical channels. To the best of our knowledge, our results are the first instance of achieving a positive rate for covert secret key generation and the first instance of achieving a positive covert rate over a quantum channel. Additionally, we show that our results are optimal when the channel is classical and the state is available non-causally at both the transmitter and the receiver.
cs.itmath.it
math
math
11-25 00:00
arXiv:2511.17530v1 Announce Type: new Abstract: In this paper, we present different characterizations of tripotent orthogonal matrices (i.e., A^3 = A = A^* ) in terms of matrix equations, integer powers of AA^* and A^*A, average of A, A^*, and A^{\dagger}, rank of matrices, and trace of matrices. We study certain properties of this class of matrices.
math.oamath.ra
math
math
11-25 00:00
arXiv:2511.17536v1 Announce Type: new Abstract: We prove that Rado's graph admits no quantum symmetries.
math.oamath.qa
math
math
11-25 00:00
arXiv:2511.17650v1 Announce Type: new Abstract: Two evolution models based on the generalized Collatz operator are introduced. These models are characterized by coefficients $\alpha$ and $\beta$ in the Collatz dynamics, and are suitably defined. Here, $\alpha=\beta=1$, and $\alpha=3$, $\beta=1$ correspond to the Nollatz and classical Collatz operators, respectively. In general, the first evolution model is a continuum, Fourier side based, motivated by the Cubic Szeg\H{o} operator of G\'erard and Grellier. The second evolution considers discrete time derivatives of the Collatz orbits. In this paper we describe the evolution of both models, with particular emphasis on dynamical properties. For the first one, it is proved local and global existence in the space $L^2(\mathbb T)$, and a one-to-one characterization of the existence of nontrivial periodic and unbounded orbits of the Collatz mapping in terms of particular set of solutions of this continuous Collatz flow. For the discrete part, a sort of discrete energy is introduced. This energy has the property of being conserved by the discrete flow. An estimate of each term in this energy is given, proving suitable growth bounds. Finally, the meaning of the discrete time derivative for the generalized Collatz orbits is discussed. It is proved that, except for the Nollatz and Collatz operators, the sum of coefficients related to this discrete time derivative is an increasing sequence in $n$ as the iteration parameter $n$ evolves.
math.apmath.ds
math
math
11-25 00:00
arXiv:2511.17718v1 Announce Type: new Abstract: We consider a two-user random access system in which each user independently selects a coding scheme from a finite set for every message, without sharing these choices with the other user or with the receiver. The receiver aims to decode only user 1 message but may also decode user 2 message when beneficial. In the synchronous setting, the receiver employs two parallel sub-decoders: one dedicated to decoding user 1 message and another that jointly decodes both users messages. Their outputs are synthesized to produce the final decoding or collision decision. For the asynchronous setting, we examine a time interval containing $L$ consecutive codewords from each user. The receiver deploys $2^{2L}$ parallel sub-decoders, each responsible for decoding a subset of the message-code index pairs. In both synchronous and asynchronous cases, every sub-decoder partitions the coding space into three disjoint regions: operation, margin, and collision, and outputs either decoded messages or a collision report according to the region in which the estimated code index vector lies. Error events are defined for each sub-decoder and for the overall receiver whenever the expected output is not produced. We derive achievable upper bounds on the generalized error performance, defined as a weighted sum of incorrect-decoding, collision, and miss-detection probabilities, for both synchronous and asynchronous scenarios.
cs.itmath.it
math
math
11-25 00:00
arXiv:2511.17719v1 Announce Type: new Abstract: Let $G$ be a finite group and $K$ a field containing an element of multiplicative order $|G|$. It is shown that if $G$ has a cyclic subgroup of index at most $2$, then the separating Noether number over $K$ of $G$ coincides with the Noether number over $K$ of $G$. The same conclusion holds when $G$ is the direct product of a dihedral group and the $2$-element group. On the other hand, the smallest non-abelian groups $G$ are found for which the separating Noether number over $K$ is strictly less than the Noether number over $K$. Along the way the exact value of the separating Noether number is determined for all groups of order at most $16$. The results show in particular that unlike the ordinary Noether number, the separating Noether number of a non-abelian finite group may well be equal to the separating Noether number of a proper direct factor of the group.
