Miracle-dz/UniFAR-FTUs huggingface dataset:
Correspondences, Ultraproducts and Model Theory

We study correspondences of tracial von Neumann algebras from the model-theoretic point of view. We introduce and study an ultraproduct of correspondences and use this ultraproduct to prove, for a fixed pair of tracial von Neumann algebras M and N, that the class of M-N correspondences forms an elementary class. We prove that the corresponding theory is classifiable, all of its completions are stable, that these completions have quantifier elimination in an appropriate language, and that one of these completions is in fact the model companion. We also show that the class of triples (M, H, N), where M and N are tracial von Neumann algebras and H is an M-N correspondence, form an elementary class. As an application of our framework, we show that a II_1 factor M has property (T) precisely when the set of central vectors form a definable set relative to the theory of M-M correspondences. We then use our approach to give a simpler proof that the class of structures (M, Phi), where M is a sigma-finite von Neumann algebra and Phi is a faithful normal state, forms an elementary class. Finally, we initiate the study of a family of Connes-type ultraproducts on C*-algebras.
Peripheral structures of relatively hyperbolic groups

In this paper, we introduce and characterize a class of parabolically extended structures for relatively hyperbolic groups. A characterization of relative quasiconvexity with respect to parabolically extended structures is obtained using dynamical methods. Some applications are discussed. The class of groups acting geometrically finitely on Floyd boundaries turns out to be easily understood. However, we also show that Dunwoody's inaccessible group does not act geometrically finitely on its Floyd boundary.
On the formation of shocks of electromagnetic plane waves in non-linear crystals

An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global $C^2$-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density, assuming no dispersion.
Proper Weak Regular Splitting and its Application to Convergence of Alternating Iterations

The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular matrices. Secondly, we propose an alternating iterative method for solving rectangular linear systems by using the Moore-Penrose inverse and discuss its convergence theory, by extending the work of Benzi and Szyld Numererische Mathematik 76 (1997) 309-321; MR1452511]. Furthermore, a comparison result is obtained which insures faster convergence rate of the proposed alternating iterative scheme.
Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations

Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) are formulated and studied. A general duality principle is established for linear backward stochastic integral equation and linear stochastic Fredholm-Volterra integral equation with mean-field. With the help of such a duality principle, together with some other new delicate and subtle skills, Pontryagin type maximum principles are proved for two optimal control problems of FBSVIEs.
Exact Lagrangian Fillings of Legendrian $(2,n)$ torus links

For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and K\'alm\'an constructed $C_n$ exact Lagrangian fillings, where $C_n$ is the $n$-th Catalan number. We show that these exact Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy. To do that, we compute the augmentations induced by the exact Lagrangian fillings $L$ to $\mathbb{Z}_2[H_1(L)]$ and distinguish the resulting augmentations.
A gradient system with a wiggly energy and relaxed EDP-convergence

For gradient systems depending on a microstructure, it is desirable to derive a macroscopic gradient structure describing the effective behavior of the microscopic scale on the macroscopic evolution. We introduce a notion of evolutionary Gamma-convergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gamma-convergence. This new notion generalizes the concept of EDP-convergence, which was introduced in [26], and is now called relaxed EDP-convergence. Both notions are based on De Giorgi’s energy-dissipation principle (EDP), however the special structure of the dissipation functional in terms of the primal and dual dissipation potential is, in general, not preserved under Gamma-convergence. By using suitable tiltings we study the kinetic relation directly and, thus, are able to derive a unique macroscopic dissipation potential. The wiggly-energy model of Abeyaratne-Chu-James (1996) serves as a prototypical example where this nontrivial limit passage can be fully analyzed.
Carbon nanotubes and liquid crystalline phases

This paper presents a review of the literature that deals with carbon nanotubes (CNTs) and liquid crystals (LCs) focusing on two main aspects. First, we describe the liquid crystalline behaviour of carbon nanotubes in solution. Via functionalization or absorption of amphiphilic molecules, CNTs can form nematic phases in water for concentrations above a few percents. Second, we explore the work done on the insertion of CNTs into thermotropic or lyotropic LCs. It is shown that it is possible to disperse small quantities of CNTs in various LC matrices and that the CNTs are responding to the LC director field. In some cases the CNTs are also strongly modifying the LC properties. These promising results indicate that carbon nanotubes and liquid crystals will certainly play an important role in the development of future applications and functional materials.
Two-eigenfunction correlation in a multifractal metal and insulator

