In this paper, we study semiconic idempotent commutative residuated lattices. After giving some properties of such residuated lattices, we obtain a structure theorem for semiconic idempotent com- mutative residuated lattices. As an application, we make use of the structure theorem to prove that the variety of strongly semiconic idempotent commutative residuated lattices has the amalgamation property.

Polarons, quasiparticles resulting from the interaction between an impurity and the collective excitations of a medium, play a fundamental role in physics, mainly because they represent an essential building block for understanding more complex many-body phenomena. In this manuscript, we study the spectral properties of a single impurity mixed with identical bosons in a one-dimensional lattice with power-law hopping. In particular, based on the so-called T-matrix approximation, we show the existence of well-defined quasiparticle branches for several tunneling ranges and for both, repulsive and attractive impurity-boson interactions. Furthermore, we demonstrate the persistence of the attractive polaron branch when the impurity-boson bound state is absorbed into the two-body continuum and that the attractive polaron becomes more robust as the range of the hopping increases. The results discussed here are of relevance for the understanding of the equilibrium properties of quantum systems with power-law interactions.

In this paper, we gave an attack on RSA when Euler function has small multiplicative inverse modulo "e" and the prime sum p+q is of the form p+q=2^nk_0+k_1 where n is a given positive integer and k_0 and k_1 are two suitably small unknown integers using sublattice reduction techniques and Coppersmith's methods for finding small roots of modular polynomial equations. When we compare this method with an approach using lattice based techniques, this procedure slightly improves the bound and reduces the lattice dimension.

A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi bound (or resonance) states. When the system is prepared in one of such quasi bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and because of quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.

Two representable substructural logics ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ are logics for finite UL and IUL-algebras, respectively. In this paper, the standard completeness of ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ is proved by the method developed by Jenei, Montagna, Esteva, Gispert, Godo and Wang. This shows that ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ are substructural fuzzy logics.

Practical entanglement distillation is a critical component in quantum information theory. Entanglement distillation is often utilized for designing quantum computer networks and quantum repeaters. The practical entanglement distillation problem is formulated as a bilevel optimization problem. A fuzzy formulation is introduced to estimate the quantum state (density matrix) from pseudo-likelihood functions (i.e., quantum state tomography). A scale-independent relationship between fuzzy relations in terms of the pseudo-likelihood functions is obtained. The entanglement distillation optimization problem was solved using the combined coupled map lattice and dual annealing approach. Comparative analysis of the results is then conducted against a standard dual annealing algorithmic implementation.

The osseointegration process in and around additively manufactured (AM) lattice structures of a new titanium alloy, Ti–19Nb–14Zr, was evaluated. Three different implants, including lattices with increasing high sidewalls gradually closing them, were designed, manufactured and implanted in the tibia and metatarsal bone of two sheep for twelve weeks. After removal, they were characterized with X-ray computed tomography (XCT). The 3D XCT images were segmented using machine learning. The bone-interface implant (BII) and bone-implant contact (BIC) were studied. The results show that, since AM naturally leads to high roughness surface finish, the wettability of the implant is increased. The new alloy possesses an increased affinity to the bone enhancing the quality of osseointegration. The lattice provides crevices, in which the biological tissue can jump in and cling. The combination of these factors is pushing ossification beyond its natural limits. Therefore, the quality and speed of the ossification and osseointegration in and around these Ti–19Nb–14Zr AM laterally closed lattice implants open the possibility of bone spline key of prostheses. This enables the stabilization of the implant into the bone while keeping the possibility of punctual hooks allowing the implant to be removed more easily if required.

Information-related measures are useful tools for multi-variable data analysis, as measures of dependence among variables, and as descriptions of order and disorder in biological and physical systems. Measures, like marginal entropies, mutual / interaction / multi -information, have long been used in a number of fields including descriptions of systems complexity and biological data analysis. The mathematical relationships among these measures are therefore of significant inherent interest. Relations between common information measures include the duality relations based on Möbius inversion on lattices. These are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). While these relationships are of significant interest there has been, to our knowledge, no systematic examination of the full range of relationships of this diverse range of functions into a unifying formalism as we do here. In this paper we define operators on functions on these lattices based on the Möbius inversions that map functions into one another (Möbius operators). We show that these operators form a simple group isomorphic to the symmetric group S₃. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is naturally generalized which yields extensive new relationships. This formalism now provides a fundamental unification of information-related measures, and the isomorphism of all distributive lattices with the subset lattice implies an even broader application of these results.

This paper presents results of the magnetic dynamics study (the microwave power absorptions at the fixed frequencies, during magnetic field sweeping) in samples of Y3Fe5O12 single crystals in the form of plates and spheres of various sizes, at frequencies exceeding 30 GHz, in magnetic fields up to 18 kOe, at room temperature and T=77 K. It was found, that in this case, the inhomogeneity’s of the magnetic state manifested itself in the Y3Fe5O12 samples in as 2D local phase separation regions. These 2D phase separation regions formed inside domain walls representing superlattices with size’s 700 – 900 Å. Landau diamagnetism or de Haas van Alphen oscillations observed in the 2D phase separation regions at room temperature and T=77 K, depending on the shape and size of the studied plates and spheres.

The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.