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We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3–7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states. [ABSTRACT FROM AUTHOR]

A new implementation of the orbital-based two-component relativistic configuration interaction approach is reported and applied to calculations of the electronic g-shifts of three diatomic radicals: AlO, HgF, and PdH. The new implementation augments efficient routines for the calculation of nonrelativistic Hamiltonians with new vectorized routines for the calculation of the action of the one-electron spin–orbit operator and allows efficient calculations for the expansion of generalized active space type. The program makes full use of double group as well as time-reversal symmetry. Particle–hole reorganization of the operators is used to improve the efficiency for expansions with nearly fully occupied orbital spaces. The flexibility of the algorithm and program is used to investigate the convergence of electronic g-shifts for the three diatomic radicals as functions of the active space, states included in the orbital optimization, and excitation levels. It was possible to converge to the valence limits within a few percent using expansions containing up to quadruple excitations. However, when excitations from the core orbitals were added, it was not possible to demonstrate convergence to within a few percent with expansions containing at most 10 × 109 determinants. [ABSTRACT FROM AUTHOR]

Summary: Traditional electric drive control methodologies, such as field oriented control (FOC) and direct torque and flux control (DTFC), predominantly rely on multiple proportional‐integral (PI) controllers that demand complex tuning. While model predictive current control (MPCC) omits PI controllers, it has inherent challenges including high computational burden and tempered dynamics. Although two‐level inverters (2LI) are prevalent in many applications, their performance wanes in high‐power applications like high performance industrial drives and marine propulsions. Multilevel inverters (MLIs) are more efficient, but combined with space vector modulation (SVM), they add computational complexity, particularly at higher levels, limiting drive sampling frequencies and causing torque ripples and harmonics, affecting performance. To address the above drawbacks, this manuscript presents a deadbeat predictive current control of five‐level inverter fed permanent magnet synchronous motor (PMSM) drive with a novel generalized SVM algorithm with reduced computational burden and improved performance. The proposed method is validated through MATLAB/Simulink‐based simulation study and experimental implementation. The results are presented and discussed. The results are compared with DTFC and MPCC where it is observed that the proposed method offers superior performance with reduced computational burden and streamlined implementation. [ABSTRACT FROM AUTHOR]

We consider evolutionary equations with fractional differentiation operators whose restrictions to certain spaces of type S coincide with pseudodifferential operators constructed on the basis of smooth symbols, which are multipliers in these spaces. We establish the well-posedness of the time-nonlocal multipoint problem for these equations with initial function, which is an element of the space of generalized functions of the ultradistribution type. It is shown that the solutions of these problems stabilize to zero in the spaces of generalized functions of the type S′ (weak stabilization) and also stabilize to zero uniformly on R in the case where the initial generalized function has a bounded support. [ABSTRACT FROM AUTHOR]

This manuscript aims to study the existence and uniqueness of solutions to a new system of differential equations. This system is a mixture of fractional operators and stochastic variables. The study has been completed under nonlocal functional boundary conditions. In the study, we used the fixed-point method to examine the existence of a solution to the proposed system, mainly focusing on the theorems of Leray, Schauder, and Perov in generalized metric spaces. Finally, an example has been provided to support and underscore our results. [ABSTRACT FROM AUTHOR]

The application of wire arc additive manufacturing (WAAM) for the production of large size components is currently limited, due to strong distortion and unprecise filling behavior. The resulting geometric and metallurgical irregularities pose a challenge to the process. The current approach of a layered structure cannot be adopted without adjustments when using wire arc additive manufacturing. Reasons include incompleteness, material accumulation and deformation. The combination of experimental weld geometry‐determination and its numerical estimation is presented here as solution to this challenge. The procedure is based on the measurement of a weld bead cross‐section‐area. By convolution of a path matrix with a weld‐geometry‐function, the planned path is filled with the seam geometry. Subsequent summation of multiple matrices results in a height profile showing discontinuities and accumulations. Further validation tests show a good agreement between the method and experimentally determined problem areas. The presented optimisation procedure can be extended with material parameters. A local compensation for deformation can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications in physics. [ABSTRACT FROM AUTHOR]

The aim of the paper is to propose design tools for pile groups when vertical and moment loads are applied simultaneously. This is done by presenting a method to derive the exact solution for the failure locus in the generalized force space, including a vertical load and a moment with components along two axes, to employ for capacity requirements which helps to get rid of overconservative assumptions usually adopted in design. Moreover, closed-form solutions for performance-based interaction domains are also provided allowing to detect all the combinations of external loads associated with a given value of settlement and/or rotation of the foundation that is extremely useful when the design is ruled by serviceability requirements. The application of these straightforward formulae provides results which are in very good agreement with the more rigorous solutions derived from a numerical procedure developed ad hoc for the problem at hand. [ABSTRACT FROM AUTHOR]

