Search

We characterize the optimal solution to the linear programming relaxation of the standard formulation for the minimum satisfiability problem. We give a O ( n m 2 ) combinatorial algorithm to solve the fractional version of the minimum satisfiability problem optimally where n ( m ) is the number of variables (clauses). As a by-product, we obtain a 2 ( 1 − 1 ∕ 2 k ) approximation algorithm for the minimum satisfiability problem where k is the maximum number of literals in any clause.

For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible combinations of the preceding), those laws of random times are precisely characterized that are rendered no bigger [rendered no smaller; left invariant] by all possible restart laws (within the classes (i), (ii), (iii), as the case may be). Partial results in the same vein for reset with branching are obtained. In particular it is found that deterministic and arbitrary stochastic restart lead to the same characterizations, but this equivalence fails to persist for exponential (constant-rate) reset.

The ‘cosmological constant problem’ (CCP) has historically been understood as describing a conflict between cosmological observations in the framework of general relativity (GR) and theoret...

Knaster-Tarski’s theorem, characterising the greatest fix- point of a monotone function over a complete lattice as the largest post-fixpoint, naturally leads to the so-called coinduction proof principle for showing that some element is below the greatest fixpoint (e.g., for providing bisimilarity witnesses). The dual principle, used for showing that an element is above the least fixpoint, is related to inductive invariants. In this paper we provide proof rules which are similar in spirit but for showing that an element is above the greatest fixpoint or, dually, below the least fixpoint. The theory is developed for non-expansive monotone functions on suitable lattices of the form$$\mathbb {M}^Y$$MY, whereYis a finite set and$$\mathbb {M}$$Man MV-algebra, and it is based on the construction of (finitary) approximations of the original functions. We show that our theory applies to a wide range of examples, including termination probabilities, behavioural distances for probabilistic automata and bisimilarity. Moreover it allows us to determine original algorithms for solving simple stochastic games.

Hadronic resonances play an important role in the study of the physics of heavy-ion collisions. In these proceedings, we discuss how the resonances can probe the reaction dynamics, the strangeness production and the properties of the hadronic phase in heavy-ion collisions at center-of-mass energies of sNN = 4–11 GeV. The resonance properties predicted by the general-purpose event generators are found to be very sensitive to the properties and space-time evolution of the medium produced in heavy-ion collisions.

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking., To appear in Theory and Practice of Logic Programming (TPLP)

Our main result is the $\mathbb {\mathcal {C}}^{0}$-rigidity of the area spectrum and the Maslov class of Lagrangian submanifolds. This relies on the existence of punctured pseudoholomorphic disks in cotangent bundles with boundary on the zero section, whose boundaries represent any integral homology class. We discuss further applications of these punctured disks in symplectic geometry.

As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes of bugs from being introduced. There is a need for similar techniques in the quantum regime. Inspired by Hoare Type Theory in the classical paradigm, we propose Quantum Hoare Types by extending the Quantum IO Monad by indexing it with pre- and post-conditions that serve as program specifications. In this paper, we introduce Quantum Hoare Type Theory (QHTT), present its syntax and typing rules, and demonstrate its effectiveness with the help of examples. QHTT has the potential to be a unified system for programming, specifying, and reasoning about quantum programs. This is a work in progress., Comment: In Proceedings QPL 2020, arXiv:2109.01534. See expanded version at arXiv:2012.02154

Microphysical processes are important for the development of clouds and thus Earth's climate. For example, turbulent fluctuations in the water vapor mixing ratio, r, and temperature, T, cause fluctuations in the saturation ratio, S. Because S is the driving factor in the condensational growth of droplets, fluctuations may broaden the cloud droplet size distribution due to individual droplets experiencing different growth rates. The small-scale turbulent fluctuations in the atmosphere that are relevant to cloud droplets are difficult to quantify through field measurements. We investigate these processes in the laboratory using Michigan Tech's Π Chamber. The Π Chamber utilizes Rayleigh–Bénard convection (RBC) to create the turbulent conditions inherent in clouds. In RBC it is common for a large-scale circulation (LSC) to form. As a consequence of the LSC, the temperature field of the chamber is not spatially uniform. In this paper, we characterize the LSC in the Π Chamber and show how it affects the shape of the distributions of r, T, and S. The LSC was found to follow a single roll with an updraft and downdraft along opposing walls of the chamber. Near the updraft (downdraft), the distributions of T and r were positively (negatively) skewed. At each measuring position, S consistently had a negatively skewed distribution, with the downdraft being the most negative.

Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal syntax. We consider an extension of nominal syntax with non-capturing atom substitutions and show that matching is decidable and finitary but unification is undecidable in general. The proof of undecidability of unification is obtained by reducing Hilbert's tenth problem to unification of extended nominal terms. We provide a general matching algorithm and characterise a class of problems for which matching is unitary, giving rise to expressive and efficient rewriting systems.

We construct a complex analytic version of an equivariant cohomology theory which appeared in a paper of Rezk, and which is roughly modelled on the Borel-equivariant cohomology of the double free loop space. The construction is defined on finite, torus-equivariant CW complexes and takes values in coherent holomorphic sheaves over the moduli stack of complex elliptic curves. Our methods involve an inverse limit construction over all finite-dimensional subcomplexes of the double free loop space, following an analogous construction of Kitchloo for single free loop spaces. We show that, for any given complex elliptic curve $\mathcal {C}$, the fiber of our construction over $\mathcal {C}$ is isomorphic to Grojnowski's equivariant elliptic cohomology theory associated to $\mathcal {C}$.

In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2 × 2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and the technique of De Blasi measure of weak noncompactness on countably subsets. We will also prove the existence of solutions for a coupled system of nonlinear equations with an example.

In this study, we are concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes Korteweg equations of a compressible fluid in the half space. We assume that the space-asymptotic states and the boundary data satisfy some conditions so that the time-asymptotic state of this solution is a rarefaction wave. Then we show that the rarefaction wave is non-linearly stable, as time goes to infinity, provided that the strength of the wave is weak and the initial perturbation is small. The proof is mainly based on $L^{2}$-energy method and some time-decay estimates in $L^{p}$-norm for the smoothed rarefaction wave.

Particles 4(3), 354 - 360 (2021). doi:10.3390/particles4030030, The Compressed Baryonic Matter experiment (CBM) at FAIR aims to study the area of the QCD phase diagram at high net baryon densities and moderate temperatures with collisions of heavy ions at sNN=2.8–4.9 GeV. The anisotropic transverse flow is one of the most important observable phenomena in a study of the properties of matter created in such collisions. Flow measurements require the knowledge of the collision symmetry plane, which can be determined from the deflection of the collision spectators in the plane transverse to the direction of the moving ions. The CBM performance for projectile spectator symmetry plane estimation is studied with GEANT4 Monte Carlo simulations using collisions of gold ions with beam momentum of 12A GeV/c generated with the DCM-QGSM-SMM model. Different data-driven methods to extract the correction factor in flow analysis for the resolution of the spectator symmetry plane estimated with the CBM Projectile Spectator Detector are investigated., Published by MDPI AG, Basel

The algebraic structures have many applications in coding theory, cryptography, and security networks. In this paper, the notion of hybrid subalgebras ofBCH-algebras is introduced and related properties are investigated. Moreover, some characterizations of hybrid subalgebras ofBCH-algebras are given. Furthermore, we state and prove some theorems in hybrid subalgebras ofBCH-algebras. The homomorphic images and inverse images of fuzzyBCH-subalgebras are studied and discussed.

The mechanical behavior of the extruded 7003-T6 aluminum profiles used as automotive buffer beams is investigated. The correlation of the texture and the formation of the adiabatic shear band is analyzed. Copper texture, R texture, and S texture are the main reasons for the anisotropy of mechanical behavior of the profile, resulting in that the stress of the profile along the extrusion direction is higher than that perpendicular to the extrusion direction. Through finite element modeling (FEM), it can be found that the adiabatic shear band is developed in the sample if the dynamic loading direction is parallel to the extrusion direction, but it does not appear if the loading direction is perpendicular to the extrusion direction. When the dynamic loading direction is parallel to the extrusion direction, higher stress results in a lower energy barrier for shear localization. Therefore, the formation of the adiabatic shear band is susceptible along but is not sensitive perpendicular to the extrusion direction. This study provides technical support for the service of 7003 aluminum alloy in automobiles, which has important academic and engineering application value.

