Scholarly Publications - Mathematics
Permanent URI for this collectionhttps://hdl.handle.net/11693/115503
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Item Embargo Enhancing energy recovery in automotive suspension systems by utilizing time-delay(Pergamon-Elsevier Science Ltd., 2024-08-01) Wu, Kaiwei; Ren, Chuanbo; Atay, Mehmet FatihcanThis study introduces time-delay active control technology to with the aim of enhancing the system's energy harvesting potential and ride smoothness. The time-delay active suspension represents a nonlinear, multivariable system, and stability analysis in this context is intricate. The mainly challenge lies in effectively leveraging time delay to augment the system's energy collection potential while harmonizing the vehicle's ride comfort and energy efficiency. Addressing this issue, our study proposes enhancing the suspension's energy recovery capability through time-delay control. Initially, the impact of time-delay control parameters on energy collection ability under various operational conditions was analyzed, establishing that appropriate time-delay parameters can enhance energy harvesting capacity. Subsequently, to balance the relationship between vehicle comfort and energy efficiency, the research introduces a method for constructing an optimized objective function based on linear equivalent excitation, thereby quantifying the relationship between system time-domain vibrational response, time-delay control parameters, and external excitations. This approach enables the comprehensive optimization of the suspension system's comfort, safety, and energy efficiency. The control system's stability was analyzed using cluster treatment of characteristic roots method. Finally, simulations and experiments were conducted to evaluate the effectiveness of time-delay active across different scenarios, confirming the efficacy of the proposed control methodology.Item Open Access Stable functorial equivalence of blocks(Mathematical Sciences Publishers, 2024-02) Bouc, Serge; Yılmaz, DenizLet k be an algebraically closed field of characteristic p > 0, let R be a commutative ring and let F be an algebraically closed field of characteristic 0. We introduce the category F1 Rppk of stable diagonal p-permutation functors over R. We prove that the category F1 F ppk is semisimple and give a parametrization of its simple objects in terms of the simple diagonal p-permutation functors. We also introduce the notion of a stable functorial equivalence over R between blocks of finite groups. We prove that if G is a finite group and if b is a block idempotent of kG with an abelian defect group D and Frobenius inertial quotient E, then there exists a stable functorial equivalence over F between the pairs (G, b) and (D ⋊ E, 1)Item Embargo An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences(Academic Press, 2024-02) Kotsireas, Ilias; Mansour, Toufik; Yıldırım, GökhanWe introduce an algorithmic approach based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes In(000,021), In(100,021), In(110,021), In(102,021), In(100,012), In(011,201), In(011,210) and In(120,210). Then we use the kernel method, obtain generating functions of each class, and find enumerating formulas. Lin and Yan studied the classification of the Wilf-equivalences for inversion sequences avoiding pairs of length-three patterns and showed that there are 48 Wilf classes among 78 pairs. In this paper, we solve six open cases for such pattern classes. Moreover, we extend the algorithm to restricted growth sequences and apply it to several classes. In particular, we present explicit formulas for the generating functions of the restricted growth sequences that avoid either {12313,12323}, {12313,12323,12333}, or {123⋯ℓ1}.Item Embargo On functorial equivalence classes of blocks of finite groups(Elsevier BV * North-Holland, 2024-12) Yılmaz, DenizLet k be an algebraically closed field of characteristic p > 0 and let F be an algebraically closed field of characteristic 0. Recently, together with Bouc, we introduced the notion of functorial equivalences between blocks of finite groups and proved that given a p -group D , there is only a finite number of pairs ( G, b ) of a finite group G and a block b of kG with defect groups isomorphic to D , up to functorial equivalence over F. In this paper, we classify the functorial equivalence classes over F of blocks with cyclic defect groups and 2 -blocks of defects 2 and 3. In particular, we prove that for all these blocks, the functorial equivalence classes depend only on the fusion system of the block.Item Embargo Some special coprime actions and their consequences(Elsevier BV * North-Holland, 2024-12) Ercan, Gülin; Güloğlu, İsmail Ş.; Kızmaz, Muhammet Yasir; Revin, Danila O.Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup C G (A) is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.Item Embargo Semisimplicity of some deformations of the subgroup category and the biset category(Elsevier BV * North-Holland, 2024-06) Barker, Laurence; Öğüt, İsmail AlperenWe introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star product. For some deformations of the subgroup category, too, we prove a semisimplicity property. The method is to embed the deformations of the biset category into the more easily described deformations of the subgroup category.Item Open Access Nash equilibria for exchangeable team-against-team games, their mean-field limit, and the role of common randomness(Society for Industrial and Applied Mathematics, 2024-05-16) Sanjari, Sina; Saldı, Naci; Yüksel, SerdarWe study stochastic exchangeable games among a finite number of teams consisting of a large but finite number of decision makers as well as their mean-field limit with infinite number of decision makers in each team. For this class of games within static and dynamic settings, we introduce sets of randomized policies under various decentralized information structures with pri- vately independent or common randomness for decision makers within each team. (i) For a general class of exchangeable stochastic games with a finite number of decision makers, we first establish the existence of a Nash equilibrium under randomized policies (with common randomness) within each team that are exchangeable (but not necessarily symmetric, i.e., identical) among decision makers within each team. (ii) As the number of decision makers within each team goes to infinity (that is, for the mean-field limit game among teams), we show that a Nash equilibrium exists under randomized policies within each team that are independently randomized and symmetric among decision makers within each team (that is, there is no common randomness). (iii) Finally, we establish that a Nash equilibrium for a class of mean-field games among teams under independently randomized symmetric policies constitutes an approximate Nash equilibrium for the corresponding prelimit (exchangeable) game among teams with finite but large numbers of decision makers. (iv) We thus establish a rigor- ous connection between agent-based-modeling and team-against-team games, via the representative agents defining the game played in equilibrium, and we furthermore show that common randomness is not necessary for large team-against-team games, unlike the case with small-sized ones.Item Embargo The pointed p-groups on a block algebra(Elsevier Ltd., 2024-12) Barker, LaurenceA pointed p-group is a pointed group P gamma such that Pis a p-group. We parameterize the pointed p-groups on a group algebra or on a block algebra of a group algebra. This is equivalent to a parameterization of the isomorphism classes of indecomposable direct summands of the algebra as a bimodule with the group acting on the left and a p-subgroup acting on the right. The parameterization involves p-subgroups and irreducible characters of centralizers of p-subgroups.Item Open Access Conics on Barth-Bauer octics(Zhongguo Kexue Zazhishe / Science in China Press, 2024-04-23) Degtyarev, AlexWe analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane (ramified at a smooth sextic curve) that contains 8,910 smooth conics.Item Open Access Uncertainty principles in holomorphic function spaces on the unit ball(Cambridge University Press, 2024-03-10) Kaptanoǧlu, Hakkı TurgayOn all Bergman-Besov Hilbert spaces on the unit disk, we find self-adjoint weighted shift operators that are differential operators of half-order whose commutators are the identity, thereby obtaining uncertainty relations in these spaces. We also obtain joint average uncertainty relations for pairs of commuting tuples of operators on the same spaces defined on the unit ball. We further identify functions that yield equality in some uncertainty inequalities.Item Open Access Localisation of regularised and multiview support vector machine learning(MIT Press, 2024-12) Gheondea, Aurelian; Tilki, C.; Oates, ChrisWe prove some representer theorems for a localised version of a semisupervised, manifold regularised and multiview support vector machine learning problem introduced by H.Q. Minh, L. Bazzani, and V. Murino, Journal of Machine Learning Research, 17 (2016) 1-72, that involves operator valued positive semidefinite kernels and their reproducing kernel Hilbert spaces. The results concern general cases when convex or nonconvex loss functions and finite or infinite dimensional underlying Hilbert spaces are considered. We show that the general framework allows infinite dimensional Hilbert spaces and nonconvex loss functions for some special cases, in particular in case the loss functions are Gateaux differentiable. Detailed calculations are provided for the exponential least squares loss functions that lead to systems of partially nonlinear equations for which some Newton's approximation methods based on the interior point method can be used. Some numerical experiments are performed on a toy model that illustrate the tractability of the methods that we propose.Item Open Access Lines on K3-quartics via triangular sets(Springer, 2024-10-06) Degtyarev, Alex; Rams, SlawomirWe prove the sharp upper bound of at most 52 lines on a complex K3-surface of degree 4 with a non-empty singular locus. We also classify the configurations of more than 48 lines on smooth complex quartics.Item Open Access Slopes and concordance of links(Mathematical Sciences Publishers, 2024-04-12) Degtyarev, Alex; Florens, V.; Lecuona, A. G.The slope is an isotopy invariant of colored links with a distinguished component, initially introducedby the authors to describe an extra correction term in the computation of the signature of the splice. Itappeared to be closely related to several classical invariants, such as the Conway potential function or theKojima –function (defined for