The significant importance of the Nile River emerges not only from the fact that it represents the main water source for Egypt but also from its being an important water path for sailing to transport goods or for Nile tourism cruises. Because of climate change and the construction of the Ethiopian Renaissance Dam, Egypt may have to reduce the discharges from the High Aswan Dam (HAD), which may cause a reduction in water depth below a safe level for navigation. Consequently, this study aims to present a quasi-real-time approach to detect the locations of bottlenecks that threat navigation path via mobile Google Maps. Accordingly, the topographic, hydraulic data, the alignment and geometry of the navigational channel, were collected from the Ministry of Water Resources and Irrigation of Egypt. AutoCAD Civil 3d is adopted in this study to determine navigational bottleneck locations of the Nile River's first reach. Two surface models were created: The Riverbed surface and the navigational path surface using a Triangular Irregular Network (TIN). As a result of the created TIN-Surface modelling via the current study; the amount of sediment, that should be dredged, was estimated (at about 2.1 million.m³). In addition, the navigation path bottlenecks map for the studied reach was created based on minimum water levels at Aswan High Dam's winter closure and the navigational path's geometry. In conclusion, this study provides a simple solution for avoiding bottlenecks by presenting a user-friendly web Google Maps of these locations to represent the Nile River's current navigation condition in quasi-real-time and support the decision-maker on river navigation conditions. [ABSTRACT FROM AUTHOR]

We offer a systematic study of generalized sober spaces. [ABSTRACT FROM AUTHOR]

Suppose $ \alpha >-1 $ α > − 1 and $ 1\leq p \leq \infty $ 1 ≤ p ≤ ∞. Let $ f=\mathcal {P}_{\alpha }[F] $ f = P α [ F ] be an α-harmonic mapping on $ {\mathbb D} $ D with the boundary F being absolute continuous and $ \dot {F}\in L^p(0,2\pi) $ F ˙ ∈ L p (0 , 2 π) , where $ \dot {F}({\rm e}^{i\theta }):=\frac {{\rm d}}{{\rm d}\theta }F({\rm e}^{i\theta }) $ F ˙ (e iθ) := d d θ F (e iθ). In this paper, we investigate the membership of $ f_z $ f z and $ f_{\bar {z}} $ f z ¯ in the space $ \mathcal {H}_{\mathcal {G}}^{p}(\mathbb {D}) $ H G p (D) , the generalized Hardy space. We prove, if $ \alpha >0 $ α > 0 , then both $ f_z $ f z and $ f_{\bar {z}} $ f z ¯ are in $ \mathcal {H}_{\mathcal {G}}^{p}(\mathbb {D}) $ H G p (D). If $ \alpha α < 0 , then $ f_z $ f z and $ f_{\bar {z}}\in \mathcal {H}_{\mathcal {G}}^{p}(\mathbb {D}) $ f z ¯ ∈ H G p (D) if and only if f is analytic. Finally, we investigate a Schwarz Lemma for α-harmonic functions. [ABSTRACT FROM AUTHOR]

We prove two rigidity results on holomorphic isometries into homogeneous Kähler manifolds. The first shows that a Kähler-Ricci soliton induced by the homogeneous metric of the Kähler product of a special generalized flag manifold (i.e. a flag of classical type or integral type) with a bounded homogeneous domain is trivial, i.e. Kähler-Einstein. In the second one we prove that: (i) a flat space is not relative to the Kähler product of a special generalized flag manifold with a homogeneous bounded domain, (ii) a special generalized flag manifold is not relative to the Kähler product of a flat space with a homogeneous bounded domain and (iii) a homogeneous bounded domain is not relative to the Kähler product of a flat space with a special generalized flag manifold. Our theorems strongly extend the results of Cheng and Hao [Ann. Global Anal. Geom. 60 (2021), pp. 167–180], Cheng, Di Scala, and Yuan [Internat. J. Math. 28 (2017), p. 1750027], Loi and Mossa [Proc. Amer. Math. Soc. 149 (2021), pp. 4931–4941], Loi and Mossa [Proc. Amer. Math. Soc. 151 (2023), pp. 3975–3984] and Umehara [Tokyo J. Math. 10 (1987), pp. 203–214]. [ABSTRACT FROM AUTHOR]

