Papers

Perturbation theory for symmetric matrices shows that eigenvalues with small spectral gaps are more sensitive to off-diagonal perturbation, implying that different entries affect the eigenvalues unevenly. Building on this insight, we incorporate spectral gap information into the Jacobi method for symmetric eigenvalue problems and propose a new pivoting strategy, which is completely different from classical ones governed solely by the magnitude of the off-diagonal entries. When combined with a mixed-precision preconditioner that diagonalizes the matrix to low precision, numerical experiments demonstrate that the resulting strategy can significantly outperform the classical greedy approach when the original matrix has clustered eigenvalues.

This work presents a two-dimensional coupled Low-to-High confinement transition system based on the phenomenological coupling mechanism between zonal flows and turbulent fluctuations at the plasma edge in tokamak magnetic confinement devices. For this two-dimensional system, the corresponding Hamilton-Jacobi equation is derived, and a machine learning approach combining physics-informed neural networks with a loss function designed via vector field decomposition is employed to numerically solve it. This yields information about the system's quasipotential, enabling further computation of the most probable path for the rare event of a state transition in the coupled system. Compared with classical two-dimensional Low-to-High confinement transition models, the proposed system features state variables that are more accessible to experimental measurement and has a more comprehensive physical foundation. Moreover, it self-consistently describes the dynamical behavior of tokamak devices during the startup phase.

In this paper, we provide two (significantly different) proofs of the well known Strong Ramadanov Conjecture for the class of real ellipsoids in the complex $2$-space.

We prove the population-level identifiability of deep generative models (DGMs) with piecewise-affine (PWA) decoders and Gaussian mixture model (GMM) priors, in a purely unsupervised setting. We introduce three algebraic contrast principles for symmetry breaking: *domain contrast*, which trivializes the mixture symmetry group, a label-free counterpart of the sufficient-variability assumption of nonlinear ICA; *mechanism contrast*, which ensures every decoder branch gets an observational boundary across which it toggles alone; and *interaction contrast*, which forbids parameter conspiracies between latent components and decoder branches. Together they exploit the interplay between the discrete combinatorics of the PWA map and the continuous symmetry structure of the latent GMM. Continuity is replaced by algebraic symmetry conditions; injectivity is decoupled from structural identification and required only for pointwise inversion. Our results form a hierarchy: from *law identifiability* (LID; latent distribution up to a global affine map) through *map identifiability* (MID; decoder up to the same map) to *posterior* and *pointwise identifiability*. The ICA-form ambiguity emerges under conditions on diagonal component covariances. The interaction contrast is the only one of our contrasts required on the estimator side. To our knowledge this is the first to develop algebraic symmetry-breaking into an identifiability engine for a concrete nonlinear model class, the first to admit discontinuous decoders, and the first to handle fully non-injective decoders, where every observation admits multiple latent codes.

Let $p \equiv 1 \pmod 6$ be prime and $K_p = \mathbf{Q}(\zeta_{3p})$. We study the reflected circular unit $\mu_p = (1+z\zeta_p)/(1+\bar z\zeta_p)$, $z = -\zeta_3^2$, and its character projections. A universal Stirling polynomial $P_m$ gives an exact identity between the anti-spectrum of $\mu_p$ and the primitive divided $\chi_{-3}$-twisted Stickelberger spectrum: $P_{p-j}(h) - P_{p-j}(1-h) = -(2h-1)(j-1)!\,b_j$, $h = z/(1+z)$. Thus the locally blind lines of the reflected unit are precisely the zeros of the corresponding divided twisted Bernoulli eigenvalues. For every $p < 500$ we enumerate these zeros. Exactly twelve character lines occur. On each line an explicit integral idempotent product of $\mu_p$ is a local $p$-th power at the conductor primes but not a global $p$-th power. Small completely split primes provide finite Artin certificates. The generalized Bernoulli number has exact $p$-adic valuation one in every case; the character-wise Main Conjecture therefore proves that each radical generates the complete Hilbert-class-field component, which has order $p$. Seven of the twelve lines occur at classically regular primes, so twisted degeneracy below 500 is more often invisible to ordinary irregularity than aligned with it. The first case, $p = 67$, is worked out in full, and a deterministic integer-arithmetic program (included as an ancillary file) reproduces the enumeration and every certificate.