We consider the correlation of two single-particle probability densities $|\Psi_{E}({\bf r})|^{2}$ at coinciding points ${\bf r}$ as a function of the energy separation $\omega=|E-E'|$ for disordered tight-binding lattice models (the Anderson models) and certain random matrix ensembles. We focus on the models in the parameter range where they are close but not exactly at the Anderson localization transition. We show that even far away from the critical point the eigenfunction correlation show the remnant of multifractality which is characteristic of the critical states. By a combination of the numerical results on the Anderson model and analytical and numerical results for the relevant random matrix theories we were able to identify the Gaussian random matrix ensembles that describe the multifractal features in the metal and insulator phases. In particular those random matrix ensembles describe new phenomena of eigenfunction correlation we discovered from simulations on the Anderson model. These are the eigenfunction mutual avoiding at large energy separations and the logarithmic enhancement of eigenfunction correlations at small energy separations in the two-dimensional (2D) and the three-dimensional (3D) Anderson insulator. For both phenomena a simple and general physical picture is suggested.
A fibered description of the vector‐valued spectrum

For Banach spaces X and Y we study the vector‐valued spectrum M∞(BX,BY) , that is the set of non null algebra homomorphisms from H∞(BX) to H∞BY , which is naturally projected onto the closed unit ball of H∞(BY,X∗∗) . The aim of this article is to describe the fibers defined by this projection, searching for analytic balls and considering Gleason parts.
Current aspects on the selection of patients who are candidates for lung transplantation

Currently, the main indications for lung transplantation worldwide are chronic obstructive pulmonary disease (COPD), pulmonary fibrosis, cystic fibrosis, alpha-1-antitrypsin (alpha-1) deficiency, idiopathic pulmonary arterial hypertension, bronchiectasis, retransplantation, sarcoidosis and severe lung injury caused by COVID-19, and these candidates must demonstrate knowledge regarding the procedure, good adherence to the medical treatment performed, adequate psychosocial structure and family support. Furthermore, the proper assessment of contraindications contributes to a lower occurrence of unfavorable clinical outcomes unrelated to the graft, benefiting patients with a greater chance of success and, thus, improving overall survival with treatment. Among the absolute contraindications, lung cancer, cardiac dysfunction unrelated to lung disease, significant organic dysfunction of any other noble organ, hepatitis B and C virus infections, active pulmonary tuberculosis and severe rib cage deformity stand out. Furthermore, among the relative contraindications, there is age over 65 years, severe clinical instability, HIV infection, obesity, severe osteoporosis and decompensated systemic diseases. nutritional status despite supplementation; pneumothorax; and/or life-threatening hemoptysis not controlled with embolization. Patients should be included in the list when there is at least one of the following criteria: chronic respiratory failure (PaCO 2 > 50 mmHg and/or PaO 2 < 60 mmHg); need for non-invasive ventilation; pulmonary hypertension; frequent hospital admissions; rapid decline in lung function; and functional class IV according to the World Health Organization. In patients with bronchiectasis secondary to cystic fibrosis, two factors must be observed: pancreatopathy, both endocrine and exocrine, which also influences the choice of immunosuppressant (tacrolimus is more pancreatotoxic than cyclosporine) and chronic sinusopathy, since colonization upper airway is a frequent cause of pulmonary infection after transplantation (post-transplant sinusectomy is quite common) (Weil et al., 2015; Higemura et al., 2022; Reynaud-Gaubert et al., 2018); Patients should be referred for evaluation when there is:
Non-left-orderable 3-manifold groups

We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of S 3 branched along links. The ﬁgure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of S 3 branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the 5 2 knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.
Exit laws from large balls of (an)isotropic random walks in random environment

We study exit laws from large balls in Zd, d≥3, of random walks in an i.i. d. random environment that is a small perturbation of the environment corresponding to simple random walk. Under a centering condition on the measure governing the environment, we prove that the exit laws are close to those of a symmetric random walk, which we identify as a perturbed simple random walk. We obtain bounds on total variation distances as well as local results comparing exit probabilities on boundary segments. As an application, we prove transience of the random walks in random environment. Our work includes the results on isotropic random walks in random environment of Bolthausen and Zeitouni [Probab. Theory Related Fields 138 (2007) 581–645]. Since several proofs in Bolthausen and Zeitouni (2007) were incomplete, a somewhat different approach was given in the first author’s thesis [Long-time behavior of random walks in random environment (2013) Zurich Univ.]. Here, we extend this approach to certain anisotropic walks and provide a further step towards a fully perturbative theory of random walks in random environment.
Photometric superoutburst observations of the short-period dwarf nova TV Corvi