The aim of this paper is to explore a Schrödinger equation that incorporates a higher‐order operator. Traditional models for electron dynamics have utilized a second‐order diffusion Schrödinger equation, where oscillatory behavior is achieved through complex domain formulations. Incorporating a higher‐order operator enables the induction of oscillatory spatial patterns in solutions. Our analysis initiates with a variational formulation within generalized spaces, facilitating the examination of solution boundedness. Subsequently, we delve into the oscillatory characteristics of solutions, drawing upon a series of lemmas originally applied to the Kuramoto–Sivashinsky equation, the Cahn–Hilliard equation, and other equations that employ higher‐order operators. Specific solution types, such as standing waves, are numerically investigated to illustrate the oscillatory spatial patterns. The discussion then extends to the theory of traveling waves to establish general conditions for positive solutions. A contribution of this work is the precise evaluation of a critical traveling wave speed, denoted as c∗$$ {c}&#x0005E;{\ast } $$, above which the first minimum remains positive. For values of the traveling wave speed c$$ c $$ significantly greater than c∗$$ {c}&#x0005E;{\ast } $$, the solutions can be entirely positive. [ABSTRACT FROM AUTHOR]

For a finite group G, Frobenius found a formula for the values of the function ∑IrrG(dim π)−s for even integers s, where IrrG is the set of irreducible representations of G. We generalize this formula to the relative case: for a subgroup H, we find a formula for the values of the function ∑IrrG(dim π)−s(dim πH)−t. We apply our results to compute the E-polynomials of Fock–Goncharov spaces and to relate the Gelfand property to the geometry of generalized Fock–Goncharov spaces. [ABSTRACT FROM AUTHOR]

In this paper, wavelet transform on a generalized helix space curves are investigated, including of local continuous wavelet transform at some point and discrete wavelet transform on a class of helix curves. Firstly, a class of helix space curves are introduced and the parameter equations are given. Then the dilation operator and translation on the function ψ (ξ 0) is properly defined by the local projection at some point from a space curve on the unit sphere onto its tangent line. The local continuous wavelet transform and its reconstruction formula are deduced at some point of a space curve on the unit sphere. On the other hand, According to the discretization of length-preserving projection, discrete wavelet transform is lifted onto a helix space curve, such as a circular helix curve. Based on length-preserving projection, the some properties are discussed, such as two-scale sequences of scaling function and wavelet, orthogonality, decomposition formula and so on. Finally, two examples are given for our discussion. One example is illustrating the application of local continuous wavelet transform at some point of a space curve. The result shows the signal at some point of a space curve can be reconstructed by local continuous wavelet method. The norm of the error is 0.3783 between original signal and reconstructed signal in this example. The other numerical example is given for decomposing and reconstructing with the signal on a circular helix curve. The result shows the signal on a helix space curve can be decomposed and reconstructed by the length-preserving projection. The norm of the error is 8.0741 × 10−11 between original signal and reconstructed signal. The figures are shown for the simulation results. [ABSTRACT FROM AUTHOR]

This article introduces a measure of noncompactness in the generalized Morrey space. We study the applications of our new definition in investigating the conditions for the existence of solutions for systems of nonlinear integral equations. We can extend many useful theorems in L p (R N) for functions belonging to the generalized Morrey spaces. Compared to the L p (R N) spaces, the advantage of studying in the Morrey spaces is that we can research no compact support functions in our problems. Finally, significant examples are presented to show the efficiency of the main results. [ABSTRACT FROM AUTHOR]

Using q-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their q-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative. [ABSTRACT FROM AUTHOR]

Approach to fuzzy differential equations in fuzzy metrics using generalized contraction theorems One of the most fascinating fields of mathematical inquiry is fixed point. In this direction, by utilizing "the triangular property of fuzzy metric", we investigate certain special common fixed point solutions for a pair of self mappings without continuity on fuzzy metric spaces under the generalized contra ction requirements. We also provide generalized Ciri's contraction theorems and weak contraction theorems. The findings are corroborated by pertinent cases. Additionally, we provide a workable application of the fuzzy differential equation s to guarantee the presence of a singular common solution to support our primary research. [ABSTRACT FROM AUTHOR]

In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS (Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, $ \sim _{1} $ ∼ 1 -complemented and $ \sim _{2} $ ∼ 2 -complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics. [ABSTRACT FROM AUTHOR]