We determine the de Rham–Betti (dRB) groups of several classes of abelian varieties over $\overline{\mathbb{Q}}$. We prove that $G_{\mathrm{dRB}}(A)=\mathrm{MT}(A)$ for every simple abelian fourfold of type IV. At present, much of what is known about the dRB structures of abelian varieties derives from Wüstholz's Analytic Subgroup Theorem, whose applications primarily control linear relations among periods of $\mathrm{H}^{1}(A)$ and divisor-class information. In comparison with the theory of Hodge structures, our understanding of dRB structures remains limited. We therefore adopt an approach different from the method of Moonen-Zarhin for determining the Mumford-Tate groups of these abelian varieties. Depending on the endomorphism type of the abelian fourfold, we use Galois-theoretic analysis, van Geemen's half-twist construction, and positivity constraints arising from polarizations, as appropriate, to exclude proper reductive subgroups of the corresponding Mumford-Tate groups as candidates for the dRB groups. We also use results on periods due to Gross and Chudnovsky. This article is an expansion of the second part of the author's PhD thesis https://pure.uva.nl/ws/files/311471255/Thesis.pdf; see also https://arxiv.org/abs/2511.01072 by the author.

Consider the tree obtained by attaching a leaf to the third vertex of a path with n-1 vertices. In this note, we prove that the characteristic polynomial of this tree is irreducible when n belongs to certain arithmetic progressions modulo 30. As a result there are infinitely many pairwise non-isomorphic trees with an irreducible the characteristic polynomial. Our proof combines several number-theoretic arguments with a result of Gross, Hironaka, and McMullen [GHM09] concerning the cyclotomic factors of the Coxeter polynomials associated with the diagrams En. This resolves affirmatively a conjecture of Akbari, Kumar, Mohar and Pragada.

The square of a graph $G$ is the graph obtained from $G$ after adding an edge between any two vertices of distance $2$. A $k$-irregular graph is a graph with maximum degree $k$ such that vertices of degree $k$ are not adjacent. A list assignment of a graph is a function $L$ that assigns to each vertex a list of permissible colors. The graph is said to be \textit{$L$-colorable} if there exists a proper coloring $f$ such that $f(v) \in L(v)$ for every vertex $v$. A graph $G$ is called \textit{$k$-choosable} if it is $L$-colorable for every list assignment where each list has exactly $k$ colors. The list chromatic number of $G$, denoted by $\chi_l(G)$, is the smallest integer $k$ for which $G$ is $k$-choosable. Cranston and Kim \cite{ck} showed that $\chi_l(G^2) \leq 8$ for all subcubic graphs except the Petersen Graph. Moreover, Cranston and Kim \cite{ck} conjectured that for graphs with maximum degree $k$ and maximum clique size $w (G^2)\leq k^2-1$, we have $\chi_l(G^2) \leq k^2-1$. We prove that for a 4-irregular graph $G$, we have $\chi_l(G^2) \leq 11$. Moreover, we provide an example to show that this bound is sharp.

Two general estimates govern the rank of an $h$-scattered $q$-system: the scattered upper bound and the lower bound for systems maximal under inclusion. We determine exactly when they coincide. Besides $m=h+1$ and $m=h+2$, equality occurs precisely when $h$ is even, $m=h+3$, and $k\equiv h/2\pmod{h+1}$. We also prove rigidity in the first two cases: every extremal system is equivalent to either $\mathbb{F}_q^k$ or a direct sum of elementary Gabidulin systems and $\mathbb{F}_q$-directions. For $h=m-3$ and $k=\ell(m-2)+s$, with $1\leq s<(m-2)/2$, the two bounds differ by one, apart from one boundary case. Starting from an arbitrary maximum scattered $q$-system, we construct extremal quasi-maximum $(m-3)$-scattered systems of rank $\ell m+s$. Every such extension preserves lower bounds on the generalized rank weights of the initial code. When an explicit independence condition holds, the construction also produces a nondegenerate dual pair of quasi-MRD codes. We parametrize these extensions by subspaces of a quotient space and derive a uniform lower bound on the number of inequivalent outputs. Known order-two families yield codes separated from every nontrivial direct sum under an explicit numerical condition, while higher-order families are separated from a specified order-one direct-sum class. We conclude with a fully explicit binary example.

A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is $k$-degenerate if each of its subgraphs contains a vertex of degree at most $k$. It was known that every 1-planar graph is 8-choosable. In this paper, we show that every 1-planar graph without 6-cycles is 5-degenerate and hence 6-choosable.