two-components links). We prove that the slope is invariant under coloredconcordance of links. Besides, we present a formula to compute the slope in terms of C –complexes andgeneralized Seifert forms.Item Open Access The method of Mn-extension: the KdV equation(Elsevier BV, 2025-01-07) Gürses, Metin; Pekcan, AslıIn this work we generalize M2-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M3-extensions of the KdV equation and their recursion operators. We give a compact form of Mn-extension of the KdV equation and recursion operator of the coupled KdV system. The method of Mn-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M3-extension of KdV.Item Open Access A note on blocks of finite groups with TI Sylow p-subgroups(Springer, 2024-03-07) Yılmaz, DenizLet F be an algebraically closed field of characteristic zero. We prove that functorial equivalence over F and perfect isometry between blocks of finite groups do not imply each other.Item Open Access On Sawada-Kotera and Kaup-Kuperschmidt integrable systems(Institute of Physics Publishing Ltd., 2024-11-15) Gürses, Metin; Pekcan, A.To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other methods that are based on integrable scalar nonlinear partial differential equations. We show that some systems of integrable equations published recently are the 2-extension of integrable such scalar equations. For illustration, we give Korteweg–de Vries, Kaup-Kupershmidt, and SawadaKotera equations as examples. By the use of such an extension of integrable scalar equations, we obtain some new integrable systems with recursion operators. We also give the soliton solutions of the systems and integrable standard nonlocal and shifted nonlocal reductions of these systems.Item Open Access LHS-spectral sequences for regular extensions of categories(Springer, 2024-01-20) Yalçın, ErgünIn (Xu, J Pure Appl Algebra 212:2555-2569, 2008), a LHS-spectral sequence for target regular extensions of small categories is constructed. We extend this construction to ext-groups and construct a similar spectral sequence for source regular extensions (with right module coefficients). As a special case of these LHS-spectral sequences, we obtain three different versions of Slominska's spectral sequence for the cohomology of regular EI-categories. We show that many well-known spectral sequences related to the homology decompositions of finite groups, centric linking systems, and the orbit category of fusion systems can be obtained as the LHS-spectral sequence of an extension.Item Embargo Frobenius and commutative pseudomonoids in the bicategory of spans(Elsevier BV * North-Holland, 2024-09-04) Contreras, I.; Mehta, R. A.; Stern, Walker H.In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar characterization for the analogous coherent structures in the bicategory of spans of sets. We show that commutative and Frobenius pseudomonoids in Span correspond, respectively, to paracyclic sets and - sets satisfying the 2-Segal conditions. These results connect closely with work of the third author on A∞ algebras in ∞-categories of spans, as well as the growing body of work on higher Segal objects. Because our motivation comes from symplectic geometry and topological field theory, we emphasize the direct and computational nature of the classifications and their proofs.Item Open Access Angle between two complex lines(Aracne Editrice, 2024) Koca, Caner; Sertoz, Ali SinanThe chordal distance function on a complex projective space algebraically definesan angle between any two complex lines, which is known as the Hermitian angle. In thisexpository paper, we show that one can canonically construct a real line corresponding to eachof these complex lines so that the real angle between these two real lines exactly agrees withthe Hermitian angle between the complex lines. This way, the Hermitian angle is interpretedas a real angle, and some well known results pertaining Hermitian angles are proved usingreal geometry. As an example, we give a direct and elementary proof that the chordal distancefunction satisfies the triangle inequalityItem Embargo Chaos in gene regulatory networks: effects of time delays and interaction structure(AIP Publishing LLC, 2024-03-01) Öztürk, Dilan; Atay, Fatihcan; Özbay, HitayIn biological system models, gene expression levels are typically described by regulatory feedback mechanisms. Many studies of gene network models focus on dynamical interactions between components, but often overlook time delays. Here we present an extended model for gene regulatory networks with time delayed negative feedback, which is described by delay differential equations. We analyze nonlinear properties of the model in terms of chaos and compare the conditions with the benchmark homogeneous gene regulatory network model. Chaotic dynamics depend strongly on the inclusion of time delays, but the minimum motifs that show chaos differ when both original and extended models are considered. Our results suggest that, for a particular higher order extension of the gene network, it is possible to observe chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of modification of the original benchmark model induced by previously unmodeled dynamics. We argue that the inclusion of additional parameters in regulatory gene circuit models substantially enhances the likelihood of observing non-periodic dynamics.