As an important part of the text-to-speech (TTS) system, vocoders convert acoustic features into speech waveforms. The difference in vocoders is key to producing different types of forged speech in the TTS system. With the rapid development of general adversarial networks (GANs), an increasing number of GAN vocoders have been proposed. Detectors often encounter vocoders of unknown types, which leads to a decline in the generalization performance of models. However, existing studies lack research on detection generalization based on GAN vocoders. To solve this problem, this study proposes vocoder detection of spoofed speech based on GAN fingerprints and domain generalization. The framework can widen the distance between real speech and forged speech in feature space, improving the detection model's performance. Specifically, we utilize a fingerprint extractor based on an autoencoder to extract GAN fingerprints from vocoders. We then weight them to the forged speech for subsequent classification to learn the forged speech features with high differentiation. Subsequently, domain generalization is used to further improve the generalization ability of the model for unseen forgery types. We achieve domain generalization using domain-adversarial learning and asymmetric triplet loss to learn a better generalized feature space in which real speech is compact and forged speech synthesized by different vocoders is dispersed. Finally, to optimize the training process, curriculum learning is used to dynamically adjust the contributions of the samples with different difficulties in the training process. Experimental results show that the proposed method achieves the most advanced detection results among four GAN vocoders. The code is available at https://github.com/multimedia-infomation-security/GAN-Vocoder-detection. [ABSTRACT FROM AUTHOR]

If Γ is a subalgebra of A , then an A -module is called a Harish-Chandra module if it is the direct sum of its generalized weight spaces with respect to Γ. Drozd, Futorny, and Ovsienko [4] defined a generalization of a central subalgebra called a Harish-Chandra subalgebra and showed that when Γ is a Harish-Chandra subalgebra of A the structure of Harish-Chandra A -modules can be described using information about the relationship between A and the cofinite maximal ideals of Γ. We extend the results of [4] by dropping the assumption that Γ is quasicommutative. We facilitate this by introducing an equivalence relation ∼ on the set cfs (Γ) of cofinite maximal ideals of Γ. We define Harish-Chandra block modules with respect to ∼ to be A -modules that are the direct sum of so called block spaces corresponding to the equivalence classes cfs (Γ) / ∼. If Γ is a Harish-Chandra block subalgebra of A with respect to ∼, then the structure of Harish-Chandra block modules can be described based on the relationship between A and cfs (Γ) / ∼. In particular, we give a decomposition of the category of Harish-Chandra block modules and the collection of isomorphism classes of irreducible Harish-Chandra block modules. Furthermore, we define a category A on cfs (Γ) / ∼ , and show the category of profinite A -modules is equivalent to the category of Harish-Chandra block modules. Taking Γ to be noetherian and quasicommutative, and ∼ to be the equality relation, we recover (in fact, a slight refinement of) results from [4]. Lastly, we provide a sufficient condition for when there are a finite number of isomorphism classes of simple Harish-Chandra block modules with a given support. [ABSTRACT FROM AUTHOR]

Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic comparisons between spacings of GOSs from one sample, as well as two samples, are developed under the more general assumptions on the parameters of the model. Specifically, the given results deal with the likelihood ratio order, the hazard rate order and the mean residual life order. Finally, an application is demonstrated for sequential systems. [ABSTRACT FROM AUTHOR]

We study generalized Morrey spaces ℳ φ , p (ℝ d) and Besov–Morrey spaces related to them. These spaces appear quite naturally in connection with the study of PDE or to characterize boundedness of certain integral operators. Here, we study unboundedness properties of functions belonging to those spaces in terms of their growth envelopes. This concept has been studied and applied successfully for a variety of smoothness spaces already. Surprisingly, for the generalized Morrey spaces we arrive at three possible cases only, i.e. boundedness, the L p -behavior or the proper Morrey behavior. These cases are characterized in terms of the limit of φ (t) and t − d / p φ (t) as t → 0 + and t → ∞ , respectively. For the generalized Besov–Morrey spaces the limit of t − d / p φ (t) as t → 0 + also plays a rôle. [ABSTRACT FROM AUTHOR]

The present research introduces a novel concept termed "neutrosophic fuzzy metric space", which extends the traditional metric space framework by incorporating the notion of neutrosophic fuzzy sets. A thorough investigation of various structural and topological properties within this newly proposed generalization of metric space has been conducted. Additionally, counterparts of well-known theorems such as the Uniform Convergence Theorem and the Baire Category Theorem have been established for this generalized metric space. Through rigorous analysis, a detailed understanding of its fundamental characteristics has been attained, illuminating its potential applications and theoretical significance. [ABSTRACT FROM AUTHOR]