We present photometric observations of the short-period dwarf nova TV Corvi during a superoutburst in 1994 June. Our high-speed photometric observations cover six nights and show well-defined superhumps. Using our measured superhump period, we confirm TV CrY as a short-period dwarf nova, with a likely orbital period of 1.50 h. Assuming that the cause of the superhumps is a 3 : 1 tidal resonance, theory allows a mass ratio of q = 0.22 to be predicted. This in turn provides mass estimates for the two components of Ml =0.52 Mo and M z =0.12 Mo' Assigning TV CrY a probable absolute magnitude based on current work on faint, large outburst amplitude dwarf novae, we find a distance of 350 pc.
Orbitally stable standing waves for the asymptotically linear one-dimensional NLS

In this article we study the one-dimensional, asymptotically linear, non-linear Schr\"odinger equation (NLS). We show the existence of a global smooth curve of standing waves for this problem, and we prove that these standing waves are orbitally stable. As far as we know, this is the first rigorous stability result for the asymptotically linear NLS. We also discuss an application of our results to self-focusing waveguides with a saturable refractive index.
The geometry of some generalized affine Springer fibers

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible components of such varieties for a reductive group $G$ to certain weight multiplicities defined by the Langlands dual group $\hat{G}$. We prove our conjecture in the case of unramified conjugacy class.
WELL-POSEDNESS OF A PHASE TRANSITION MODEL WITH THE POSSIBILITY OF VOIDS

The paper deals with a phase transition model applied to a two-phase system. There is a wide literature on the study of phase transition processes in case that no voids nor overlapping can occur between the two phases. The main novelty of our approach is the possibility of having voids during the phase change. This aspect is described in the model by the mass balance equation whose effects are included by means of the pressure of the system in the dynamical relations. The state variables are the absolute temperature (whose evolution is ruled by the entropy balance equation), the strain tensor (satisfying a quasi-static macroscopic equation of motion), and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to the microscopic motions). Well-posedness of the initial-boundary value problem associated to the PDEs system resulting from this model is proved.
On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties

In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a special case. Particularly, in the Euclidean signature this classification turns out be really simple. Then it is shown that the integrability condition of maximally isotropic distributions can be described in terms of the invariance of certain subbundles under the action of these operators. Here it is also proved a new generalization of the Goldberg-Sachs theorem, valid in all even dimensions, stating that the existence of an integrable maximally isotropic distribution imposes restrictions on the optical matrix. Also the higher-dimensional versions of the self-dual manifolds are investigated. These topics can shed light on the integrability of Einstein's equation in higher dimensions.
Intertwining operators of the quantum Teichmüller space

In arXiv:0707.2151 the authors introduced the theory of local representations of the quantum Teichm\"uller space $\mathcal{T}^q_S$ ($q$ being a fixed primitive $N$-th root of $(-1)^{N + 1}$) and they studied the behaviour of the intertwining operators in this theory. One of the main results [Theorem 20, arXiv:0707.2151] was the possibility to select one distinguished operator (up to scalar multiplication) for every choice of a surface $S$, ideal triangulations $\lambda, \lambda'$ and isomorphic local representations $\rho, \rho'$, requiring that the whole family of operators verifies certain Fusion and Composition properties. By analyzing the constructions of arXiv:0707.2151, we found a difficulty that we eventually fix by a slightly weaker (but actually optimal) selection procedure. In fact, for every choice of a surface $S$, ideal triangulations $\lambda, \lambda'$ and isomorphic local representations $\rho, \rho'$, we select a finite set of intertwining operators, naturally endowed with a structure of affine space over $H_1(S;\mathbb{Z}_N)$ ($\mathbb{Z}_N$ is the cyclic group of order $N$), in such a way that the whole family of operators verifies augmented Fusion and Composition properties, which incorporate the explicit behavior of the $\mathbb{Z}_N$-actions with respect to such properties. Moreover, this family is minimal among the collections of operators verifying the "weak" Fusion and Composition rules (in practice the ones considered in arXiv:0707.2151). In addition, we adapt the derivation of the invariants for pseudo-Anosov diffeomorphisms and their hyperbolic mapping tori made in arXiv:0707.2151 and arXiv:math/0407086 by using our distinguished family of intertwining operators.
The supersingular locus of unitary Shimura varieties with exotic good reduction

