Gauge Space Research Articles

Existence results for some fractional order coupled systems with impulses and nonlocal conditions on the half line

Abstract. In this paper, we deal with initial value problems for coupled systems of nonlinear fractional differential equations, subject to coupled nonlocal initial and impulsive conditions on the half line. Global existence-uniqueness results are obtained under weak conditions allowing the reaction part of the problem to increase indefinitely with time. Our approach relies mainly to some fixed point theorem of Perov’s type in generalized gauge spaces. The obtained results improve, generalize and complement many existing results in the literature. An example illustrating our main finding is also given. Mathematics Subject Classification (2010): 26A33, 93C23, 35E15, 47H10. Keywords: Fractional differential equation, coupled systems, generalized spaces in Perov’s sens, nonlocal initial conditions, impulses.

Chiral effective dynamo and torsion time loops holonomy on dislocated Dirac materials

Chiral torsional anomalies have recently been applied in condensed matter and models of gravitation and quantum field theory, in particular in Dirac and Weyl materials. Moreover, Einstein–Cartan space–time elastic gauge spaces with vanishing spin connection have appeared in the teleparallelism framework. Recently, Ciappina et al. (PRD (2020)) have investigated torsion in quantum field theory through time loops on Dirac materials endowed with torsion in (2 + 1)-dimensional space–time where the third dimension is replaced by time dimension. They considered Riemann-flat spaces graphenes for example. In this paper, a space–time teleparallel geometry is used where we encoded physical information of Burgers vectors on Dirac curved materials (GdA, CQG 38 (2021)). It is shown that when the magnetic or pseudo-magnetic field is encoded in this metric one obtains an interesting (2 + 1)-dimensional space–time is shown to lead to pseudo-Maxwell equations. We also show that a Riemann-flat grapheno, for example, imposes a vanishing Nieh–Yan (NY) torsional anomaly, whereas a curved Dirac material presents a non-vanishing NY anomaly. Torsion-induced holonomy on Dirac materials is investigated. Signatures of chiral dynamo effects in Dirac materials from the chiral chemical potential encoded into the covariant derivative are found. It is shown that in the absence of chiral effect the magnetic field torsion contribution decays, whereas in the chiral dynamo case, a dynamo effect is found. It is shown that from the interaction of chiral chemical potential with torsion an effective chiral chemical potential is found, which depends on the zero-component of Cartan torsion.

Collective-subspace requantization for sub-barrier fusion reactions: Inertial functions for collective motions

The adiabatic self-consistent collective coordinate (ASCC) method is used to determine the optimum reaction path and to calculate the potential and the inertial functions of the reaction model. The properties of the inertial functions are investigated with the ASCC method, in comparison with those of the cranking formulae. In addition, the properties of the pair rotation are investigated in the BCS pair model. The moments of inertia for rotation in both the real and the gauge spaces may decrease as the deformation develops.

Periodic and fixed points for mappings in extended b-gauge spaces equipped with a graph

Periodic and fixed points for mappings in extended <i>b</i>-gauge spaces equipped with a graph

Adaptation of multipurpose tractors to row spaces of cotton crops

In the Republic of Uzbekistan, cotton cultivation is carried out on row spacings of 60; 76 and 90 cm. The machine-tractor parks of cotton-growing farms are equipped with agricultural machines designed for these inter-row spacings and they are aggregated by tractors with gauges designed for them. Such a variety of tractor gauges creates the problem of mismatch between the gauge and row spacing when moving from one row spacing to another, increases the variety of spare parts and narrows the scope of their use only within one type of row spacing. The discrepancy between the gauge of serial universal row-crop tractors and the cultivated row spacing leads to damage to the plant and compaction of the soil in the area where its root system is located. Overconsolidation of the soil by more than 1.1 g/cm3 leads to a slowdown in plant growth and development, an increase in soil resistivity during subsequent tillage operations and, most importantly, a decrease in crop yield. Studies have established that, despite the variety of designs of known devices used to adjust the track, they change the track stepwise and in an insufficient range, as a result of which the tractor does not fit into the row spacing. To eliminate the shortcomings of the known methods for adjusting the track, a device has been developed for adapting the tractor running system to work on different row spacings. The developed device allows, without the use of attachments or interchangeable axle shafts and their casings, to accurately adapt the tractor’s running system to the aisle of crops cultivated by it, thereby eliminating the existing shortcomings of serial universal row-cultivator tractors. The article provides a description of the proposed technical solution and the method of its application.