In this paper, we find a necessary and sufficient condition for a non-zero vector to be a geodesic vector in homogeneous generalized m-Kropina space. Further, we prove the existence of at least one homogeneous geodesic. However, it is conjectured that the outcomes and proofs in the case of Finsler geometry are not ideal, since general Finsler metrics are non-reversible. In Finsler geometry, the trajectory of unique homogeneous geodesic should be regarded as two geodesics with initial vectors X and -X. Hence, we construct an (n + 1)-dimensional and a 4-dimensional space to find homogeneous geodesics explicitly. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a random coupled system with multiple fractional derivatives of ψ-Caputo of different orders subject to non-local integral and boundary condition and proves the uniqueness of random solution by applying random versions of the Pervo fixed point theorem. while the existence of solutions is derived by a random version of a Krasnoselskii-type fixed point theorem. Also, we study the Hyers-Ulam stability of the proposed problem. Obtained results are illustrated by an example. [ABSTRACT FROM AUTHOR]

We consider generalized magnetohydrodynamics (MHD) equations in ℝd(d≥2)$$ {\mathrm{\mathbb{R}}}&amp;amp;#x0005E;d\kern0.1em \left(d\ge 2\right) $$ with fractional diffusions νΛ2αu$$ \nu {\Lambda}&amp;amp;#x0005E;{2\alpha }u $$ and ηΛ2βb$$ \eta {\Lambda}&amp;amp;#x0005E;{2\beta }b $$ for the velocity u$$ u $$ and magnetic field b$$ b $$, respectively, where α,β,ν,η$$ \alpha, \beta, \nu, \eta $$ are nonnegative constants and Λs=(−Δ)s/2$$ {\Lambda}&amp;amp;#x0005E;s&amp;amp;#x0003D;{\left(-\Delta \right)}&amp;amp;#x0005E;{s/2} $$ is the fractional Laplacian of order s$$ s $$. Using the smoothing effect of Λs$$ {\Lambda}&amp;amp;#x0005E;s $$ for any s>0$$ s&amp;gt;0 $$, we establish local existence results for the generalized MHD equations when the initial data (u0,b0)$$ \left({u}_0,{b}_0\right) $$ belong to Hs1×Hs2$$ {H}&amp;amp;#x0005E;{s_1}\times {H}&amp;amp;#x0005E;{s_2} $$ with possibly different orders s1$$ {s}_1 $$ and s2$$ {s}_2 $$. Here, Hs=Hs(ℝd)$$ {H}&amp;amp;#x0005E;s&amp;amp;#x0003D;{H}&amp;amp;#x0005E;s\left({\mathrm{\mathbb{R}}}&amp;amp;#x0005E;d\right) $$ denotes the standard L2$$ {L}&amp;amp;#x0005E;2 $$‐based Sobolev space on ℝd$$ {\mathrm{\mathbb{R}}}&amp;amp;#x0005E;d $$ of order s$$ s $$. To prove our existence results, we also derive new product and commutator estimates in fractional Sobolev spaces Hs$$ {H}&amp;amp;#x0005E;s $$ which are of independent interest in themselves. [ABSTRACT FROM AUTHOR]

We characterize the boundedness and compactness of dual Toeplitz operators on the orthogonal complement of the generalized Fock space. We study the problem when the finite sum of the dual Toeplitz products is compact. Additionally, we also consider when the sum of the dual Toeplitz operators is equal to another dual Toeplitz operator. [ABSTRACT FROM AUTHOR]

Lack of biomimicry in geometry and flow conditions of emissions systems for analytical testing and biological exposure has led to fundamental limitations, including a poor understanding of dose delivered to specific airway locations. This work characterizes mass distribution of a JUUL® brand e-cigarette in a Biomimetic Aerosol Exposure System (BAES). A combination of mass balance, direct measurements, and inferences based on direct measurements were used to characterize regional and local dose as a function of system flow path configuration and emissions topography profile. Doses produced by the emissions topography profile with only puffing were significantly different from profiles with clean air inhalation following puffs. Mass characterization results support that dose can be manipulated using flow path geometry. Local and regional deposition was mapped throughout the system. We estimate the fraction of yield to the mouth deposited at several locations throughout the system for a variety of puffing and respiration topographies and show that emissions topography profile and system flow path geometry affect dose. This work provides proof-of-concept for assessing mass distribution as a function of aerosol generator (e-cigarette product), user airway geometry, and inhalation and puffing topography. [ABSTRACT FROM AUTHOR]