math.acmath.rtmath.gr
math
math
11-25 00:00
arXiv:2511.17723v1 Announce Type: new Abstract: In the space of equioriented type $A$ quiver representations, placing strict rank conditions on the maps cuts out subvarieties that we call "open quiver loci." Their closures are the quiver loci, whose equivariant cohomology classes are the quiver polynomials of Buch and Fulton. We present a geometric and a combinatorial formula to compute equivariant Chern--Schwartz--MacPherson (CSM) classes of open quiver loci. These classes naturally associate an element of equivariant cohomology to each open quiver locus, and they include the data of the quiver polynomials, along with additional data about Euler characteristic. The combinatorial formula is in terms of "chained generic pipe dreams," which modify the pipe dreams of Fomin and Kirillov to more strongly resemble the lacing diagrams developed by Knutson-Miller-Shimozono. We also present three new formulas for quiver polynomials, two of which are combinatorial; these are streamlined versions of the previously known Knutson-Miller-Shimozono formulas, in the sense that they contain fewer terms.
math.agmath.co
math
math
11-25 00:00
arXiv:2511.17510v1 Announce Type: new Abstract: In this research article, we formulate and prove multidimensional Widder--Arendt theorem and integrated form of multidimensional Widder--Arendt theorem for functions with values in sequentially complete locally convex spaces. Established results seem to be new even for scalar-valued functions.
math.fa
math
math
11-25 00:00
arXiv:2511.17521v1 Announce Type: new Abstract: In this note it is proven that an idempotent ring cannot be Morita equivalent to its idempotent proper ideal.
math.ra
math
math
11-25 00:00
arXiv:2511.17522v1 Announce Type: new Abstract: The concepts of derivations and right derivations for Leibniz algebras and $K$-B quasi-Jordan algebras naturally arise from the inner derivations determined by their algebraic structures. In this paper we introduce the corresponding analogues for dialgebras, which we call diderivations, and examine their properties in relation to antiderivations and right derivations. Our approach is based on the study of multiplicative operators and on the construction of the Leibniz algebra generated by biderivations, thereby providing a systematic framework that unifies several types of derivation-like operators. In addition to the general theory, we present a complete classification of the spaces of diderivations for dialgebras of dimensions two and three, obtained through explicit computations. These low-dimensional results not only exemplify the general constructions but also reveal structural patterns that inform possible extensions to higher dimensions and more intricate algebraic contexts.28
math.ra
math
math
11-25 00:00
arXiv:2511.17534v1 Announce Type: new Abstract: This paper is concerned with the Cauchy problem of the evolutionary Faddeev model, a system that maps from the Minkowski space $\mathbb{R}^{1+3}$ to the unit sphere $\mathbb{S}^2$. The model is a system of nonlinear wave equations whose nonlinearities exhibit a null structure and include semilinear terms, quasilinear terms, and the unknowns themselves. By considering a class of large initial data (in energy norm) of the short pulse type, we prove that the evolutionary Faddeev model admits a globally smooth solution via energy estimates. The main result is achieved through the selection of appropriate multipliers that are specially adapted to the geometry of the system.
math.ap
math
math
11-25 00:00
arXiv:2511.17538v1 Announce Type: new Abstract: This paper intends to develop a $q$-difference operator $\nabla^{(\gamma)}_q$ of fractional order $\gamma$, and give several intriguing properties of this new difference operator. Our main focus remains on the construction of sequence spaces $\ell_p(\nabla^{(\gamma)})$ and $\ell_\infty (\nabla^{(\gamma)})$, at the same time comparing these spaces with those already exist in the literature. Apart from obtaining Schauder basis, we determine $\alpha$-, $\beta$-, and $\gamma$-duals of the newly defined spaces. A section is also devoted for characterizing matrix classes $(\ell_p(\nabla^{(\gamma)}),\mathfrak X),$ where $\mathfrak X$ is any of the spaces $\ell_\infty,$ $c,$ $c_0$ and $\ell_1$.
