General Results Research Articles

2D Skyrmion topological charge of spin textures with arbitrary boundary conditions: a two-component spinorial BEC as a case study

Abstract We derive the most general expression for the Skyrmion topological charge for a two-dimensional spin texture, valid for any type of boundary conditions or for any arbitrary spatial region within the texture. It reduces to the usual one for the appropriate boundary conditions. The general expression resembles the Gauss-Bonet theorem for the Euler-Poincaré characteristic of a 2D surface, but it has definite differences, responsible for the assignment of the proper signs of the Skyrmion charges. Additionally, we show that the charge of a single Skyrmion is the product of the value of the normal component of the spin texture at the singularity times the Index or winding number of the transverse texture, a generalization of a Poincaré theorem. We illustrate our general results analyzing in detail a two-component spinor Bose–Einstein condensate (BEC) in 2D in the presence of an external magnetic field, via the Gross-Pitaevskii equation. The condensate spin textures present Skyrmions singularities at the spatial locations where the transverse magnetic field vanishes. We show that the ensuing superfluid vortices and Skyrmions have the same value for their corresponding topological charges, in turn due to the structure of the magnetic field.

Composition of some positive linear integral operators

Abstract This article is devoted to constructing sequences of integral operators with the same Voronovskaja formula as the generalized Baskakov operators, but having different behavior in other respects. For them, we investigate the eigenstructure, the inverses, and the corresponding Voronovskaja type formulas. A general result of Voronovskaja type for composition of operators is given and applied to the new operators. The asymptotic behavior of differences between the operators is investigated, and as an application, we obtain a formula involving Euler’s gamma function.

Maximal $$L_p$$-regularity for x-dependent fractional heat equations with Dirichlet conditions

AbstractWe prove optimal regularity results in $$L_p$$ L p -based function spaces in space and time for a large class of linear parabolic equations with a nonlocal elliptic operator in bounded domains with limited smoothness. Here the nonlocal operator is given by a strongly elliptic and even pseudodifferential operator P of order 2a ($$0<a<1$$ 0 < a < 1 ) with nonsmooth x-dependent coefficients. This includes the prominent case of the fractional Laplacian $$(-\Delta )^a$$ ( - Δ ) a , as well as elliptic operators $$(-\nabla \cdot A(x)\nabla +b(x))^a$$ ( - ∇ · A ( x ) ∇ + b ( x ) ) a . The proofs are based on general results on maximal $$L_p$$ L p -regularity and its relation to $$\mathcal {R}$$ R -boundedness of the resolvent of the associated (elliptic) operator. Finally, we apply these results to show existence of strong solutions locally in time for a class of nonlinear nonlocal parabolic equations, which include a fractional nonlinear diffusion equation and a fractional porous medium equation after a transformation. The nonlinear results are new in the case of domains with boundary; the linear results are so when P is x-dependent nonsymmetric.

Association of the modified creatinine index with quality of life in haemodialysis patients.

Aims/Background The evaluation of health-related quality of life in patients undergoing maintenance haemodialysis has garnered increasing attention. The modified creatinine index, a surrogate marker for muscle mass, has been linked to various clinical outcomes. However, the relationship between modified creatinine index and health-related quality of life in maintenance haemodialysis patients remains unclear. This study aims to elucidate the association between modified creatinine index and health-related quality of life in individuals receiving maintenance haemodialysis. Methods This cross-sectional study included 217 maintenance haemodialysis patients. Health-related quality of life was assessed using the Kidney Disease Quality of Life Instrument. Collected data included general patient information, laboratory results, and haemodialysis-related parameters. The modified creatinine index was calculated based on gender, age, single-pool Kt/V (spKt/V), and pre-dialysis serum creatinine levels. Multiple linear regression models and smooth curve fitting were used to investigate the relationship between modified creatinine index and health-related quality of life. Subgroup analyses and interaction tests were performed to identify potential effect modifiers. Results The 217 maintenance haemodialysis patients had a mean age of 53.66±13.15 years and a median dialysis vintage of 39 (25-84) months; 120 (55.30%) were male. The mean health-related quality of life score was 55.76±10.33, and the mean modified creatinine index was 22.72±2.95 mg/kg/day. After adjusting for confounding factors, an increase in modified creatinine index was associated with an improvement in health-related quality of life (β=0.55, 95% CI: 0.04, 1.06, p = 0.033). No nonlinear relationship was identified between modified creatinine index and health-related quality of life by smooth curve fitting. Subgroup and interaction analyses indicated that the relationship between modified creatinine index and health-related quality of life was stable and not significantly influenced by age, gender, dialysis vintage, diabetes status, or body mass index (p > 0.05). Conclusion Modified creatinine index is positively correlated with health-related quality of life in maintenance haemodialysis patients, suggesting its potential utility in evaluating patient quality of life. Modified creatinine index could be clinically useful to improve the predictability of health-related quality of life in maintenance haemodialysis patients.