We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ -convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT( κ ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.

The ACl-ThCl4 (A = Li, Na, K) systems could be of relevance to the nuclear industry in the near future. A thermodynamic investigation of the three binary systems is presented herein. The excess Gibbs energy of the liquid solutions is described using the quasi-chemical formalism in the quadruplet approximation. The phase diagram optimisations are based on the experimental data available in the literature. The thermodynamic stability of the liquid solutions increases in the order Li < Na < K, in agreement with idealised interactions and structural models.

Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with CPT inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in PT-symmetric quantum theory is preserved.

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems which has some important applications. It is well-known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail and to deal with this issue one could reformulate it as a mathematical program with disjunctive constraints (MPDC). In this paper we first survey recent results on constraint qualifications and optimality conditions for MPDC and then apply them to MPSC to obtain the corresponding constraint qualifications and optimality conditions. Moreover we provide two types of sufficient conditions for the local error bound and exact penalty results for MPSC. One comes from the directional quasi-normality for MPDC and the other is obtained by using the local decomposition approach.

In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebra A , f , whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebra A to become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence on A having a given fuzzy ideal as its kernel.

In this paper, we introduce extended b -gauge spaces and the extended family of generalized extended pseudo- b -distances. Moreover, we define the sequential completeness and construct the Caristi-type G -contractions in the framework of extended b -gauge spaces. Furthermore, we develop periodic and fixed point results in this new setting endowed with a graph. The obtained results of this paper not only generalize but also unify and improve the existing results in the corresponding literature.

Particles 4(2), 275 - 287 (2021). doi:10.3390/particles4020024, The size and evolution of the matter created in relativistic heavy-ion collisions strongly depend on collision geometry, defined by the impact parameter. However, the impact parameter cannot be measured directly in an experiment but might be inferred from final state observables using the centrality procedure. We present the procedure of centrality determination for the Multi-Purpose Detector (MPD) at the NICA collider and its performance using the multiplicity of produced charged particles at midrapidity. The validity of the procedure is assessed using the simulated data for Au + Au collisions at $√s_{NN}$ = 4–11 GeV., Published by MDPI AG, Basel

We investigate the spectrum of the non-backtracking matrix of a graph. In particular, we show how to obtain eigenvectors of the non-backtracking matrix in terms of eigenvectors of a smaller matrix. In doing so, we create a block diagonal decomposition of the non-backtracking matrix, more clearly expressing its eigenvalues. Furthermore, we find an expression for the eigenvalues of the non-backtracking matrix in terms of eigenvalues of the adjacency matrix, and use this to upper-bound the spectral radius of the non-backtracking matrix, and to give a lower bound on the spectrum. Specifically, an upper-bound on the spectral radius is found in terms of the number of nodes and edges of the graph. We also investigate properties of a graph that can be determined by the spectrum. Specifically, we prove that the number of components, the number of degree 1 vertices, and whether or not the graph is bipartite are all determined by the spectrum of the non-backtracking matrix.

By a molecular dynamics (MD) simulation method which ensures the system will be under hydrostatic pressure, dynamic and elastic properties of glassy metatstable states are investigated. In the MD method, the simulation cell fluctuates not only in volume but also in shape under constant hydrostatic pressure and temperature. As observed in experiments for many glass forming materials, metastable states in our simulation show a sharp increase in mean-square-displacement at certain temperatures TD. Dynamic heterogeneity is also observed at TD. Elastic properties are calculated from stress and strain relations obtained from the spontaneous fluctuation of internal stress tensor and simulation cell parameters. Each investigated state shows distinctive dynamics while maintaining solid-like elastic properties. The elastic properties stay intact even above TD. It has been shown that the rigidity and mobility of glassy metastable states are compatible under dynamic heterogeneity.

This paper furthers the study on the confluence number of a graph. In particular results for certain derivative graphs such as the line graph of trees, cactus graphs, linear Jaco graphs and novel graph operations are reported.

