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The wheels of decelerating vehicles in braking mode roll with increased slip, up to complete lock-up, which is a negative phenomenon. This is effectively managed by the anti-lock braking system (ABS). However, in the course of braking, especially before the system activation, self-excited oscillatory processes with high amplitudes may occur, causing increased dynamic loads on the drive system. The paper studies the braking processes of a vehicle with an electromechanical individual traction drive in both electrodynamic regenerative and combined braking modes, utilizing the drive and the primary braking system. The theoretical framework is provided for identifying the self-excited oscillation onset conditions and developing a technique to detect wheel slips during braking to suppress these oscillations. To check the functionality of the wheel-slip observer in braking mode, the performance of the self-excited oscillation pulse suppression algorithm was studied in the MATLAB Simulink 2018b software package. The study results can be used to develop control systems equipped with the function of suppressing self-excited oscillations by vehicle motion. [ABSTRACT FROM AUTHOR]

We study the n$n$‐point differentials corresponding to Kadomtsev–Petviashvili (KP) tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their ℏ2$\hbar ^2$‐deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov–Scherbin partition functions that do satisfy the natural analytic assumptions, and for these families, we prove in addition the so‐called projection property and thus the full statement of the Chekhov–Eynard–Orantin topological recursion. A particular feature of our argument is that it clarifies completely the role of ℏ2$\hbar ^2$‐deformations of the Orlov–Scherbin parameters for the partition functions, whose necessity was known from a variety of earlier obtained results in this direction but never properly understood in the context of topological recursion. As special cases of the results of this paper, one recovers new and uniform proofs of the topological recursion to all previously studied cases of enumerative problems related to weighted double Hurwitz numbers. By virtue of topological recursion and the Grothendieck–Riemann–Roch formula, this, in turn, gives new and uniform proofs of almost all Ekedahl–Lando–Shapiro–Vainshtein (ELSV)‐type formulas discussed in the literature. [ABSTRACT FROM AUTHOR]

We develop the deformation theory of cohomological field theories (in short, CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion of a CohFT: homotopy (necessary algebraic toolkit to develop chain-level Gromov–Witten invariants) and quantum (with examples found in the works of Buryak and Rossi on integrable systems). The universal group of symmetries of morphisms of modular operads, based on Kontsevich's graph complex, is shown to be trivial. Using the tautological rings on moduli spaces of curves, we introduce a natural enrichment of Kontsevich's graph complex. This leads to universal groups of non-trivial symmetries of both homotopy and quantum CohFTs, which, in the latter case, is shown to contain both the prounipotent Grothendieck–Teichmüller group and the Givental group. [ABSTRACT FROM AUTHOR]

Auto-oscillations may occur in moving vehicles in the area where the tire interacts with the support base. The parameters of such oscillations depend on the sliding velocity in the contact patch. As they negatively affect the processes occurring in the electric drive and the mechanical transmission, reducing their energy efficiency, such processes can cause failures in various elements. This paper aims to conduct a theoretical study into the peculiarities of oscillatory processes in the nonlinear system and an experimental study of the auto-oscillation modes of an individual traction drive. It presents the theoretical basis used to analyze the peculiarities of oscillation processes, including their onset and course, the results of simulation mathematical modeling and the experimental studies into the oscillation phenomena in the movement of the vehicle towards the supporting base. The practical value of this study lies in the possibility to use the results in the development of algorithms for the exclusion of auto-oscillation phenomena in the development of vehicle control systems, as well as to use the auto-oscillation processes onset and course analysis methodology to design the electric drive of the driving wheels. [ABSTRACT FROM AUTHOR]