Polymer concentration regimes from fractional microrheology

In this work, a framework for deriving theoretical equations for mean squared displacement (MSD) and fractional Fokker–Planck is developed for any arbitrary rheological model. The obtained general results are then specified for different fractional rheological models. To test the novel equations extracted from our framework and bridge the gap between microrheology and fractional rheological models, microrheology of polystyrene in tetrahydrofuran solutions at several polymer concentrations is measured. By comparing the experimental and theoretical MSDs, we find the fractional rheological parameters and demonstrate for the first time that the polymer concentration regimes can be distinguished using the fractional exponent and relaxation time data because of the existence of a distinct behavior in each regime. We suggest simple approximations for the critical overlap concentration and the shear viscosity of viscoelastic liquidlike solutions. This work provides a more sensitive approach for distinguishing different polymer concentration regimes and measuring the critical overlap concentration and shear viscosity of polymeric solutions, which is useful when conventional rheological characterization methods are unreliable due to the volatility and low viscosity of the samples.

Enumeration and Growth Functions for Uniform Tilings of the Hyperbolic Plane

The geometrical properties of a plane determine the tilings that can be built on it. Because of the negative curvature of the hyperbolic plane, we may find several types of groups of symmetries in patterns built on such a surface, which implies the existence of an infinitude of possible tiling families. Using generating functions, we count the vertices of a uniform tiling from any fixed vertex. We count vertices for all families of valence 5 and for general vertices with valence 6 , with even-sized faces. We also give some general results about the behavior of the vertices and edges of the tilings under consideration.

Mpemba Effects in Open Nonequilibrium Quantum Systems.

We generalize the classical thermal Mpemba effect (where an initially hot system relaxes faster to the final equilibrium state than a cold one) to open quantum systems coupled to several reservoirs. We show that, in general, two different types of quantum Mpemba effects are possible. They may be distinguished by quantum state tomography. However, the existence of a quantum Mpemba effect (without determining the type) can already be established by measuring simpler observables such as currents or energies. We illustrate our general results for the experimentally feasible case of an interacting two-site Kitaev model coupled to two metallic leads.

Hagedorn temperature in holography: world-sheet and effective approaches

We provide general results on the Hagedorn temperature of planar, strongly coupled confining gauge theories holographically dual to type II superstring models on curved backgrounds with Ramond-Ramond and Kalb-Ramond fluxes and non-trivial dilaton. For exact backgrounds the Hagedorn temperature is determined up to next-to-next-to-next-to-leading order (NNNLO) in an expansion in α′; in all the other cases the results can be safely trusted up to NNLO. To reach these goals we exploit two complementary approaches. On the one hand, we perform an extrapolation to the Hagedorn regime of world-sheet results obtained from the semiclassical quantization of string configurations winding around the compact Euclidean time direction. En passant, we provide a detailed derivation of the fermionic part of the world-sheet spectrum, which is hard to find in the literature. On the other hand, we perturbatively solve the equations of motion for the thermal scalar field corresponding to the lightest mode of the winding string, which in flat space becomes tachyonic above the Hagedorn temperature. The interplay between different approaches is surely convenient, but we provide insights about a possible derivation of the whole NNLO correction to the Hagedorn temperature from a pure world-sheet perspective; furthermore, we determine the effective mass of the thermal scalar from the world-sheet in full generality.

