Miracle-dz/UniFAR-FTUs huggingface dataset:
On the measure-theoretic entropy and topological pressure of free semigroup actions

In this paper we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action we assign a skew-product transformation whose fiber topological pressure is taken to be the topological pressure of the initial action. Some properties of these two notions are given, followed by two main results. One is the relationship between the topological pressure of the skew-product transformation and the topological pressure of the free semigroup action, the other is the partial variational principle about the topological pressure. Moreover, we apply this partial variational principle to study the measure-theoretic entropy and the topological entropy of finite affine transformations on a metrizable group.
Zero-one law for directional transience of one-dimensional random walks in dynamic random environments

We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under space-time translations, ergodicity under spatial translations, and a mild ellipticity condition. In particular, the result applies to general uniformly elliptic models and also to a large class of non-uniformly elliptic cases that are i.i. d. in space and Markovian in time. An immediate consequence is the recurrence of models that are symmetric with respect to reflection through the origin.
GMRES as a multi-step transport sweep accelerator

Abstract It is shown that GMRES can provide a multi-step transport sweep accelerator which operates by finding the linear combination of transport sweep iterates that minimize an estimate of the error in the flux. Because of the minimization process, a linear combination of only a relatively few transport sweep iterates can in fact well approximate a many-times collided flux. However, the number of iterations required increases with the optical thickness of the system; this reflects the need to capture the physics of the very highly collided particles present in the thicker system. Unlike a direct application of GMRES to the integro-differential form of the transport equation, which requires storage for several angular fluxes, the approach described here requires storage only for scalar fluxes in the case of isotropic scattering, or more generally only for those flux moments required for the order of scattering being used. In general it is not as efficient as DSA, but it is much faster than standard sweep.
Potential theory associated with the Dunkl Laplacian

Abstract The main goal of this paper is to develop a potential theoretical approach to study the Dunkl Laplacian Δ k {\Delta_{k}} , which is a standard example of differential-difference operators. Introducing the Green kernel relative to Δ k {\Delta_{k}} , we prove that the Dunkl Laplacian generates a Balayage space and we investigate the associated family of harmonic measures. Therefore, by means of harmonic kernels, we give a characterization of all Δ k {\Delta_{k}} -harmonic functions on a large class of open subsets U of ℝ d {\mathbb{R}^{d}} . We also establish existence and uniqueness results of a solution of the corresponding Dirichlet problem.
Partitioning a macroscopic system into independent subsystems

We discuss the problem of partitioning a macroscopic system into a collection of independent subsystems. The partitioning of a system into replica-like subsystems is nowadays a subject of major interest in several fields of theoretical and applied physics. The thermodynamic approach currently favoured by practitioners is based on a phenomenological definition of an interface energy associated with the partition, due to a lack of easily computable expressions for a microscopic (i.e. particle-based) interface energy. In this article, we outline a general approach to derive sharp and computable bounds for the interface free energy in terms of microscopic statistical quantities. We discuss potential applications in nanothermodynamics and outline possible future directions.
Commercial prospects for enzyme engineering

Despite great enthusiasm for enzyme technology over the last two decades, the number and scale of commercial applications remains disappointing. To change this, protein engineering must concentrate on improving the properties of current commercial enzymes for specific process needs. Construction of novel enzymes with robust properties and tailored specificities will create new markets. The technology to do this is already fast and efficient, but lack of relevant tertiary-structure models is a serious constraint. Improved thermostability could be achieved by introducing new sulphide bridges, increasing internal bonding and modifying surface charges. There are other obvious modifications that should improve stability to oxidation, extremes of pH, and heavy metals. These principles are illustrated by work in progress on subtilisin which is the major industrial enzyme.
Hybrid Current Controller for Permanent-Magnet Synchronous Motors Using Robust Switching Techniques