math.fa
math
math
11-25 00:00
arXiv:2511.17539v1 Announce Type: new Abstract: In this work we study the following classical still challenging Calculus problem: {\it If $f:(0,\infty)\to\mathbb{R}$ is a continuous function, for which the sequence $\{f(nx)\}$ tends to zero, for every positive $x$, as $n$ tends to infinity, then $f(x)$ also tends to zero, as $x$ tends to infinity.}
math.fa
math
math
11-25 00:00
arXiv:2511.17544v1 Announce Type: new Abstract: This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the braiding symmetry is required to be invertible, distorted monoidal categories admit non-invertible binary distortions and unit distortions while preserving coherent tensorial reasoning. We show that these structures naturally assemble into a strict 2-category whose composition and interchange laws hold on the nose, not merely up to isomorphism. Beyond the abstract 2-monad justification, our contribution is a fully constructive and type-safe calculus that enables formal reasoning about non-invertible interchange. We provide explicit construction schemes for such distortions, including idempotent twists of classical braidings and graded unit distortions arising from characters on monoidal gradings. This framework extends the expressive power of monoidal categories to model irreversible, resource-sensitive, and direction-dependent processes --such as those in directed homotopy theory, categorical quantum mechanics, and non-symmetric operadic structures--while remaining amenable to mechanization and formal verification.
math.ct
math
math
11-25 00:00
arXiv:2511.17548v1 Announce Type: new Abstract: This paper is devoted to the analysis of a focusing nonlinear biharmonic Schr\"odinger equation in the presence of an unbounded growing up inhomogeneous term. The first main contribution of this work is the derivation of an inhomogeneous Gagliardo-Nirenberg inequality adapted to the unbounded weight, which provides the necessary control over the nonlinear term in terms of Sobolev norms. Building on this inequality, we then investigate the long-time behavior of solutions and establish a sharp dichotomy: solutions with initial data below the ground state energy either exist globally in time or experience finite-time blow-up. A distinctive feature of our results is that the analysis of the unbounded inhomogeneous term requires the imposition of radial symmetry on the initial data, which allows us to exploit certain Strauss type Sobolev estimates that would not hold in the general non-radial case. This work complements previous studies on biharmonic Schr\"odinger equations with singular inhomogeneities, highlighting both the challenges and the new phenomena that arise when the nonlinearity is weighted by a growing up unbounded function, which broke the space translation invariance of the standard homogeneous associated equation.
math.ap
math
math
11-25 00:00
arXiv:2511.17613v1 Announce Type: new Abstract: We are concerned with the Steiner chains consisting of four circles. More precisely, we deal with the invariants of chains introduced in the recent papers of J.Lagarias, C.Mallows, A.Wilks, R.Schwartz and S.Tabachnikov. We also establish certain algebraic relations between those invariants. To this end we use the invariance of certain moments of curvatures of poristic Steiner chains established by R.Schwartz and S.Tabachnikov, combined with the computation of these moments for the socalled symmetric Steiner 4-chains. We also present analogous results for Steiner 3-chains and give an application of our results to the feasibility problem for the radii of Steiner 4-chains. Keywords: Steiner chain, parent circles, Steiner porism, poristic Steiner chains, Descartes circle theorem, invariant moments of curvatures, algebraic relations between invariants
math.gm
math
math
11-25 00:00
arXiv:2511.17640v1 Announce Type: new Abstract: Type-2 fuzzy set (T2 FS) were introduced by Zadeh in 1965, and the membership degrees of T2 FSs are type-1 fuzzy sets (T1 FSs). Owing to the fuzziness of membership degrees, T2 FSs can better model the uncertainty of real life, and thus, type-2 rule-based fuzzy systems (T2 RFSs) become hot research topics in recent decades. In T2 RFS, the compositional rule of inference is based on triangular norms (t-norms) defined on complete lattice (L, \le ) ( L is the set of all convex normal functions from [0,1] to [0,1], and , \le is the so-called convolution order). Hence, the choice of t-norm on (L,\le) may influence the performance of T2 RFS. Therefore, it is significant to broad the set of t-norms among which domain experts can choose most suitable one. To construct t-norms on (L,\le), the mainstream method is convolution which is induced by two operators on the unit interval [0,1]. A key problem appears naturally, when convolution is a t-norm on (L,\le). This paper gives the necessary and sufficient conditions under which convolution is a t-norm on (L,\le). Moreover, note that the computational complexity of operators prevent the application of T2 RFSs. This paper also provides one kind of convolutions which are t-norms on (L,\le) and extremely easy to calculate.