Rough set theory is an advanced uncertainty tool that is capable of processing sophisticated real-world data satisfactorily. Rough approximation operators are used to determine the confirmed and possible data that can be obtained by using subsets. Numerous rough approximation models, inspired by neighborhood systems, have been proposed in earlier studies for satisfying axioms of Pawlak approximation spaces (P-approximation spaces) and improving the accuracy measures. This work provides a formulation a novel type of generalized approximation spaces (G-approximation spaces) based on new neighborhood systems inspired by Ij-neighborhoods and ideal structures. The originated G-approximation spaces are offered to fulfill the axiomatic requirements of P-approximation spaces and give more information based on the data subsets under study. That is, they are real simulations of the P-approximation spaces and provide more accurate decisions than the previous models. Several examples are provided to compare the suggested G-approximation spaces with existing ones. To illustrate the application potentiality and efficiency of the provided approach, a numerical example for Chikungunya disease is presented. Ultimately, we conclude our study with a summary and direction for further research. [ABSTRACT FROM AUTHOR]

This paper explores different notions of extreme states on operator systems and on operator spaces. We prove that boundary points of the generalized state space of an operator system in finite dimensions are precisely the restrictions of boundary representations of the generated C ∗ -algebra. We study weak TRO-extreme states on operator spaces in ternary rings of operators as a non self-adjoint version of C ∗ -extreme states on operator systems in C ∗ -algebras. Rectangular boundary point for a rectangular matrix convex set is introduced and its connection with boundary representations of the associated operator space is established in finite dimensional setting. Also, we show that the set of all rectangular boundary points is the minimal spanning set for a compact rectangular matrix convex set in finite dimensions. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain the results on the degree of convergence of an H$$ H $$‐periodic continuous function in generalized Hölder spaces using Hausdorff operator with monotonically non‐decreasing and monotonically non‐increasing rows of its hexagonal Fourier series. Some important corollaries are also deduced from our main theorems. Applications of main theorems are also obtained in this paper. [ABSTRACT FROM AUTHOR]

We propose an efficient and robust multiscale preconditioner for large-scale incompressible flow in highly heterogeneous porous media. We start from the discretization of the first-order form for the single phase incompressible flow and apply a velocity elimination strategy to obtain an equation with pressure as the only unknown. Then an efficient preconditioner is designed to solve this equation. The key component of the preconditioner is the adoption of a nonstandard coarse space that contains the media's heterogeneity information. We solve a carefully constructed spectral problem in each coarse element to form the nonstandard coarse space. Then a rigorous convergence analysis for the proposed two-grid algorithm is carried out where the key ingredients lie in the smoothing property of the ILU(0) smoother and the approximation property. In particular, our analysis shows that our preconditioner is robust and efficient thanks to this newly constructed coarse space. Rich numerical tests with several types of large-scale, three-dimensional, highly heterogeneous permeability fields with resolutions up to 1024³ are presented. The experimental results show that our generalized multiscale space--based preconditioner is robust with respect to the contrast, size, and geometry of the permeability fields. Moreover, the complexity of the preconditioner is close to O(Dof). We also successfully apply this preconditioner for multiphase flow simulation and transport problems arising from reservoir simulation. [ABSTRACT FROM AUTHOR]

In this paper, we give necessary and sufficient conditions for a continuous on $ \mathbb R_+ $ R + function f to belong the symmetric generalized Lipschitz classes defined by the Mellin translation in terms of growth or decay of some integrals connected with the Mellin transform. The results are counterparts of ones for classical Lipschitz classes and the classical (complex) Fourier transform obtained earlier by the author. [ABSTRACT FROM AUTHOR]

Let (X , d , μ) be an RD-space. In this paper, we prove that a bilinear generalized fractional integral T ~ α is bounded from the product of generalized Morrey spaces L φ 1 , p 1 (X) × L φ 2 , p 2 (X) into spaces L φ , q (X) , and it is also bounded from the product of spaces L φ 1 , p 1 (X) × L φ 2 , p 2 (X) into generalized weak Morrey spaces W L φ , q (X) , where the Lebesgue measurable functions φ 1 , φ 2 and φ satisfy certain conditions and φ 1 φ 2 = φ , α ∈ (0 , 1) and 1 q = 1 p 1 + 1 p 2 - 2 α for 1 < p 1 , p 2 < 1 α . Furthermore, we establish the boundedness of the commutator T ~ α , b 1 , b 2 formed by b 1 , b 2 ∈ BMO (X) (or Lip β (X)) and T ~ α on spaces L φ , q (X) and on spaces W L φ , q (X) . As applications, we show that the T ~ α and its commutator T ~ α , b 1 , b 2 are bounded on grand generalized Morrey spaces L θ , φ , p) (X) over (X , d , μ) . [ABSTRACT FROM AUTHOR]