This study proposes a hybrid current controller for a permanent-magnet synchronous motor fed by a two-level inverter. It combines the advantages of model predictive control (MPC) and field-oriented control (FOC), which results in fast dynamics and a zero steady-state error. In addition, space vector pulse width modulation is used to ensure a constant switching frequency and simplify the switching signal generation for the two-level inverter. Two optimal switching methods were proposed to maintain a smooth transition between FOC and MPC and eliminate any undesired bumps or oscillations. These two methods are based on hysteresis average current ripple and artificial neural networks. The proposed switching methods (PSMs) were compared with two recent conventional switching methods (CSMs). Simulation and experimental results were given to validate the effectiveness of the PSMs over the CSMs. The results show that the PSMs have a robust and smooth transition between MPC and FOC in various setups with faster dynamics, minimal overshoot, and zero steady-state error.
Deforming complete Hermitian metrics with unbounded curvature

We produce solutions to the K\"ahler-Ricci flow emerging from complete initial metrics $g_0$ which are $C^0$ Hermitian limits of K\"ahler metrics. Of particular interest is when $g_0$ is K\"ahler with unbounded curvature. We provide such solutions for a wide class of $U(n)$-invariant K\"ahler metrics $g_0$ on $n$ dimensional complex Euclidean space, many of which having unbounded curvature. As a special case we have the following Corollary: The K\"ahler-Ricci flow has a smooth short time solution starting from any smooth complete $U(n)$-invariant K\"abler metric on $\C^n$ with either non-negative or non-positive holomorphic bisectional curvature, and the solution exists for all time in the case of non-positive curvature.
Improved Laboratory Transition Probabilities for Neutral Chromium and Redetermination of the Chromium Abundance for the Sun and Three Stars

Branching fraction measurements from Fourier transform spectra in conjunction with published radiative lifetimes are used to determine transition probabilities for 263 lines of neutral chromium. These laboratory values are employed to derive a new photospheric abundance for the Sun, log ϵ(Cr )☉ = 5.64 ± 0.01 (σ = 0.07). The individual Cr I solar abundances do not exhibit any trends with line strength nor with excitation energy, and there were no obvious indications of departures from LTE. In addition, oscillator strengths for singly ionized chromium recently reported by the FERRUM Project are used to determine log ϵ(Cr )☉ = 5.77 ± 0.03 (σ = 0.13). Transition probability data are also applied to the spectra of three stars: HD 75732 (metal-rich dwarf), HD 140283 (metal-poor subgiant), and CS 22892-052 (metal-poor giant). In all of the selected stars, Cr I is found to be underabundant with respect to Cr II. The possible causes for this abundance discrepancy and apparent ionization imbalance are discussed.
Cohomology and Deformations of Hom-algebras

The purpose of this paper is to define cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were introduced by Makhlouf and Silvestrov in the study of one-parameter formal deformations theory. Among the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and a Chevalley-Eilenberg cohomology for Hom-Lie algebras, we define Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and Nijenhuis-Richardson bracket on the space of multilinear mappings of Hom-Lie algebras. Also we enhance the deformations theory of this Hom-algebras by studying the obstructions.
The Influence of Low-Carbohydrate and Low-Fat Diet on Cardiovascular Disease

It has become a consensus that low fat diet is the key to lose weight and keep slim. This study is important for obese and overweight individuals, who are at increased risk of CVD. The reduction of total fat in food is directly related to the reduction of individual cholesterol level and blood pressure, which also reveals the beneficial role of low-fat diet in preventing the risk of heart problems. Low-carb diets and low-fat diets can both help to lower the risk of CVD, but there’s no direct link between them. The basic mechanism is to improve other factors like hypertension and obesity which can be altered by healthy diets. Cutting back on saturated fatty acids can lower heart problems and stroke risk, because less cholesterol and saturated fats re consumed. Therefore, it is essential for us to eat correctly and healthily and take more exercise to prevent happening of CVD.
On the degree distribution of a growing network model