Researches on feeding behaviors of Nezara viridula (Linnaeus, 1758)(Hemiptera: Pentatomidae) adults in intermittent CO2 applications

In this study, the effects of 3 different doses (430, 600 and 670 ppm) of intermittent CO2 applications on the feeding behaviors of Nezara viridula L. (Hemiptera: Pentatomidae) Adults were determined. As nutritional behavior, the total nutrition duration of adult male and female individuals other than nutrients was examined. As a result of the study, no statistically significant difference was found between the total feeding times of female and male individuals of N. viridula. A statistically significant difference was found between the duration of stay on the nutrients of female and male individuals of N. viridula who received 600 ppm and 670 ppm doses of CO2. The duration of stay on the nutrients of male individuals who received 600 ppm and 670 ppm doses of CO2 was found to be significantly lower than the duration of stay on the nutrients of female individuals. The duration of stay on the nutrients of male individuals who received 670 ppm doses of CO2 was found to be significantly lower than the duration of stay on the nutrients of female individuals. No statistically significant difference was found between the CO2 dose groups of N. viridula and the total feeding times of the control group. A statistically significant difference was found between the CO2 dose groups of N. viridula and the duration of stay apart from the nutrients and the duration of stay on the nutrients of the control group. The duration of stay on the nutrients of individuals exposed to 600 and 670 ppm CO2 doses was found to be significantly lower than the duration of stay on the nutrients of individuals in the control group. In addition, the duration of stay apart from the nutrients of the individuals to whom 600 and 670 ppm CO2 doses were applied was found to be significantly higher than the duration of stay apart from the nutrients of the individuals in the control group. As a general result of this study, it was determined that as the application dose increased, the feeding behaviors of male and female individuals changed, male individuals reacted more to dose administration and remained on nutrients less than female individuals.

Dynamics of a pituitary–adrenal model with distributed time delays

This paper investigates the effects of distributed time delays on the dynamics of the pituitary–adrenal axis. Our two-dimensional model incorporates distributed time delays with general delay kernels, specifically illustrating interactions between adrenocorticotropic hormone (ACTH) and cortisol (CORT). We derive general theoretical results for general delay kernels, exemplified by Dirac and weak Gamma kernels, revealing stability transitions characterized by Hopf bifurcations. We establish conditions for the local asymptotic stability of the unique equilibrium and discuss the existence of periodic solutions. Numerical simulations demonstrate that periodic oscillations appear for appropriate values of the average time delays. Including an external input results in both ultradian and circadian rhythms, highlighting the system’s dynamic responsiveness to external stimuli.

A memory-type thermoelastic laminated beam with structural damping and microtemperature effects: Well-posedness and general decay

Abstract In previous work, Fayssal considered a thermoelastic laminated beam with structural damping, where the heat conduction is given by the classical Fourier’s law and acting on both the rotation angle and the transverse displacements established an exponential stability result for the considered problem in case of equal wave speeds and a polynomial stability for the opposite case. This article deals with a laminated beam system along with structural damping, past history, and the presence of both temperatures and microtemperature effects. Employing the semigroup approach, we establish the existence and uniqueness of the solution. With the help of convenient assumptions on the kernel, we demonstrate a general decay result for the solution of the considered system, with no constraints regarding the speeds of wave propagations. The result obtained is new and substantially improves earlier results in the literature.

Chebyshev–Padé approximants for multivalued functions

The paper discusses the connection between the linear Chebyshev–Padé approximants for an analytic function f f and diagonal type I Hermite–Padé polynomials for the set of functions [ 1 , f 1 , f 2 ] [1, f_1, f_2] , where the pair of functions f 1 , f 2 f_1, f_2 forms a Nikishin system. Both problems can ultimately be reduced to certain convergence problems for multipoint Padé approximants. On the other hand, the denominators of multipoint Padé approximants are non-Hermitian orthogonal polynomials with analytical weights. Thus, to study all the above problems, the general method created by Herbert Stahl can be applied. Stahl’s method is not yet sufficiently developed to obtain general results on these problems. In particular, many key convergence problems for Chebyshev–Padé approximants for functions with arbitrary configurations of branch points remain open. In this paper, we consider several important general and particular results related to this case, some already well known, and also formulate two general hypotheses in the indicated direction.

Edge-on anchored discotic liquid crystals in spherical shells: A computational study of the phases and defects.