Many applications from computational mathematics can be identified for a system of non-linear equations in more generalized Banach spaces. Analytical methods do not exist for solving these type of equations, and so we solve these equations using iterative methods. We introduced a new numerical technique for finding the roots of non-linear equations in Banach space. The method is tenth-order and it is an extension of the fifth-order method which is developed by Arroyo et.al. [1]. We provided a convergence analysis to demonstrate that the method exhibits tenth-order convergence. Also, we discussed the local convergence properties of the suggested method which depends on the fundamental supposition that the first-order Fréchet derivative of the involved function Υ satisfies the Lipschitz conditions. This new approach is not only an extension of prior research, but also establishes a theoretical concept of the radius of convergence. We validated the efficacy of our method through various numerical examples. Our method is comparable with the methods of Tao Y et al. [2]. We also compared it with higher-order iterative methods, and we observed that it either performs similarly or better for the numerical examples. We also gave the basin of attraction to demonstrate the behaviour in the complex plane. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define bipolar soft generalized compact sets and bipolar soft generalized compact spaces. The structures of -centralized bipolar soft generalized closed sets collection in a bipolar soft generalized compact space are given. Moreover, some main properties of bipolar soft generalized compactness are discussed and their relationships are studied. The concept of a bipolar soft generalized compactness is introduced and it investigates under what condition a bipolar soft generalized topological space forms a bipolar soft generalized compact space. The relation between bipolar soft generalized compact space and soft generalized compact space is proposed. Furthermore, some further properties of bipolar soft mappings, such as bipolar soft composite mappings, are presented and some of their characteristics are explained. Additionally, novel classes of bipolar soft mapping such as bipolar soft generalized continuous, bipolar soft generalized open, and bipolar soft generalized closed mappings are defined. Finally, some results and counterexamples are obtained. [ABSTRACT FROM AUTHOR]

Based on the orthogonal experimental method, a simulation case of the flow field of the ejector nozzle was designed to investigate the influence of the structural parameters of the ejector nozzle on the internal and external flow. This study explored the effects of throat area, outlet area, throat position, and ejector nozzle length on the ejector flow rate ratio, thrust coefficient, and net thrust coefficient. Subsequently, flow path geometry optimization was conducted to maximize the thrust coefficient or net thrust coefficient. The results revealed that the throat area ratio and the outlet area of the ejector nozzle are the primary factors affecting the aerodynamic performance. Compared to the baseline ejector nozzle model, the optimal model for thrust coefficient exhibited a 16.333% improvement, while the optimal model for net thrust coefficient demonstrated a significant enhancement of 46.674%. [ABSTRACT FROM AUTHOR]

In this paper, we study the differentially private empirical risk minimization problem where the parameter is constrained to a Riemannian manifold. We introduce a framework for performing differentially private Riemannian optimization by adding noise to the Riemannian gradient on the tangent space. The noise follows a Gaussian distribution intrinsically defined with respect to the Riemannian metric on the tangent space. We adapt the Gaussian mechanism from the Euclidean space to the tangent space compatible to such generalized Gaussian distribution. This approach presents a novel analysis as compared to directly adding noise on the manifold. We further prove privacy guarantees of the proposed differentially private Riemannian (stochastic) gradient descent using an extension of the moments accountant technique. Overall, we provide utility guarantees under geodesic (strongly) convex, general nonconvex objectives as well as under the Riemannian Polyak-Łojasiewicz condition. Empirical results illustrate the versatility and efficacy of the proposed framework in several applications. [ABSTRACT FROM AUTHOR]

The space of generalized gradient approximation (GGA) and meta-GGA (mGGA) exchange approximations is systematically explored by training 25 new functionals to produce accurate lattice parameter, cohesive energy, and bandgap predictions. The trained functionals are used to reproduce exact constraints in a data-driven way and to understand the accuracy trade-off between the mentioned properties. The functionals are compared to notable mGGA functionals to analyze how changes in the enhancement factor maps influence the accuracy of predictions. Some of the trained functionals are found to perform on par with specialized functionals for bandgaps, while outperforming them on the other two properties. The error surface of our trained functionals can serve as a soft-limit of what mGGA functionals can achieve. [ABSTRACT FROM AUTHOR]