The $N$-th order rational rogue wave of the nonlinear Schrödinger equation (NLS), which depends on $2 N-2$ real parameters, has been shown to be impossible to generate by the nonlinear superposition formula. We here generate this sequence by a three-term recurrence relation, each step only requiring the computation of three $N-1$-th order determinants of $2 N-2$ variables, while the previous method requires two determinants of order $2 N$ in $2 N$ variables. This allows us to obtain explicitly the seventh wave with its six arbitrary complex parameters. These very compact expressions open the possibility to investigate the possible existence of new patterns in addition to the already observed ones (concentric rings, polygonal configurations, \dots).

Let $L/K$ be a Galois extension of number fields, and let $C_1, C_2$ be conjugacy classes of $\mathrm{Gal}(L/K)$. By introducing algebraic parameters related to $C_1$ and $C_2$, we provide a conditional characterization for Chebyshev's bias logarithmic density $\delta_{L/K}(C_1,C_2)$ to lie in the interval $(1/2, 1)$, meaning that the prime ideal race is biased. Unlike existing examples in the literature, where the bias comes from a difference in the number of square roots, the order of vanishing of Artin $L$-functions at $s=1/2$, or a combination of both, we use this criterion to construct Galois extensions where neither of these aspects plays a role. In our constructions, the bias arises entirely from a difference in the number of $2p$-th roots for an odd prime $p$. We prove that the minimal Galois group order required for this phenomenon is $96$ for $p=3$ and $320$ for $p=5$, where in both cases the group structure is a direct product of two generalized quaternion groups. Furthermore, we provide generalized constructions for all odd primes. Finally, these same algebraic parameters enable us to prove that an estimate established by Aoki and Koyama under the Deep Riemann Hypothesis holds unconditionally in certain cases.

A tournament is a \emph{$k$-majority tournament} if it is the pairwise majority relation of an election with $2k-1$ voters: there are $2k-1$ linear orders of the vertex set, repetitions allowed, such that $u\to v$ exactly when $u$ precedes $v$ in at least $k$ of them. Let $F(k)$ be the maximum domination number of a $k$-majority tournament. In 2006, Alon, Brightwell, Kierstead, Kostochka and Winkler proved that $F(k)$ is finite and that $c_1k/\log k\le F(k)\le c_2k\log k$ for absolute constants $c_1,c_2>0$; the order of growth of $F(k)$ has been open since. We prove that $F(k)=\Theta(k\log k)$. As a consequence, the maximum domination number of a tournament realized by fair $m$-sided dice is $\Theta(m\log m)$, closing the corresponding gap in the bounds of Alon et al.

We study the category $\mathsf{AtoMon}$ of atomic monoids and atom-preserving homomorphisms. We prove that $\mathsf{AtoMon}$ is locally finitely presentable by exhibiting a strong generator consisting of compact objects. We show that $\mathsf{AtoMon}$ admits (regular epi, mono)-factorizations but that it is not a regular category: we construct a regular epimorphism which is not pullback-stable. We also establish adjunctions for the group of units and explicitly construct the “cofree atomic monoid” over an arbitrary monoid. Finally, we exhibit a way to lift torsion theories of $\mathsf{Grp}$ to pretorsion theories of $\mathsf{AtoMon}$ and extend this construction to a more general setting.

We introduce a Physics-Informed Token Transformer (PITT) methodology for nonlinear hyperbolic balance laws in one space dimension, using piecewise steady-state profiles for the representation of approximate weak solutions. The method combines symbolic equation tokenization, a Fourier neural operator encoder, an explicit Rankine–Hugoniot law for shock motion, and a learned correction term. For clarity, we present it here for the relativistic Schwarzschild–Burgers equation, a scalar model for spherically symmetric fluid flows on a Schwarzschild background. For this model the steady-state invariant and the generalized Riemann solutions are explicit, and they can therefore be built into the neural evolution. In particular, the leading discontinuities are advanced by the analytical jump condition, while the learned part reconstructs smooth regions, rarefaction fans, geometric dependence, and finite-resolution effects. The method is designed to locate wave fronts accurately and to preserve the relevant steady states. We test our PITT method on moving shocks, stationary shocks, rarefaction waves, and compare it with a standard high-order finite-volume approximation. We also analyze the standard Burgers limit (when the Schwarzschild mass tends to zero). The Rankine–Hugoniot prior plays the dominant role in these tests, while equation tokenization gives a systematic additional gain. The method is relevant for problems involving geometric effects and/or complex shock-wave dynamics, and is used here to study the long-time dynamics of perturbations of steady-state solutions. In particular, we exhibit an asymptotic law of propagation for the shock location of perturbed steady-state flows.