Prospects of cargo transportation within the borders of the countries of the 1520 Railway Gauge Space

Objective: to assess the importance of cargo transportation for the economy of the 1520 countries. This study confirms the need to expand the capabilities of the railway infrastructure despite the consequences of sanctions restrictions, the uncertainty of the international political situation and the imbalance of trans-Eurasian container transportation in order to achieve economic growth of the national economies of the 1520 countries. Methods: methods of data analysis and diagnostics (observation, analysis, synthesis) of regulatory legal provisions regulating relations within the framework of freight transportation on the railway network, as well as reports of leading railway companies of the 1520 countries - JSC “Russian Railways”, JSC “NC “Kazakhstan Temir Zholy”, Belarusian Railway are used etc., Russian and foreign forwarding companies, carrier operators, data from the Federal Customs Service of the Russian Federation and foreign customs authorities, statistical and analytical information databases. Results: The characteristic of the main railway systems of the leading countries of the 1520 Space is given, specifying the number of international and domestic container and container-trailer routes. The factors influencing the development of cargo transportation on the territory of Russia along the 1520 gauge are identified, the prospects for cargo transportation are assessed taking into account the current state of the transport and logistics market in Russia. Practical significance: the results obtained are of an applied nature, since they propose and justify a number of measures to ensure the effective development of cargo transportation, taking into account existing infrastructure constraints.

Pre-Hausdorffness and Hausdorffness in Quantale-Valued Gauge Spaces

In this paper, we characterize each of T0, T1, Pre-Hausdorff and Hausdorff separation properties for the category L-GS of quantale-valued gauge spaces and L-gauge morphisms. Moreover, we investigate how these concepts are related to each other in this category. We show that T0, T1 and T2 are equivalent in the realm of Pre-Hausdorff quantale-valued gauge spaces. Finally, we compare our results with the ones in some other categories.

Nonminimal non-Abelian quantum vector fields in curved spacetime

The quantum effective action of non-minimal vector fields with Abelian or non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca or Yang-Mills fields are coupled to a local mass-like term acting in both coordinate and gauge spaces. Pathologies due to gauge invariance in the ultraviolet are avoided through the introduction of a non-Abelian version of the Stueckelberg field. It is found that the breaking of gauge invariance induced by the mass term affects only the tree level part of the effective action. The ultraviolet divergent part of the effective action to one loop is obtained using the method of covariant symbols and dimensional regularization. Formulas are given valid for any spacetime dimension and explicit results are shown for the two-dimensional case. As already happened for a single vector field, the ultraviolet divergences are local but not of polynomial type.

Stochastic quantization of Yang–Mills

We review two works [Chandra et al., Publ. Math. l’IHÉS (published online, 2022) and Chandra et al., arXiv:2201.03487 (2022)] that study the stochastic quantization equations of Yang–Mills on two- and three-dimensional Euclidean space with finite volume. The main result of these works is that one can renormalize the 2D and 3D stochastic Yang–Mills heat flow so that the dynamic becomes gauge covariant in law. Furthermore, there is a state space of distributional 1-forms S to which gauge equivalence approximately extends and such that the renormalized stochastic Yang–Mills heat flow projects to a Markov process on the quotient space of gauge orbits S/∼. In this Review, we give unified statements of the main results of these works, highlight differences in the methods, and point out a number of open problems.

Effective field theory of pairing rotations

Low-energy effective theories have become a powerful tool in nuclear physics and elsewhere in the past several decades. This paper describes a large amount of experimental data in this framework as ``pairing rotational bands'' with just a few parameters. The pairing rotational tensor is akin to a moment of inertia in the gauge space of two interacting superfluids. Its eigenvectors rotate with respect to the ($N$,$Z$) coordinate system, and they approximately point in the direction of the valley of $\ensuremath{\beta}$ stability and perpendicular to it. Combining superfluidity with deformation shows that the lowest-lying excitations in atomic nuclei are model-independent and based on emergent symmetry breaking.