In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum degree at least $k$, new vertices are added one by one. Each new vertex $v$ first chooses a random vertex $w$ to join to, where the probability of choosing $w$ is proportional to its degree. Then $k$ edges are added from $v$ to randomly chosen neighbours of $w$.
On the denseness of minimum attaining operators

Let $H_1,H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator (not necessarily bounded). It is proved that for each $\epsilon>0$, there exists a bounded operator $S$ with $\|S\|\leq \epsilon$ such that $T+S$ is minimum attaining. Further, if $T$ is bounded below, then $S$ can be chosen to be rank one.
On the existence of weak solutions for steady flows of generalized viscous fluids

In this work we investigate the existence of weak solutions for steady flows of generalized incompressible and homogeneous viscous fluids. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes the flow depends on the space variable: $q=q(\mathbf{x})$. For the associated boundary-value problem we prove the existence of weak solutions for any variable exponent $q\geq\alpha>\frac{2N}{N+2}$, where $\alpha=\mathrm{ess}\inf q$. This work improves all the known existence results in the sense that the lowest possible bound of $q$ is attained and no other assumption on the regularity of $q$ is required.
Solving nonlinear optimal control problems with state and control delays by shooting methods combined with numerical continuation on the delays

In this paper we introduce a new procedure to solve nonlinear optimal control problems with delays which exploits indirect methods combined with numerical homotopy procedures. It is known that solving this kind of problems via indirect methods (which arise from the Pontrya-gin Maximum Principle) is complex and computationally demanding because their implementation is faced to two main difficulties: the extremal equations involve forward and backward terms, and besides, the related shooting method has to be carefully initialized. Here, starting from the solution of the non-delayed version of the optimal control problem, delays are introduced by a numerical continuation. This creates a sequence of optimal delayed solutions that converges to the desired solution. We establish a convergence theorem ensuring the continuous dependence w.r. t. the delay of the optimal state, of the optimal control (in a weak sense) and of the corresponding adjoint vector. The convergence of the adjoint vector represents the most challenging step to prove and it is crucial for the well-posedness of the proposed homotopy procedure. Two numerical examples are proposed and analyzed to show the efficiency of this approach.
Regioregular poly(3-hexyl-thiophene) helical self-organization on carbon nanotubes

Mixtures of regioregular poly(3-hexyl-thiophene) (rrP3HT) and multiwall carbon nanotubes have been investigated by scanning tunneling microscopy in ultrahigh vacuum. Carbon nanotubes covered by rrP3HT have been imaged and analyzed, providing a clear evidence that this polymer self-assembles on the nanotube surface following geometrical constraints and adapting its equilibrium chain-to-chain distance. Largely spaced covered nanotubes have been analyzed to investigate the role played by nanotube chirality in the polymer wrapping, evidencing strong rrP3HT interactions along well defined directions.
Packing and covering indices for a general Lévy process

There has been substantial interest in the indices 0 ≤ β ≤ β' ≤ β ≤ 2, defined by Blumenthal and Getoor, determined by a general Levy process in R d . Pruitt defined an index γ which determines the covering dimension and Taylor showed that an index γ', first considered by Hendricks, determines the packing dimension for the trajectory. In the present paper we prove that B/2 ≤ γ' ≤ min( β,d), and give examples to show that the whole range is attainable. However, we cannot completely determine the set of values of(γ, γ',β) which can be attained as indices of some Levy process.
Maximal operators and decoupling for $\Lambda(p)$ Cantor measures

For $2\leq p 2/p$, and $\delta>0$, we construct Cantor-type measures on $\mathbb{R}$ supported on sets of Hausdorff dimension $\alpha 0$, and have no Fourier decay. The proof is based on a decoupling inequality similar to that of Laba and Wang.
Projections of patterns and mode interactions

ABSTRACT We study solutions of bifurcation problems with periodic boundary conditions, with periods in an n + 1-dimensional lattice and their projection into n-dimensional space through integration of the last variable. We show that generically the projection of a single-mode solution is a mode interaction. This can be applied to the study of black-eye patterns.
Effects of watering regime on the morphological, physiological and functional traits of seedlings of cacao provenances under screen house conditions