The self-assembly of liquid crystal droplets and shells represents a captivating frontier in soft matter physics, promising precision engineering of functional materials. In this study, we delve into the phase behavior and investigate defect formation patterns in spherical shell-confined discotic liquid crystals (DLCs) through NpT Monte Carlo simulations. These shells are created by confining DLCs between two spherical surfaces, promoting the same anchoring. In this study, we focus on the case when both surfaces promote edge-on (planar) anchoring. Our study confirms a general result which states that, when a liquid crystal is under strong confinement, the nature of the isotropic-nematic transition changes from first order into continuous. Furthermore, as expected, topological defects at the spherical surface arise due to the topological constraints on the director field. Notably, our investigation reveals a unique topological defect configuration, characterized by the formation of four disclination lines that bridge the inner and external surfaces. Additionally, we observe a mixed ±1/2 wedge-twist disclination line that forms an arch that terminates at the outer surface. This arch decreases its length with decreasing temperature to eventually disappear.

Carroll geodesics

Using effective field theory methods, we derive the Carrollian analog of the geodesic action. We find that it contains both “electric” and “magnetic” contributions that are in general coupled to each other. The equations of motion descending from this action are the Carrollian pendant of geodesics, allowing surprisingly rich dynamics. As an example, we derive Carrollian geodesics on a Carroll–Schwarzschild background and discover an effective potential similar to the one appearing in geodesics on Schwarzschild backgrounds. However, the Newton term in the potential turns out to depend on the Carroll particle’s energy. As a consequence, there is only one circular orbit localized at the Carroll extremal surface, and this orbit is unstable. For large impact parameters, the deflection angle is half the value of the general relativistic light-bending result. For impact parameters slightly bigger than the Schwarzschild radius, orbits wind around the Carroll extremal surface. For small impact parameters, geodesics get reflected by the Carroll black hole, which acts as a perfect mirror.

Examining the efficacy of biological filters in the removal of agricultural pesticides and nutrient elements from agricultural drainage water

The high water consumption in agriculture has led to an obvious water crisis in this sector, and the use of unconventional water sources, especially agricultural drains, is considered necessary. For this purpose, the present study was carried out to evaluate the efficiency of biological filters with different types of substrates for treating agricultural wastewater in Khuzestan province, located in the south of Iran, to use receptive resources and reuse them in agriculture. Next, the efficiency of four types of biological filters for treating agricultural drainage water with different retention times was evaluated. Sawdust, cotton stalks, wheat straw, stubble, and rice husk were used as filters. Qualitative factors included agricultural pesticides (Atrazine, Randup, Paraquat, and 2, 4-D) and nutrients (nitrate, nitrogen, phosphate, and phosphorus). By examining the trend of increasing the retention time and the corresponding removal percentage, it was observed that the retention time has a direct relationship with the amount of removal efficiency of nutrients and agricultural toxins. As the residence time increases, the average amount of nutrient compounds in different filters decreases, and their removal percentage increases. The highest removal percentage of nitrate, total nitrogen, phosphate, and total phosphorus was 74.03, 71.66, 57.97, and 61.85% in the sawdust filter and was assigned to 10 days. The highest percentage of removal of Atrazine, Tofudi, Paraquat, and Roundup toxins with a removal efficiency of 91.73, 84.27, 89.81, and 88.46% was also observed in the treatment of sawdust for 10 days. The sawdust filter showed a good performance in removing the parameters of agricultural toxins and nutrient compounds in a retention time of 10 days compared to other filters and retention times. As a general result, the sawdust filter can be cited as a reliable substrate with acceptable efficiency compared to other filters.

Optimization of reservoir operation by sine cosine algorithm: A case of study in Algeria

The optimal operation of the reservoir has vital importance in water engineering. In the presented article, a new optimization method, named sine cosine algorithm (SCA) was employed to obtain operating policy for an irrigation system. The SCA was utilized for the monthly operation of the Boukerdane Dam placed in the north of Algeria. The fitness function was the minimization of the total shortage for the studied period. Three scenarios considering three different seasons of inflow (dry, normal and wet) are used to optimize the reservoir system’s operation. The SCA outputs were compared with particle swarm optimization (PSO) and kidney algorithm (KA). The outcomes indicated that the SCA surpassed the PSO and KA in convergence rate. The general results indicated the low speed of KA and PSO in achieving convergence. The results indicated that the highest RES (resiliency index), SUS (sustainability index) and REL (reliability index) achieved by the SCA were 65, 86 and 92 %, respectively. Comparing the third scenario with the first and second scenarios, it was observed that the third scenario (wet seasons) improved the results.