Multivalued and random version of Perov fixed point theorem in generalized gauge spaces

Abstract In this paper, we present some random fixed point theorems in complete gauge spaces. We establish then a multivalued version of a Perov–Gheorghiu’s fixed point theorem in generalized gauge spaces. Finally, some examples are given to illustrate the results.

Some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations

&lt;abstract&gt;&lt;p&gt;In this paper, applying the theory of fixed points in complete gauge spaces, we establish some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations. Moreover, the paper contains an application of the theoretical results to the study of a class of systems of nonlinear ordinary differential equations.&lt;/p&gt;&lt;/abstract&gt;

Strength and life estimation for assigning the useful life of wheelpairs of high-speed flat wagons

Aim. The most vital unit of railway rolling stock is a wheelpair, as a broken wheel or axle may have catastrophic consequences. Therefore, before the production of a highspeed flat wagon designed for operation at speeds of up to 140 km/h, which is unique for the 1520 mm gauge space, could commence, it was required to research the applicability of the standard wheelpair for high-speed movement. Ensuring the safe operation of a wheelpair involves compliance with the requirements that are to be confirmed by means of assessment of strength and durability parameters [1]. Product conformity assessment may be based on the requirements of standards, whose voluntary fulfilment ensures compliance with [1], or other documents. Methods. The paper describes the computational and experimental methods used for confirming the strength and estimating the life (durability) of wheelpair elements in the probabilistic setting. As experimental data, the authors used the results of full-scale bench testing of wheelpairs for fatigue using the method of rotational bending as it best approximates the loading conditions in operation. The results confirmed the endurance limits of the axle and wheel as parts of an assembled wheelpair. Using design analysis, the authors examined the stress-strain state of the wheelpair caused by installation and operational loads in various running modes. Results. The conducted studies confirmed the wheelpair’s compliance with the requirements of [1–3] in terms of safety factors of fatigue strength and endurance, which eliminates the possibility of hazardous situations in the course of high-speed flat wagon operation. The time to fatigue crack nucleation in wheelpair components was evaluated using the fatigue resistance figures of the parts and equivalent amplitudes of dynamic stress caused by operational loads. It appears that this assessment allows establishing – with the assumed probability of destruction – the assigned useful life of a wheelpair axle at 32 years, which corresponds to the assigned useful life of the flat wagon according to the combined criterion. Corresponding standards and regulations required for developing the container-carrying flat wagon are being updated and a new State Standard is being developed. Conclusion. The conducted conformity assessment established that the flat wagon wheelpair meets the safety requirements of [1] and ensures the absence of unacceptable risks associated with harm to life and health of people, animals and plants, the environment and property of individuals and companies in the course of flat wagon operation.

3d gravity in Bondi-Weyl gauge: charges, corners, and integrability

We introduce a new gauge and solution space for three-dimensional gravity. As its name Bondi-Weyl suggests, it leads to non-trivial Weyl charges, and uses Bondi-like coordinates to allow for an arbitrary cosmological constant and therefore spacetimes which are asymptotically locally (A)dS or flat. We explain how integrability requires a choice of integrable slicing and also the introduction of a corner term. After discussing the holographic renormalization of the action and of the symplectic potential, we show that the charges are finite, symplectic and integrable, yet not conserved. We find four towers of charges forming an algebroid given by mathfrak{vir}oplus mathfrak{vir}oplus Heisenberg with three central extensions, where the base space is parametrized by the retarded time. These four charges generate diffeomorphisms of the boundary cylinder, Weyl rescalings of the boundary metric, and radial translations. We perform this study both in metric and triad variables, and use the triad to explain the covariant origin of the corner terms needed for renormalization and integrability.

Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis

Maintaining local interactions in the quantum simulation of gauge field theories relegates most states in the Hilbert space to be unphysical -- theoretically benign, but experimentally difficult to avoid. Reformulations of the gauge fields can modify the ratio of physical to gauge-variant states often through classically preprocessing the Hilbert space and modifying the representation of the field on qubit degrees of freedom. This paper considers the implications of representing SU(3) Yang-Mills gauge theory on a lattice of irreducible representations in both a global basis of projected global quantum numbers and a local basis in which controlled-plaquette operators support efficient time evolution. Classically integrating over the internal gauge space at each vertex (e.g., color isospin and color hypercharge) significantly reduces both the qubit requirements and the dimensionality of the unphysical Hilbert space. Initiating tuning procedures that may inform future calculations at scale, the time evolution of one- and two-plaquettes are implemented on one of IBM's superconducting quantum devices, and early benchmark quantities are identified. The potential advantages of qudit environments, with either constrained 2D hexagonal or 1D nearest-neighbor internal state connectivity, are discussed for future large-scale calculations.

Quantum entanglement in nuclear Cooper-pair tunneling with γ rays

While Josephson-like junctions, transiently established in heavy ion collisions ($\tau_{coll}\approx10^{-21}$ s) between superfluid nuclei --through which Cooper pair tunneling ($Q$-value $Q_{2n}$) proceeds mainly in terms of successive transfer of entangled nucleons-- is deprived from the macroscopic aspects of a supercurrent, it displays many of the special effects associated with spontaneous symmetry breaking in gauge space (BCS condensation), which can be studied in terms of individual quantum states and of tunneling of single Cooper pairs. From the results of studies of one- and two- neutron transfer reactions carried out at energies below the Coulomb barrier we estimate the value of the mean square radius (correlation length) of the nuclear Cooper pair. A quantity related to the largest distance of closest approach for which the absolute two-nucleon tunneling cross section is of the order of the single-particle one. Furthermore, emission of $\gamma$-rays of (Josephson) frequency $\nu_J=Q_{2n}/h$ distributed over an energy range $\hbar/\tau_{coll}$ is predicted.

Solutions of Integral Equations via Fixed-Point Results on Orthogonal Gauge Structure

The main outcome of this paper is to introduce the notion of orthogonal gauge spaces and to present some related fixed-point results. As an application of our results, we obtain existence theorems for integral equations.

Equivalence between logarithmic Sobolev inequality and hypercontractivity in a probability gage space

AbstractIn this paper, we prove the equivalence between logarithmic Sobolev inequality and hypercontractivity of a class of quantum Markov semigroup and its associated Dirichlet form based on a probability gage space.

An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.

Spatial pattern and developing mechanism of railway geo-systems based on track gauge: A case study of Eurasia

The railway is an indispensable feature of a nation’s infrastructure, and the gauge is an internal and objective technical regulation of the railway. In the large-scale regional space, the track gauges reflect the development differences, historical relations and mutual influences between countries and regions. This makes the railway, originally as a regional connection, have special social, political, military and other multiple attributes. Based on this, the paper, from the perspective of railway gauge, takes the Eurasian continent as the case region to explore the spatial pattern, formation mechanism and organizational mode of communication of the Eurasian continental railway geo-system. The results show that 11 kinds of railway gauge structures exist in Eurasia, which respectively belong to three types of wide-gauge, standard-gauge, and narrow-gauge, but the mainstream gauge only includes 1520 mm, 1435 mm and 1067 mm. Considerable variation in the coverage length and space range of different gauges is apparent, which provides a physical and technological basis for railway system differentiation and network fragmentation, which leads to the formation of eight railway geo-systems. Due to different modes for railway transport management in different geographical locations, the geographical pattern and geographical relationship of four transport organizations are formed. What especially important is the emergence of “1435 gauge space” and “1520 gauge space”, as well as the railway geo-space confrontation between them, on the Eurasian continent. Besides, we also find that the railway geo-system of Eurasia is mainly affected by the technology dissemination, path dependence, geopolitics, national defense and the colonial expansion of military latitude, and on this basis, five geo-modes of railway gauge propagation are formed.