Given a contraction with an invariant subspace and a row contraction with a joint invariant subspace, a factorization of their characteristic functions was obtained by Sz.-Nagy and Foiaş, and by Haria, Maji, and Sarkar, respectively. In this article, we investigate the regularity of this factorization in both the single-variable and multivariable cases. We construct examples of a contraction $T$ with an invariant subspace such that this factorization is not regular in general. If $T$ is completely non-unitary, we prove that this factorization is either regular or strange. Furthermore, we obtain a characterization of the regularity of this factorization. Using this characterization, we identify several classes of contractions and row contractions for which this factorization is regular. Among these classes, the most notable classes are pure contractions and pure row contractions. Additionally, for any integer $k>2$, we introduce the concept of $k$-strange factorizations for contractive analytic functions, which extend the concept of strange ($2$-strange) factorizations introduced by Sz.-Nagy and Foiaş. Finally, we prove that if a contraction is pure or is a completely non-unitary contraction for which $\Delta_{\Theta_T}(t)$ has finite rank almost everywhere, then its characteristic function does not admit any $k$-strange factorization.

Goppa codes play an important role in code-based cryptography due to their efficient decoding algorithms and their use as underlying private codes in the McEliece cryptosystem. To determine the true minimum distances of Goppa codes is a notoriously difficult problem. In this paper, we establish a criterion for a Goppa code to attain its designed distance. We consider Goppa polynomials of the form $G(x)=U(x)H(x)+V(x)H'(x)$, where $\deg(G)=t$ and $H(x)\in\mathbb{F}_q[x]$ is a monic irreducible polynomial of degree $t+1$ whose roots are contained in the support $L$. We prove that the corresponding Goppa code $\Gamma(L,G)$ contains a codeword of weight $t+1$ if and only if \[ \frac{V(\alpha_{i_{t+1}})}{V(\alpha_{i_j})}\in\mathbb{F}_q^*, \qquad 1\leq j\leq t, \] where $\alpha_{i_1},\ldots,\alpha_{i_{t+1}}$ are the roots of $H(x)$. Based on this criterion, we derive a general family of Goppa codes that attain their designed distance by developing an interpolation-based construction of Goppa polynomials. We further obtain families of Goppa codes whose Goppa polynomials are determined by considering monomial, binomial, and their product of the auxiliary polynomial $V(x)$. By taking $H(x)$ to be different irreducible binomials and trinomials, we obtain several explicit families of Goppa codes whose minimum distances are equal to designed distance.

Continuous-variable quantum computing (CVQC) is a computing paradigm in which measurements yield values over a continuous domain. CVQC is both a convenient computational framework for modeling physical quantum systems, and a good abstraction for hardware platforms based on quantum optics. Yet, the semantic foundations of CVQC remain underdeveloped. To address this gap, we develop a formal semantics for a core CV quantum programming language, and sound verification methods for program correctness. A main contribution of this work is to isolate a well-behaved quantitative predicate domain that achieves sufficient expressiveness to accommodate unbounded values as they arise in the infinite-dimensional, continuous setting. Specifically, we choose closed positive quadratic forms as semantic predicates, representing finite expectations, domains of finiteness, and infinite penalties in one ordered object. We validate our choice by establishing that our semantic predicates satisfy desirable closure properties including the definition of weakest preconditions. We validate our design with two case studies, including an example based on the celebrated GKP error-correcting code, for which we establish a second moment bound.

Classical multi-user diversity theory predicts that throughput over Rayleigh fading channels grows as $\log_2\!\log_2 K$. In this work, we demonstrate a fundamental shift in this scaling law under heavy-tailed composite fading. Specifically, under Fisher–Snedecor $\mathcal{F}$ composite fading, the channel power acquires a regularly varying upper tail, shifting extreme-value statistics from the Gumbel to the Fréchet domain. We prove that the maximum SINR among $K$ users scales polynomially as $K^{1/m_s}$, where $m_s$ is the shadowing severity parameter, leading to an ergodic capacity scaling of $\frac{1}{m_s}\log_2 K$. Crucially, this scaling persists in interference-limited Poisson networks, where aggregate co-channel interference alters the scaling constant but not the exponent. This polynomial gain is most relevant in severe-to-moderate shadowing ($m_s \le 3$), as encountered in body-area networks, vehicular/industrial IoT, and dense indoor environments, where Fréchet asymptotics overtake industry-standard lognormal models at practical user counts. Finally, we establish the conditions necessary to harvest this gain (showing that proportional-fair scheduling under quasi-static shadowing reverts to Gumbel scaling) and validate all analytical findings through Monte Carlo simulations, including MIMO random beamforming.