Selection functions of strong lens finding neural networks

ABSTRACT We show that convolution neural networks (CNNs) trained to find strong gravitational lens systems are biased towards systems with larger Einstein radii and large concentrated sources. This selection function is key to fully realizing the potential of the large samples of strong gravitational lens systems that will be found in upcoming wide-field surveys. In this paper, we use a CNN and three training data sets to quantify the network selection function and its implication for the many scientific applications of strong gravitational lensing. We use CNNs with similar architecture as is commonly found in the literature. The networks preferentially select systems with larger Einstein radii and larger sources with more concentrated source-light distributions. Increasing the detection significance threshold to 12$\sigma$ from 8$\sigma$ results in 50 per cent of the selected strong lens systems having Einstein radii $\theta _\mathrm{E}$$\ge$ 1.04 arcsec from $\theta _\mathrm{E}$$\ge$ 0.879 arcsec, source radii $R_S$$\ge$ 0.194 arcsec from $R_S$$\ge$ 0.178 arcsec, and source Sérsic indices $n_{\mathrm{Sc}}^{\mathrm{S}}$$\ge$ 2.62 from $n_{\mathrm{Sc}}^{\mathrm{S}}$$\ge$ 2.55. The model trained to find lensed quasars shows a stronger preference for higher lens ellipticities than those trained to find lensed galaxies. The selection function is independent of the slope of the power law of the mass profiles, hence measurements of this quantity will be unaffected. The lens finder selection function reinforces that of the lensing cross-section, and thus we expect our findings to be a general result for all galaxy–galaxy and galaxy–quasar lens finding neural networks.

Creating a Cleaned Dataset for Ease of Use

ObjectiveThe Welsh Longitudinal General Practice (WLGP) dataset contains over 4 billion records. Due to the size and the need to filter the dataset to get the necessary general practice interaction results, query performance is poor. To overcome this, a ‘cleaned’ version of the dataset needed to be created. ApproachAn R package was created that would be run when a new refresh of the WLGP data is provided. Two new tables would be created based on the original WLGP Events table. ResultsA WLGP Cleaned Dataset R Package was produced and creates a reformatted events table and events look up table. The reformatted GP events table reduces the original events table from 14 columns to 8 key columns. The events look up table takes distinct events from the original WLGP events table and produces a new table including columns such as the event description, type and hierarchy levels. Both tables are then linked using an event code ID. ConclusionThe R package now creates a new reformatted events table as well as an events look up table which is run after a WLGP refresh is provided. The new tables are then provisioned to any projects that have access to the dataset. ImplicationsThe new tables has improved query performance for our researchers, providing them with a table with all the necessary information and an easy way to decipher events codes. This has improved the amount of time researchers have spent manipulating and querying the tables.

Time-dependent uniform upper semicontinuity of pullback attractors for non-autonomous delay dynamical systems: Theoretical results and applications

In this paper we provide general results on the uniform upper semicontinuity of pullback attractors with respect to the time parameter for non-autonomous delay dynamical systems. Namely, we establish a criteria in terms of the multi-index convergence of solutions for the delay system to the non-delay one, locally pointwise convergence and local controllability of pullback attractors. As an application, we prove the upper semicontinuity of pullback attractors for a non-autonomous delay reaction-diffusion equation to the corresponding nondelay one over any bounded time interval as the delay parameter tends to zero.

Modular linear differential operators and generalized Rankin-Cohen brackets

The aim of this paper is to give expressions for modular linear differential operators (MLDOs) of any order. In particular, we show that they can all be described in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by Kaneko and Koike. We also give more uniform descriptions of MLDOs in terms of canonically defined higher Serre derivatives and an extension of Rankin-Cohen brackets, as well as in terms of quasimodular forms and almost holomorphic modular forms. The last of these descriptions involves the holomorphic projection map. The paper also includes some general results on the theory of quasimodular forms on both cocompact and non-cocompact subgroups of S L 2 ( R ) SL_2(\mathbb {R}) , as well as a slight sharpening of a theorem of Martin and Royer on Rankin-Cohen brackets of quasimodular forms.