The paper describes the developed curvilinear motion simulation model for a vehicle with two traction electric motors moving on a solid surface used to study the dynamic properties of a wheeled vehicle and to subject the developed methods to virtual testing. The simulation model of the electric all-wheel drive vehicle is carried out in the Simcenter Amesim environment to account for the dynamic characteristics and features of the vehicle. The simulation model was developed based on the drawn requirements while the assumptions were justified. Inertia characteristics, tire characteristics, suspension elements, grip characteristics, and surface and air resistance were considered, as these factors affect the vehicle longitudinal and transverse dynamics. The article presents the model implemented in the "Labcar" system and confirms its adequacy by comparing it with the data obtained during the full-scale prototype tests. The bench and range tests of a test vehicle with electric transmission equipped with a measuring complex confirmed the adequacy of the developed model. The results of comparative tests allow for the conclusion that the developed model complex is suitable for modeling purposes, including studying, debugging and initial calibrations of the algorithm of torque distribution on the driving axles of all-wheel drive electric vehicle. [ABSTRACT FROM AUTHOR]

We study a duality for the n-point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for the duality between maps and fully simple maps observed by Borot and Garcia-Failde. Our approach allows to transfer the algebraicity properties between the systems of n-point functions related by this duality, and gives direct tools for the analysis of singularities. As an application, we give a proof of a recent conjecture of Borot and Garcia-Failde on topological recursion for fully simple maps. [ABSTRACT FROM AUTHOR]

In the classical Batalin–Vilkovisky formalism, the BV operator Δ is a differential operator of order two with respect to the commutative product. In the differential graded setting, it is known that if the BV operator is homotopically trivial, then there is a tree level cohomological field theory induced on the homology; this is a manifestation of the fact that the homotopy quotient of the operad of BV algebras by Δ is represented by the operad of hypercommutative algebras. In this paper, we study generalized Batalin–Vilkovisky algebras where the operator Δ is of the given finite order. In that case, we unravel a new interesting algebraic structure on the homology whenever Δ is homotopically trivial. We also suggest that the sequence of algebraic structures arising in the higher order formalism is a part of a "trinity" of remarkable mathematical objects, fitting the philosophy proposed by Arnold in the 1990s. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we construct the weighed sums which are given by Orlov's hypergeometric solutions of the 2-component BKP hierarchy. We derive the closed algebraic formulas for the correlation functions associated with these tau-functions, and under reasonable analytical assumptions we prove the loop equations (the blobbed topological recursion). Finally, we prove a version of topological recursion for the spin Hurwitz numbers with the spin completed cycles (a generalized version of the Giacchetto–Kramer–Lewański conjecture). [ABSTRACT FROM AUTHOR]

The Dubrovin–Zhang hierarchy is a Hamiltonian infinite-dimensional integrable system associated to a semi-simple cohomological field theory or, alternatively, to a semi-simple Dubrovin–Frobenius manifold. Under an extra assumption of homogeneity, Dubrovin and Zhang conjectured that there exists a second Poisson bracket that endows their hierarchy with a bi-Hamiltonian structure. More precisely, they gave a construction for the second bracket, but the polynomiality of its coefficients in the dispersion parameter expansion is yet to be proved. In this paper we use the bi-Hamiltonian recursion and a set of relations in the tautological rings of the moduli spaces of curves derived by Liu and Pandharipande in order to analyze the second Poisson bracket of Dubrovin and Zhang. We give a new proof of a theorem of Dubrovin and Zhang that the coefficients of the dispersion parameter expansion of the second bracket are rational functions with prescribed singularities. We also prove that all terms in the expansion of the second bracket in the dispersion parameter that cannot be realized by polynomials because they have negative degree do vanish, thus partly confirming the conjecture of Dubrovin and Zhang. [ABSTRACT FROM AUTHOR]

We propose a conjectural formula for DRg(a,-a)λg and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Guéré and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way. [ABSTRACT FROM AUTHOR]

We identify the formulas of Buryak and Okounkov for the |$n$| -point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous Witten conjecture/Kontsevich theorem, where the link between the intersection theory of the moduli spaces and integrable systems is established via the geometry of double ramification cycles. [ABSTRACT FROM AUTHOR]

We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support the conjecture. [ABSTRACT FROM AUTHOR]