Slot waveguides based on silicon-rich materials are proposed and experimentally demonstrated, which consist of a silicon-rich oxide (SRO) slot layer sandwiched by two silicon-rich nitride (SRN) layers. Measurements show the waveguides have a low propagation loss of $\sim$2.2 dB/cm and a 50-$\mu \text{m}$-radius micro-ring resonator can achieve a loaded quality factor ($Q_{load}$) of $\sim 10^5$. Four-wave mixing experiments in the slot waveguides reveal a high nonlinearity $\gamma$ of 16 W$^{-1}$m$^{-1}$ of the waveguide and an averaged nonlinear index $n_2$ of 2.5 x 10$^{-18}$ m $^2$/W of the silicon-rich materials, 10 times larger than that of stoichiometric silicon nitride (Si$_3$N$_4$). Supercontinuum generation (SCG) experiments have shown a large fabrication tolerance of such slot waveguides that 1.2 octave spectral broadening in a 1510-nm-wide slot waveguide can be achieved while that is 0.9 octave in a slot waveguide with a width shrinking as large as 220 nm.

Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown to be driven by a transient threading–unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.

We obtain an effective embedding of the classical predicate logic into the logic of partial quasiary predicates. The embedding has the property that an image of a non-theorem of the classical logic is refutable in a model of the logic of partial quasiary predicates that has the same cardinality as the classical countermodel of the non-theorem. Therefore, we also obtain an embedding of the classical predicate logic of finite models into the logic of partial quasiary predicates over finite structures. As a consequence, we prove that the logic of partial quasiary predicates is undecidable—more precisely, $\varSigma ^0_1$-complete—over arbitrary structures and not recursively enumerable—more precisely, $\varPi ^0_1$-complete—over finite structures.

Let X X be the solution of a stochastic differential equation in Euclidean space driven by standard Brownian motion, with measurable drift and Sobolev diffusion coefficient. In our main result we show that when the drift is measurable and the diffusion coefficient belongs to an appropriate Sobolev space, the law of X X satisfies Talagrand’s inequality with respect to the uniform distance.

This paper presents exact dual semi-definite programs (SDPs) for robust SOS-convex polynomial optimization problems with affinely adjustable variables in the sense that the optimal values of the ro...

Firstly, we introduce the definitions of G -asymptotic tracking property, G -asymptotic average tracking property, and G -quasi-weak almost-periodic point. Secondly, we study their dynamical properties and characteristics. The results obtained improve the conclusions of asymptotic tracking property, asymptotic average tracking property, and quasi-weak almost-periodic point in the inverse limit space and provide the theoretical basis and scientific foundation for the application of tracking property in computational mathematics, biological mathematics, and computer science.

In this paper, we investigate the β -stability in q-th moment for neutral impulsive stochastic functional differential equations with Markovian switching (NISFDEwMS). Moreover, β -stability in q-th moment is studied by using the Lyapunov techniques and a new Razumikhin-type theorem to prove our result. Finally, we check the main result by a numerical example.

We prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of $\mathbb {C}^2$ . Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable manifolds of saddle points have uniform geometry.

Zircon Raman dating based on irradiation damage is a debated concept but not an established geo-/thermochronological method. One issue is the temperature range of radiation-damage annealing over geological timescales. We conducted isochronal and isothermal annealing experiments on radiation-damaged zircons between 500 and 1000 ∘C for durations between 10 min and 5 d to describe the annealing kinetics. We measured the widths (Γ) and positions (ω) of the ν1(SiO4), ν2(SiO4), and ν3(SiO4) internal Raman bands, and the external rotation Raman band at ∼974, 438, 1008, and 356 cm−1 after each annealing step. We fitted a Johnson–Mehl–Avrami–Kolmogorov and a distributed activation energy model to the fractional annealing data, calculated from the widths of the ν2(SiO4), ν3(SiO4), and external rotation bands. From the kinetic models, we determined closure temperatures Tc for damage accumulation for each Raman band. Tc ranges from 330 to 370 ∘C for the internal ν2(SiO4) and ν3(SiO4) bands; the external rotation band is more sensitive to thermal annealing (Tc∼260 to 310 ∘C). Our estimates are in general agreement with previous ones, but more geological evidence is needed to validate the results. The Tc difference for the different Raman bands offers the prospect of a multi-closure-temperature zircon Raman thermochronometer.

