Narrow Results

We consider a Schrödinger operator with a Hermitian $2\times 2$ matrix-valued potential which is lattice-periodic and can be diagonalized smoothly on the whole ${ℝ}^n.$ In the case of the potential taking its minimum only on the lattice, we prove that the well-known semiclassical asymptotics of the first band spectrum for a scalar potential remains valid for our model.

Multi-source Weber problem (MWP) is an important model in facility location, which has wide applications in various areas such as health service management, transportation system management, urban planning, etc. The location-allocation algorithm is a well-known method for solving MWP, which consists of a location phase and an allocation phase at each iteration. In this paper, we consider more general and practical case of MWP–the constrained multi-source location problem (CMSLP), i.e., the location of multiple facilities with considering interactive transportation between facilities, locational constraints on facilities and the gauge for measuring distances. A variational inequality approach is contributed to solving the location subproblem called the constrained multi-facility location problem (CMFLP) in location phase, which leads to an efficient projection-type method. Then a new location-allocation algorithm is developed for CMSLP. Global convergence of the projection-type method as well as local convergence of new location-allocation algorithm are proved. The efficiency of proposed methods is verified by some preliminary numerical results.

Field theoretic models possessing a global internal fermionic shift symmetry are considered. When such a symmetry is realized locally, spin-3/2 fields appear naturally as gauge fields. Implementation of the gauging procedure requires not only the usual replacement of ordinary derivatives by covariant derivatives containing the spin-3/2 fields, but also the inclusion of additional monomials. The Higgs mechanism and the high energy Nambu–Goldstone fermion equivalence theorem are explicitly demonstrated.

The relationship between local Weyl scaling invariant models and local dilatation invariant actions is critically scrutinized. While actions invariant under local Weyl scalings can be constructed in a straightforward manner, actions invariant under local dilatation transformations can only be achieved in a very restrictive case. The invariant couplings of matter fields to an Abelian vector field carrying a nontrivial scaling weight can be easily built, but an invariant Abelian vector kinetic term can only be realized when the local scale symmetry is spontaneously broken.

Utilizing the gauge framework, software under development at Baylor University, we explicitly construct all layer 1 weakly coupled free fermionic heterotic string (WCFFHS) gauge models up to order 32 in four to ten large spacetime dimensions. These gauge models are well suited to large scale systematic surveys and, while they offer little phenomenologically, are useful for understanding the structure of the WCFFHS region of the string landscape. Herein, we present the gauge groups statistics for this swath of the landscape for both supersymmetric and non-supersymmetric models.

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

We discuss a question whether the observed Weinberg angle and Higgs mass are calculable in the formalism based on a construction in which the electroweak gauge group $SU(2)\times U{(1)}_Y$ is embedded in the graded Lie group $SU(2/1)$. Here, we follow original works of Ne’eman and Fairlie believing that bosonic fields take their values in the Lie superalgebra and fermionic fields take their values in its representation space. At the same time, our approach differs significantly. The main one is that while for them the gauge symmetry group is $SU(2/1)$, here we consider only symmetries generated by its even subgroup, i.e. symmetries of the standard electroweak model. The reason is that such formalism fixes the quartic Higgs coupling and at the same time removes the sign and statistics problems. The main result is that the presented model predicts values of the Weinberg angle and the Higgs mass correctly up to the two-loop level. Moreover, the model sets the unification scale coinciding with the electroweak scale and automatically describes the fermions correctly with the correct quark and lepton charges.

We argue that it is the effect of non-commutative geometry of spacetime that leads to the generation of mass, thus pleasingly complementing earlier results.

The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper bound is given in cases relevant for applications such as varieties of matrix product states and projected entangled pairs states. We provide a range (the “supercritical range”) of the parameters where the upper bound is sharp.

A comprehensive review of applying Taguchi’s optimization methodology to medical facilities was evaluated in this study. Taguchi’s optimization methodology is one kind of robust designation and is reputed for integrating multiple factors to pursue one goal. According to Taguchi’s suggestion, the efficient and reliable arrangement of experimental groups with numerous factors shortened the observed timing and provided bountiful statistical data. Although this method is widely used in mechanical, civil, and chemical engineering fields, it became adopted in medical facilities only in the last decade. Most of Taguchi’s analyses focused on optimizing the imaging quality for diagnosis. The medical facilities include regular X-ray, cardiac X-ray, CT (computed tomography), CTA (computed tomography angiography), LINAC (medical linear accelerator), or gamma camera scans. The images were all manipulated according to various radiation-induced interactions; thus, the optimization process of imaging resolution can offer an essential contribution to this kind of facility. In this study, we summarized the Taguchi-related papers in medical facilities and evaluated common principles in organizing the unique orthogonal array, assigning various signal-to-noise ratios, using quantified gauges, and ranking or grading the obtained imaging quality in the datum analysis process. The further elaboration on how to preset the user demanded goal in the optimization process, the necessity of focusing on cross interaction among factors, dynamic analysis superiority over static one preset in Taguchi’s analysis, and how to preset an ideal signal-to-noise ratio to satisfy the researcher demand, the importance of verification or testification in clinical cases or the assistance of ANOVA to depict a complete concept of applying Taguchi’s optimization methodology.

The characteristics of the replication is investigated in this paper. By invoking the Potts model versus holographic superconductors for “gauge” versus “string”, the pair forms as a duality in natural manner. It can be shown that resulted characteristics of replication hence deserves to be called as an Autopoietic Smart Grid. Furthermore, we are able to trace the factors contributed to these characteristics; the autopoiesis is contributed via gauge self-energy; the surveillance is due to Maxwell’s demon; the organizational adaptivity is due to the communication capacity of the string and the oscillations of the gauge. Finally, it can also be shown that such a Smart Grid replication exists as long as the string is stable and gauge is synchronized.

We review the formulation of gauge fields in terms of the frame of reference as well as the space in which the frame is defined. We highlighted some recent applications of gauge physics in the momentum space — in the modern fields of the spin Hall effect, the magnon Hall, the optical Magnus and the graphene valley Hall. General procedures of gauge transformation which lead to the construction of the gauge curvature and the equations of motion (EOM) are outlined. Central to this review is our intention to illustrate the impact of gauge physics on the past and future development of many new research fields emerging out of condensed matter physics, particularly in quantum nanosciences and nanoelectronics.