We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2‐discs, framed little 2‐discs, and Deligne–Mumford compactifications of moduli spaces of genus zero curves with marked points. These operads exhibit all the remarkable algebraic and geometric features that their classical analogues possess; in particular, it is possible to define a noncommutative analogue of the notion of cohomological field theory with similar Givental‐type symmetries. This relies on rich geometry of the analogues of the Deligne–Mumford spaces, coming from the fact that they admit several equivalent interpretations: as the toric varieties of Loday's realisations of the associahedra, as the brick manifolds recently defined by Escobar, and as the De Concini–Procesi wonderful models for certain subspace arrangements. [ABSTRACT FROM AUTHOR]

We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants. [ABSTRACT FROM AUTHOR]

We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this problem. Then we consider the generalized case of four-colored maps and outline the idea of the proof of the corresponding spectral curve topological recursion. [ABSTRACT FROM AUTHOR]

We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with $$\psi $$ -classes are reproduced via the Chekhov-Eynard-Orantin topological recursion. As an application, we prove that the Johnson-Pandharipande-Tseng formula for the orbifold Hurwitz numbers is equivalent to the topological recursion for the orbifold Hurwitz numbers. In particular, this gives a new proof of the topological recursion for the orbifold Hurwitz numbers. [ABSTRACT FROM AUTHOR]

We construct the quantum curve for the Gromov--Witten theory of the complex projective line. [ABSTRACT FROM AUTHOR]

This article describes some technical issues regarding the adaptation of a production car to a platform for the development and testing of autonomous driving technologies. A universal approach to performing the reverse engineering of electric power steering (EPS) for the purpose of external control is also presented. The primary objective of the related study was to solve the problem associated with the precise prediction of the dynamic trajectory of an autonomous vehicle. This was accomplished by deriving a new equation for determining the lateral tire forces and adjusting some of the vehicle parameters under road test conductions. A Mivar expert system was also integrated into the control system of the experimental autonomous vehicle. The expert system was made more flexible and effective for the present application by the introduction of hybrid artificial intelligence with logical reasoning. The innovation offers a solution to the major problem of liability in the event of an autonomous transport vehicle being involved in a collision. [ABSTRACT FROM AUTHOR]

We study the set of solutions (ωg,n)g⩾0,n⩾1 of abstract loop equations. We prove that ωg,n is determined by its purely holomorphic part: this results in a decomposition that we call “blobbed topological recursion”. This is a generalisation of the theory of the topological recursion, in which the initial data (ω0,1, ω0,2) is enriched by non-zero symmetric holomorphic forms in n variables (φg,n)2g−2+n>0. In particular, we establish for any solution of abstract loop equations: (1) a graphical representation of ωg,n in terms of φg,n; (2) a graphical representation of ωg,n in terms of intersection numbers on the moduli space of curves; (3) variational formulas under infinitesimal transformation of φg,n; (4) a definition for the free energies ωg,0 = Fg respecting the variational formulas. We discuss in detail the application to the multi-trace matrix model and enumeration of stuffed maps. [ABSTRACT FROM AUTHOR]

describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus g curves with n marked points. [ABSTRACT FROM AUTHOR]

We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the Korteweg-de Vries case, we obtain that BHpd(F,d1, d2) is isomorphic to R for (p,d)=(0,0), to C8(R) for (p,d)=(1,1), (2,1), (2,3), (3,3), and vanishes otherwise. [ABSTRACT FROM AUTHOR]

Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular, this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups. [ABSTRACT FROM AUTHOR]

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition. [ABSTRACT FROM AUTHOR]

Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy. [ABSTRACT FROM AUTHOR]

In this note, we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux–Egoroff system. As an application, we explain how Shramchenko’s deformations of Frobenius manifold structures on Hurwitz spaces fit into the general formalism of Givental–van de Leur twisted loop group action on the space of semi-simple Frobenius manifolds. [ABSTRACT FROM AUTHOR]