In the present study, morphological and physiological responses of cocoa provenances to watering regimes under screen house conditions and the implications of the measured variables as drought tolerance strategy in Theobroma was discussed. A 4 by 3 factorial scheme involving four cacao provenances and watering regimes (well watering at full field capacity, 60 and 40% field capacity: 1.5, 0.9 and 0.6 L/plant at each watering event) the cocoa genotypes evaluated are PA 150 Series (the elite varieties), F3 Amazon and Amelonado. Observations were made on the morphological and physiological traits of seedlings of the cacao genotypes affected by watering regimes. The measured variables were deployed to rank the drought performance of cacao genotypes following nursery desiccation studies. Data on root and shoot biomass, water use, stomatal conductance, proline, water soluble carbohydrate and leaf chlorophyll concentrations of cacao seedlings were collected. The results showed that root zone moisture status affected the morphological and physiological characteristics of cacao provenances. Differences were obtained in root and shoot biomass, water use, the densities of stomatal and its conductance of gases, and the concentrations of leaf chlorophyll, and shoot and leaf proline and water soluble carbohydrates among the watering regimes imposed. Cacao provenances evaluated also differed in their responses to watering regimes and in morphological and physiological characters. The imposed root zone moisture scenarios elicited differences in the responses of cacao provenances evaluated. Most of the measured morphological and physiological variables were driven by root zone moisture status among cacao provenances, the measured traits appeared to have played important roles as root zone moisture deficit stress tolerance mechanisms in cacao. Seedlings of cocoa provenances had better vigour of growth when grown under 100 and 60% field capacity watering compared with 40% FC. Adequacy of soil moisture promotes growth and physiological functions in the seedlings of cacao provenances tested. The measured morpho-physiological variables were statistically superior under well watered situations (100% FC) compared with the 40% FC. The results confirmed that cocoa seedlings cannot withstand soil moisture deficit stress as was obtained for seedlings that were watered with 40% FC. It is recommended that watering cacao seedlings at full field capacity (FC) and at 70% FC (mild root zone moisture stress) will ensure the production of vigorous seedlings of cacao in the nursery.
On the Regularity and Koszulness of Modules Over Local Rings

Koszul modules over Noetherian local rings R were introduced by Herzog and Iyengar and they possess good homological properties, for instance their Poincaré series is rational. It is an interesting problem to characterize classes of Koszul modules. Following the idea traced by Avramov, Iyengar, and Sega, we take advantage of the existence of special filtration on R for proving that large classes of R-modules over Koszul rings are Koszul modules. By using this tool we reprove and extend some results obtained by Fitzgerald.
A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator

This paper provides a weak factorization for the Meyer-type Hardy space $H^1_b(\mathbb{R})$, and characterizations of its dual ${\rm BMO}_b(\mathbb{R})$ and its predual ${\rm VMO}_b(\mathbb{R})$ via boundedness and compactness of a suitable commutator with the Cauchy integral $\mathscr{C}_{\Gamma}$, respectively. Here $b(x)=1+iA'(x)$ where $A'\in L^{\infty}(\mathbb{R})$, and the Cauchy integral $\mathscr{C}_{\Gamma}$ is associated to the Lipschitz curve $\Gamma=\{x+iA(x)\, : \, x\in \mathbb{R}\}$.
The GLAST Satellite Calorimeter