math.gm
math
math
11-25 00:00
arXiv:2511.17642v1 Announce Type: new Abstract: This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different choices of the spanning vectors influence the resulting dynamical tramsitions and pattern formations. As the basic steady-state loses its linear stability, the binary system undergoes a dynamic transition which is shown to be characterized by both the geometry of the domain and the choice of physical parameters of the model. Unlike rectangular domains, we are able to observe the emergence of hexagonally-packed circles, as well as the familiar rolls and square structures. We begin with the decomposition of our function space into a stable and unstable eigenspace before calculating the center manifold that maps the former to the later. In analyzing the resulting reduced equations, we consider the different multiplicities that the critical eigenvalue can have, which is shown to be geometry-dependent. We briefly consider the long-range interaction model and determine that it produces similar results to the original model.
math.ap
math
math
11-25 00:00
arXiv:2511.17653v1 Announce Type: new Abstract: Multi-Agent Reinforcement Learning (MARL) has emerged as a powerfulparadigm for cooperative decision-making in connected autonomous vehicles(CAVs); however, existing approaches often fail to guarantee stability, optimality,and interpretability in systems characterized by nonlinear dynamics,partial observability, and complex inter-agent coupling. This study addressesthese foundational challenges by introducing MARL-CC, a unified MathematicalFramework for Multi-Agent Reinforcement Learning with Control Coordination.The proposed framework integrates differential geometric control, Bayesian inference,and Shapley-value-based credit assignment within a coherent optimizationarchitecture, ensuring bounded policy updates, decentralized belief estimation,and equitable reward distribution. Theoretical analyses establish convergence andstability guarantees under stochastic disturbances and communication delays.Empirical evaluations across simulation and real-world testbeds demonstrate upto a 40% improvement in convergence rate and enhanced cooperative efficiencyover leading baselines, including PPO, DDPG, and QMIX.These results signify a decisive advance in control-oriented reinforcement learning,bridging the gap between mathematical rigor and practical autonomy.The MARL-CC framework provides a scalable foundation for intelligent transportation,UAV coordination, and distributed robotics, paving the way toward interpretable, safe, and adaptive multi-agent systems. All codes and experimentalconfigurations are publicly available on GitHub to support reproducibilityand future research.
math.gm
math
math
11-25 00:00
arXiv:2511.17679v1 Announce Type: new Abstract: Let $G$ be a connected graph, and let $b$ and $k$ be two positive integers with $b\equiv1$ (mod 2). A $[1,b]$-odd factor of $G$ is a spanning subgraph $F$ of $G$ with $d_F(v)\equiv1$ (mod 2) and $1\leq d_F(v)\leq b$ for every $v\in V(G)$. A graph $G$ is called $k$-critical with respect to $[1,b]$-odd factor if $G-X$ contains a $[1,b]$-odd factor for every $X\subseteq V(G)$ with $|X|=k$. Let $\mathcal{D}(G)$ denote the distance matrix of $G$. The largest eigenvalue of $\mathcal{D}(G)$, denoted by $\mu(G)$, is called the distance spectral radius of $G$. In this paper, we prove an upper bound for $\mu(G)$ in a connected graph $G$ which guarantees $G$ to be $k$-critical with respect to $[1,b]$-odd factor.
math.co
math
math
11-25 00:00
arXiv:2511.17686v1 Announce Type: new Abstract: Let $A$ be a dissipative operator on a Banach space with a dense domain. It is proved that $A$ has a quasi-dissipative extension (possibly in an enlarged Banach space) which generates a quasi-contractive $C_0$-semigroup. \par This gives a positive answer to the question posed by P.R.Chernoff and H.F.Trotter.
math.fa
math
math
11-25 00:00
arXiv:2511.17700v1 Announce Type: new Abstract: Given a closed immersion between arbitrary smooth complex projective varieties, we prove that the two operations: (1) taking the moduli space of stable sheaves, and (2) taking the deformation to the normal cone, commute in a precise sense. In the case of curves inside symplectic surfaces, previously studied by Donagi-Ein-Lazarsfeld, the corresponding deformation to the normal cone space is an open subset of the relative moduli space of sheaves. As an application, we show generalized Kummer varieties degenerate to natural symplectic subvarieties of the Hitchin system for curves of genus at least 2.
math.ag
math
math
11-25 00:00
arXiv:2511.17716v1 Announce Type: new Abstract: We consider the problem of representing the fraction $5/P$ as a sum of three distinct unit fractions $1/A+1/B+1/C$ with $A
math.nt