In this article, we define a new sequence space generated by the domain of r -Cesàro matrix in Nakano sequence space. Some geometric and topological properties of this sequence space, the multiplication maps defined on it, and the eigenvalue distributions of map ideal with s -numbers that belong to this sequence space have been examined.

Using the inverse of the once common but now largely forgotten versine function, series containing reciprocals of the central binomial coefficients and series containing reciprocals of the Catalan ...

The static energetics of a wide variety polytypes for 17 kinds of metallic elements is systematically evaluated based on the computational method coupled with three theoretical tools (PGA: polytype generation algorithm; FPC-DFT: first-principle calculations based on the density functional theory; and ANNNI: axial next-nearest-neighbor Ising model). We present the ANNNI parameters including interactions up to the third-nearest neighbor layer with four-spin term that can illustrate various trends of structural and energetic properties for the metallic polytypes.

A non-hardware method for computer control of the geometric parameters of a twisted thread using a two-dimensional Fourier transform program of its computer image is proposed. First, the program calculates the diffraction pattern from the investigated image of the thread. Then, the same program builds a diffraction pattern from the image of the first pattern, which does not contain speckles in the proposed method. This makes it possible to carry out its automatic computer analysis with the output to the digital values ​​of the calculated parameters. The effectiveness of the method is illustrated on model and industrial samples of synthetic threads.

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α -fuzzy fixed point theorems in the context of extended b -metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α -fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.

The use of organic radicals as building blocks is an effective approach to the production of open-shell coordination polymers (CPs). Two-dimensional (2D) CPs with honeycomb spin-lattices have attracted attention because of the unique electronic structures and physical properties afforded by their structural topology. However, radical-based CPs with honeycomb spin-lattices tend to have low chemical stability or poor crystallinity, and thus novel systems with high crystallinity and persistence are in strong demand. In this study, a novel triangular organic radical possessing three pyridyl groups, tris(3,5-dichloro-4-pyridyl)methyl radical (trisPyM) was prepared. It exhibits luminescence, high photostability, and a coordination ability, allowing formation of defined and persistent 2D CPs. Optical measurements confirmed the luminescence of trisPyM both in solution and in the solid state, with emission wavelengths, λ

According to the length-preserving projection and Euler discretization method, biorthogonal wavelet function on a smooth curve C is constructed in this paper, such as a logarithm curve. The properties of biorthogonal wavelet filters on a smooth curve C are discussed, such as induced refinable equation and symmetry. Moreover, an example is given for discussing the biorthogonal scaling function and its dual on a logarithm curve C . Finally, a numerical application is given for dealing with financial data.

We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordstr\"om geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function $\Psi_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $\chi$ which relates the perturbations of the radiative Maxwell scalars $\varphi_2$ and the Weyl scalar $\Psi_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the results obtained previously for instance in Chandrashekhar's book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on a basis of spin weighted spherical harmonics and the Reissner-Nordstr\"om spacetime in Kerr-Schild type coordinates a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we solve completely a system which generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitating the gravitational wave detection via the electromagnetic signal., Comment: 21 pages, 6 figures, 1 table

The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

A novel fiber sensor based on photonic crystal fiber (PCF) for simultaneous measurement of temperature and humidity is proposed. The PCF is filled with alcohol, which is sensitive to temperature. A...

In this study, the nonlinear unwinding behavior of cables in a transient state wound in a cylindrical spool package was analyzed using unwinding dynamics. In previous studies, investigations were conducted using constant unwinding velocity. However, this method is limited due to complexities regarding the analysis of the actual behavior where the unwinding velocity increases or decreases. In this paper, to prevent problems, such as twisting, entanglement, and cutting, that occur during the rapid unwinding process, an experimental device that converts unwinding velocity over time was developed. Using a cable unwinding system, high-speed camera, and tension sensor, the equation of motion, which was derived in a previous study using the expanded Hamilton theorem, was experimentally verified. Moreover, the cable’s tension change and behavior in the unwinding process were analyzed, and a method to solve the unwinding problem was studied.