The Gamma Ray Large Area Space Telescope (GLAST) is a multi-national satellite mission with aim to study the high-energy gamma ray sky. The main instrument is the Large Area Telescope (LAT) that consists of 16 towers, each housing a silicon strip precision tracker and a CsI(Tl) calorimeter. The calorimeter is made in a hodoscopic fashion from position sensitive crystal rods measuring 333.0 × 26.7 × 19.9 mm^3. Each calorimeter tower contains 8 layers of crystals (approximately 8.6 radiation lengths deep) with 12 crystals in each layer. The energy range is 30 MeV – 300 GeV. The crystal production comprised over 2000 crystals, of which 1536 build up the GLAST calorimeter and the rest are spare and test modules. All crystals had to pass an acceptance test. The quality control procedure included tests of optical and mechanical properties and radiation hardness. The test program was successfully developed and carried through within the given time frame. Light output was found to be within 10 % for more than 1800 crystals. Light output tapering could be made within the desired range for all crystals. Mechanical dimensions were held within ±0.3 mm. All data well met the design goals for GLAST. During production of flight crystals small sample crystals were irradiated using a hot 60 Co gamma source to verify the material’s radiation hardness. Correlation tests of full-sized crystals using both gamma rays and 180 MeV proton irradiation showed an accurate correspondence to the degradation of a sample crystal. The average light yield loss of a sample crystal after the specified total dose of 100 Gy was 12 %. All crystal boules were found to be well within the specified requirement of no more than 50 % light loss. An assembly of 48 crystals arranged in 8 layers of six crystals each was tested in an accelerated particle beam at CERN in order to verify the shower reconstruction capability of the GLAST LAT calorimeter. The crystals, wrap- ping material and read-out photo diodes were identical with flight specifications. The test calorimeter was calibrated with muons and shower reconstruction was performed with electron beams with energies of 20, 50, 80 and 120 GeV. The required performance of the GLAST calorimeter was specified to have an energy resolution σ of maximum 20 % (for photons) in the tested energy range, position resolution σ (for muons) better than 1.5 cm and angular resolution σ (for muons) better than 15 · cos^2 θ degrees (with θ being the off-axis angle). The analysis of the prototype calorimeter showed that the energy resolution σ could be made better than 13 %, the position resolution σ (for showers) was of the order of a few mm, both along the longitudinal axis of the crystal and transverse, and the angular resolution σ (for showers) was better than 1 degree.
Physically cross-linked PVA-quaternized chitosan-Ag NPs composite hydrogel membranes for potential topical wound healing applications: Synthesis, physicochemical properties, and in vitro bioevaluation

Physically cross-linked composite hydrogel membranes composed of different ratios of polyvinyl alcohol- (PVA-) grafted modified chitosan (Cs) with glycidyltrimethylammonium chloride (GTMAC) loaded with Ag nanoparticles as an active ingredient were synthesized by the freezing-thawing (F-T) cycle technique. F-T cycles were conducted repetitively three times to guarantee PVA-Cs chains entanglement occurring. The reactants, membrane composition, and cross-linking process were verified and characterized by several instrumental analyses. The physicochemical properties of the PVA-Cs-g-GTMAC hydrogel membrane, such as swelling ratio, mechanical properties, gel fraction % (GF %), hydrolytic degradation, and thermal stability, were discussed in detail. The results revealed that, with increasing of the Cs-g-GTMAC content in the hydrogel membranes, the swelling ratio, mechanical properties, and hydrolytic degradation of the cross-linked membranes increased clearly; however, GF % decreased progressively. Furthermore, in order to assess in vitro bioevaluation of the tested composite membranes, e.g
Higher order generalized geometric polynomials

According to generalized Mellin derivative (Kargin), we introduce a new family of polynomials called higher order generalized geometric polynomials. We obtain some properties of them.We discuss their connections to degenerate Bernoulli and Euler polynomials. Furthermore, we find new formulas for the Carlitz's (Carlitz) and Howard's (Howard2) finite sums. Finally, we evaluate several series in closed forms, one of which has the coefficients include values of the Riemann zeta function. Moreover, we calculate some integrals in terms of generalized geometric polynomials.
Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach

We consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a $3$-dimensional Bessel process. Considering the successive hitting times of two, three, and four fixed levels by these random walks yields non-trivial identities that involve higher-order Bernoulli and Euler polynomials.