Active Flux is a third-order accurate, fairly novel finite volume method for hyperbolic conservation laws that is becoming increasingly popular. It evolves additional nodal degrees of freedom (DOF) located on cell interfaces and shared by neighboring cells. The numerical fluxes are then computed from these DOFs. A crucial component of Active Flux methods is the evolution operator of the point values, which enables the natural use of semi-Lagrangian ideas and makes Active Flux an attractive candidate for a grid-based approach to the Vlasov equation. Here, we compare two recently proposed Active Flux methods for the 1D1V Vlasov-Poisson system: a split-step method and an unsplit method.

Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. We study the smooth mod $p$ representations of $\mathrm{GL}_2(K)$ appearing in a tower of mod $p$ Hecke eigenspaces of the cohomology of Shimura curves, under mild genericity assumptions but notably no multiplicity one assumption at tame level, and prove that they are of finite length, thereby extending some recent results of Breuil, Herzig, Hu, Morra and Schraen to higher multiplicity. In a previous companion article we investigated the case where the local Galois representation attached to the Hecke eigensystem is semisimple; this article treats the non-semisimple case.

For North-East lattice paths (which we simply call lattice paths), we define intersection in terms of common edges. We prove that a family of paths from $(0,0)$ to $(n,n)$ in which every two distinct paths have an even number of common edges has size at most $2^n$, and that this bound is attained. If $M_{\mathrm{odd}}(n)$ denotes the maximum size of a family in which every two distinct paths have an odd number of common edges, then we prove \[ M_{\mathrm{odd}}(n)\le n(n-1)+1 \] and construct families showing that $M_{\mathrm{odd}}(n)=\Theta(n^2)$. Finally, we construct at least $C_n$ distinct extremal even-intersecting families, where $C_n$ is the $n$th Catalan number, and conjecture that these are all the extremal families.

Time-dependent routing recognizes that the same journey can take a different time depending on when it begins. Under duration minimization, even the departure time of each vehicle becomes a decision. Exact methods for this setting exist in the literature, but researchers and practitioners have lacked a ready-to-use open solver that combines rich piecewise-linear travel times, early feasible solutions and optimality claims. KAYROS fills this gap with two modes on one checker-consistent engine: an Iterated Local Search that streams improving solutions and a Branch-Price-and-Cut method that can issue computational optimality certificates under explicit arithmetic and search assumptions. It installs with one command and has no proprietary dependency. The public MAMUT-routing store currently contains 704 KAYROS certificates under a four-solve publication protocol, which has also led to the retraction and repair of invalid earlier claims. The report presents two complementary benchmark contributions to MAMUT-routing. The first integrates Blauth2024, a benchmark from the literature whose travel times derive from measured Uber speeds, for which KAYROS provides new best-known solutions on all 40 instances. The second proposes Poryos2026, a new benchmark of 1,080 paired static and time-dependent instances built from OpenStreetMap road networks and controlled synthetic traffic. Finally, the report describes the intensive human-AI collaboration behind this work and the verification practices that kept its outputs independently verifiable.

We prove several topological zero-one laws. First, we show that, if a subset $A$ of a Banach space $X$ has the Baire property, then $A$ admits a somewhere dense set of vectors $x \in X$ such that $A+x$ agrees with $A$ modulo meager sets if and only if it is either meager or comeager. Additional equivalent conditions are given if $X=\mathbb{R}$. Second, we prove that if $A_1,\ldots,A_k\subseteq \mathbb{R}$ are subsets with the Baire property, $\alpha_1,\ldots,\alpha_k$ are nonzero reals with distinct finite sums, and $(x_{n,i}: n\in \omega)$ are injective real sequences which converge to $0$ for each $i=1,\ldots,k$, then $$ \sum_{i=1}^k \alpha_i(1_{A_i+x_{n,i}}-1_{A_i})=0 $$ modulo meager sets for all $n \in \omega$ if and only if each $A_i$ is either meager or comeager. Finally, we provide some additional results in the case where the $\alpha_1,\ldots,\alpha_k$ do not have distinct finite sums. For instance, if $k=2$ and $\alpha_1=\alpha_2$, then the above equality holds modulo meager sets for all $n \in \omega$ if and only if each $A_i$ is either meager or comeager or if $\{A_1,A_2\}$ is a partition of $\mathbb{R}$ modulo meager sets. Additional characterizations are given in the case $k\ge 3$. These results yield the category analogues of several results by Fejzić, Freiling, and Rinne in [J. London Math. Soc.~82 (2010), no. 3, 717–732].