Cirrus cloud radiative effects are largely affected by ice microphysical properties, including ice water content (IWC), ice crystal number concentration (Ni) and mean diameter (Di). These characteristics vary significantly due to thermodynamic, dynamical and aerosol conditions. In this work, a global-scale observation dataset is used to examine regional variations of cirrus cloud microphysical properties, as well as several key controlling factors, i.e., temperature, relative humidity with respect to ice (RHi), vertical velocity (w) and aerosol number concentrations (Na). Results are compared with simulations from the National Center for Atmospheric Research (NCAR) Community Atmosphere Model version 6 (CAM6). Observed and simulated ice mass and number concentrations are constrained to ≥62.5 µm to reduce potential uncertainty from shattered ice in data collection. The differences between simulations and observations are found to vary with latitude and temperature. Comparing with averaged observations at ∼100 km horizontal scale, simulations are found to underestimate (overestimate) IWC by a factor of 3–10 in the Northern (Southern) Hemisphere. Simulated Ni is overestimated in most regions except the Northern Hemisphere midlatitudes. Simulated Di is underestimated by a factor of 2, especially for warmer conditions (−50 to −40 ∘C), possibly due to misrepresentation of ice particle growth/sedimentation. For RHi effects, the frequency and magnitude of ice supersaturation are underestimated in simulations for clear-sky conditions. The simulated IWC and Ni show bimodal distributions with maximum values at 100 % and 80 % RHi, differing from the unimodal distributions that peak at 100 % in the observations. For w effects, both observations and simulations show variances of w (σw) decreasing from the tropics to polar regions, but simulations show much higher σw for the in-cloud condition than the clear-sky condition. Compared with observations, simulations show weaker aerosol indirect effects with a smaller increase of IWC and Di at higher Na. These findings provide an observation-based guideline for improving simulated ice microphysical properties and their relationships with key controlling factors at various geographical locations.

In the current article, we investigate the boundedness of commutators of the bilinear fractionalp-adic Hardy operator onp-adic Herz spaces andp-adic Morrey-Herz spaces by considering the symbol function from central bounded mean oscillations and Lipschitz spaces.

Detection rates for the elastic and inelastic scattering of weakly interacting massive particles (WIMPs) off 23Na are calculated within the framework of Deformed Shell Model (DSM) based on Hartree-Fock states. At first, the spectroscopic properties of the detector nucleus, like energy spectra and magnetic moments, are evaluated and compared with experimental data. Following the good agreement of these results, DSM wave functions are used for obtaining elastic and inelastic spin structure functions, nuclear structure coefficients and so forth for the WIMP-23Na scattering. Then, the event rates are also computed with a given set of supersymmetric parameters. In the same manner, using DSM wavefunctions, nuclear structure coefficients and event rates for elastic scattering of WIMPs from 40Ar are also obtained. These results for event rates and also for annual modulation will be useful for the ongoing and future WIMP detection experiments involving detector materials with 23Na and 40Ar nuclei.

Using data on the proton fluxes of the Earth's radiation belts (ERBs) with energy ranging from 0.2 to 100 MeV on the drift L shells ranging from 1 to 8, the quasi-stationary distributions over the drift frequency fd of protons around the Earth are constructed. For this purpose, direct measurements of proton fluxes of the ERBs during the period from 1961 to 2017 near the geomagnetic equator were employed. The main physical processes in the ERB manifested more clearly in these distributions, and for protons with fd>0.5 mHz at L>3, their distributions in the {fd,L} space have a more regular shape than in the {E,L} space. It has also been found that the quantity of the ERB protons with fd ∼ 1–10 mHz at L∼2 does not decrease, as it does for protons with E > 10–20 MeV (with fd>10 mHz), but increases with an increase in solar activity. This means that the balance of radial transport and loss of ERB low-energy protons at L∼2 is disrupted in favor of transport of these protons: the effect of an increase in the radial diffusion rates with increasing solar activity overpowers the effect of an increase in the density of the dissipative medium.