In this paper, we use a group-theoretic approach to give a concrete description of the geometric structure of the supersingular locus of unitary Shimura varieties with exotic good reduction. This approach also is a more uniform way to prove results of this form obtained previously by, for example, Vollaard-Wedhorn and Rapoport-Terstiege-Wilson.
Landweber–Kaczmarz for parameter identification in time-dependent inverse problems: all-at-once versus reduced version

In this study, we consider a general time-space system, whose model operator and observation operator are locally Lipschitz continuous, over a finite time horizon and parameter identification by using Landweber–Kaczmarz regularization. The problem is investigated in two different modeling settings: an all-at-once and a reduced version, together with two observation scenarios: continuous and discrete observations. Segmenting the time line into several subintervals leads to the idea of applying the Kaczmarz method. A loping strategy is incorporated into the method to yield the loping Landweber–Kaczmarz iteration.
On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on $\mathbb{R}^3$

We consider energy sub-critical defocusing nonlinear wave equations on R 3 and establish the existence of unique global solutions al- most surely with respect to a unit-scale randomization of the initial data on Euclidean space. In particular, we provide examples of initial data at super-critical regularities which lead to unique global solutions. The proof is based on probabilistic growth estimates for a new modied en-
The Mathematical Structure of the Second Law of Thermodynamics

The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose increase characterizes the possible state changes under adiabatic conditions. It is one of the few really fundamental physical laws (in the sense that no deviation, however tiny, is permitted) and its consequences are far reaching. This principle is independent of models, statistical mechanical or otherwise, and can be understood without recourse to Carnot cycles, ideal gases and other assumptions about such things as `heat', `temperature', `reversible processes', etc., as is usually done. Also the well known formula of statistical mechanics, S = -\sum p log p, is not needed for the derivation of the entropy principle. This contribution is partly a summary of our joint work (Physics Reports, Vol. 310, 1--96 (1999)) where the existence and uniqueness of S is proved to be a consequence of certain basic properties of the relation of adiabatic accessibility among equilibrium states. We also present some open problems and suggest directions for further study.
Differential Operators and Families of Automorphic Forms on Unitary Groups of Arbitrary Signature

In the 1970's, Serre exploited congruences between q-expansion coefficients of Eisenstein series to produce p-adic families of Eisenstein series and, in turn, p-adic zeta functions. Partly through integration with more recent machinery, including Katz's approach to p-adic differential operators, his strategy has influenced four decades of developments. Prior papers employing Katz's and Serre's ideas exploiting differential operators and congruences to produce families of automorphic forms rely crucially on q-expansions of automorphic forms. The overarching goal of the present paper is to adapt the strategy to automorphic forms on unitary groups, which lack q-expansions when the signature is of the form (a,b), a≠b. In particular, this paper completely removes the restrictions on the signature present in prior work. As intermediate steps, we achieve two key objectives. First, partly by carefully analyzing the action of the Young symmetrizer on Serre-Tate expansions, we explicitly describe the action of differential operators on the Serre-Tate expansions of automorphic forms on unitary groups of arbitrary signature. As a direct consequence, for each unitary group, we obtain congruences and families analogous to those studied by Katz and Serre. Second, via a novel lifting argument, we construct a p-adic measure taking values in the space of p-adic automorphic forms on unitary groups of any prescribed signature. We relate the values of this measure to an explicit p-adic family of Eisenstein series. One application of our results is to the recently completed construction of p-adic L-functions for unitary groups by the first named author, Harris, Li, and Skinner.
Flux modelling in the finite-volume lattice Boltzmann approach

In this article, a novel approach for flux treatment is presented in conjunction with cell-centred Finite-Volume Lattice Boltzmann Method (FVLBM). The distribution functions are determined by using a pressure-based flux weighting factor on a D2Q9 lattice. A consistent open and solid boundary treatment is also addressed, which resulted in a wider domain of stability and faster convergence. For time discretisation, a fifth-order Runge–Kutta algorithm was applied. An in-house FORTRAN code has been written by the authors which uses the time-marching along with FVLBM. Two test cases, namely, flow over a backward-facing step and around a circular cylinder are carried out. The results are compared with the available solutions in which favourable agreement was observed.