A numerical semigroup is a cofinite additive submonoid of ${\mathbb N}$. The largest element of the complement is its Frobenius number and the cardinality of its complement is the genus. We propose a new approach to counting semigroups by the Frobenius number and by the genus, by introducing two ad-hoc trees. Those are leaf-discriminating trees in the sense that their leaves correspond exactly to the objects we want to count and, so, exploring these trees instead of general trees is optimal. Our approach reduces the search space for genus to 23% and for Frobenius to 0.03% of that required by previous approaches and this allowed to obtain an important number of unkown terms from both sequences. We implemented a recursive descending algorithm based on the so-called seeds structure, trimming the general semigroup tree exactly at those nodes with no descendants with a given genus, in the first case, or with no descendants with a given Frobenius number, in the second case. We refined the parallelizing strategies and we overcame the previous limitation of the length of integers in the bitwise representation of the gap sequence and the seed sequence. We computed multiparameter decomposition of the numbers of semigroups of each Frobenius number up to $135$, the number of irreducible semigroups of Frobenius number up to $135$, and of the numbers of semigroups of each genus up to $80$.

We study a timetabling problem faced by Finnish universities, where the challenge is to balance the preferences of three key stakeholders: the university, teachers, and students. Educational timetabling is an essential task that ensures that everything runs effortlessly and collaboratively. Its efficiency significantly impacts the smooth operation of the institution's educational programs and its financial success. As universities have evolved and competition among them has intensified, the features of the university timetabling problem have changed. This paper describes an ongoing optimization project with three Finnish universities and a leading provider of educational management systems for universities. The main goal of this cooperation is not merely to streamline the creation of timetables, but to enable an entirely new approach to manage the entire planning process. The project consists of three six-month phases: the feasibility study, the preparation phase, and the implementation. During the feasibility study, several research-related gaps and novel practical goals were identified. To address these gaps and goals, this paper presents a unique CRONOPT model for tackling three targets simultaneously: effective use of university resources, teacher workload and well-being, and smooth progression of students' studies. The optimization solution developed through the project integrates directly with the market-leading educational management system for Finnish universities.

Autocatalytic subnetworks govern sustained production and balanced growth in chemical reaction systems and can be naturally represented as directed multihypergraphs that jointly encode stoichiometric structure and reaction kinetics. Existing optimization approaches identify such subnetworks by maximizing their structural amplification, typically measured through the Maximum Amplification Factor (MAF). However, structural amplification alone does not determine growth potential, since highly amplifying subnetworks may be kinetically inefficient. Motivated by recent kinetic–stoichiometric bounds on balanced growth under scalable dynamics, we study the problem of selecting the autocatalytic subnetwork maximizing the growth bound $(\alpha^*-1)\|\mathbb{S}|_{\mathcal A'}\|_\kappa$, where $\alpha^*$ is the MAF and $\|\mathbb{S}|_{\mathcal A'}\|_\kappa$ is a kinetic consumption norm. We formulate the problem as a mixed-integer bilinear optimization model combining hypergraph selection with generalized fractional amplification constraints. Exploiting the discrete structure of the kinetic norm, we develop an exact parametric algorithm in which each subproblem reduces to MAF maximization and is solved through a Dinkelbach-type generalized fractional programming method. Finite convergence and global optimality are established. Applications to the Oregonator, the formose reaction, carbon-fixation cycles, and synthetic benchmark networks show when maximizing the kinetic–stoichiometric bound differs from maximizing the MAF alone, revealing the interplay between stoichiometric amplification, reaction kinetics, and balanced growth. The proposed framework provides an exact optimization methodology for identifying reaction subnetworks with the highest theoretical growth potential.

Employing the techniques of transporting a factorization system from one category to another via an adjunction, developed in our earlier papers, a factorization system is related to a radical on a homological category.

In this paper, by the method of comparing coefficients, we establish a new generating function of multivariable Al-Salam-Carlitz polynomials which contains both Rogers' and Bowman's symmetirc expansion formulas and the classical $q$-Mehler formula as special cases. Some new $q$-series identities related to the multivariable Al-Salam-Carlitz polynomials are also presented.

We study local derivations on a Block-type Lie algebra \(\mathcal B\). Using the structure of the derivation algebra of \(\mathcal B\) and a series of normalizations and coefficient comparisons, we prove that every local derivation on \(\mathcal B\) is a derivation.