We analyze the influence of concentrated forces on a disk-shaped inclusion operating the conditions of smooth contact in the plane of joint of two different transversely isotropic half spaces. The problem is reduced to the Riemann boundary-value problem with respect to a part of variables in the space of generalized functions. Its solution is constructed in the explicit form, which enables us to determine the dependence of translational and circular displacements of the inclusion and the jumps of stresses and displacements on the inclusion on concentrated forces and the relationship between the elastic constants of the half spaces. We also study the influence of presence of the concentrated forces (either in a single or in both half spaces) on the translational displacements and the jumps of normal stresses for different combinations of the materials of the half spaces and the shapes of the inclusion. [ABSTRACT FROM AUTHOR]

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-per cent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (fpfs), using jax , which is publicly available as part of a new suite of analytic shear algorithms called anacal. This code can analytically calibrate the shear response of any non-linear observable constructed with the fpfs shapelets and detection modes utilizing autodifferentiation (ad), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the ad capability of jax , it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new anacal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the 10 yr LSST. For the generic shear estimator, the magnitude of the multiplicative bias | m | is below 3 × 10−3 (99.7 per cent confidence interval), and the effective galaxy number density is improved by 5 per cent . We also discuss some planned future additions to the anacal software suite to extend its applicability beyond the fpfs measurements. [ABSTRACT FROM AUTHOR]

Brownian motion on manifolds with non-trivial diffusion coefficient can be constructed by stochastic development of Euclidean Brownian motions using the fiber bundle of linear frames. We provide a comprehensive study of paths for such processes that are most probable in the sense of Onsager–Machlup, however with path probability measured on the driving Euclidean processes. We obtain both a full characterization of the resulting family of most probable paths, reduced equation systems for the path dynamics where the effect of curvature is directly identifiable, and explicit equations in special cases, including constant curvature surfaces where the coupling between curvature and covariance can be explicitly identified in the dynamics. We show how the resulting systems can be integrated numerically and use this to provide examples of most probable paths on different geometries and new algorithms for estimation of mean and infinitesimal covariance. [ABSTRACT FROM AUTHOR]

Elasto-plastic deformations of micropolar continuum are discussed by a non-Riemannian geometry. The non-locality of micropolar continuum is described in a second-order vector bundle of displacements and microrotations. With a decomposition of total elasto-plastic field, geometric quantities are divided into the elastic and plastic components independently. Especially, when an intrinsic parallelism of displacements and microrotations holds, integrability conditions of the elasto-plastic field are represented by a torsion tensor or the curvature of nonlinear connection. Then, Burgers and Frank vectors and an energy release rate around crack tips are related to the torsion tensor or the curvature of nonlinear connection. Moreover, the non-locality of microrotation is discussed based on a kink band as a disclination. It is found a generalized expression of Burgers vector which can describe the kink interface including the disclination. [ABSTRACT FROM AUTHOR]

This paper presents the energy-optimal trajectories for skid-steer rovers on hard ground, without obstacles. We obtain 29 trajectory structures that are sufficient to describe minimum-energy motion, which are enumerated and described geometrically; 28 of these structures are composed of sequences of circular arcs and straight lines; there is also a special structure called whirls consisting of different circular arcs. Our analysis identifies that the turns in the trajectory structures (aside from whirls) are all circular arcs of a particular turning radius, R′, the turning radius at which the inner wheels of a skid-steer rover are not commanded to turn. This work demonstrates its paramount importance in energy-optimal path planning. There has been a lack of analytical energy-optimal trajectory generation for skid-steer rovers, and we address this problem by a novel approach. The equivalency theorem presented in this work shows that all minimum-energy solutions follow the same path irrespective of velocity constraints that may or may not be imposed. This non-intuitive result stems from the fact that with this model of the system the total energy is fully parameterized by the geometry of the path alone. With this equivalency in mind, one can choose velocity constraints to enforce constant power consumption, thus transforming the energy-optimal problem into an equivalent time-optimal problem. Pontryagin's Minimum Principle can then be used to solve the problem. Accordingly, the extremal paths are obtained and enumerated to find the minimum-energy path. Furthermore, our experimental results by using Husky UGV provide the experimental support for the equivalency theorem. [ABSTRACT FROM AUTHOR]

Let X be a Banach space with norm ∥ ⋅ ∥ . Let A : D ⁢ (A) ⊂ X → X be an (possibly unbounded) operator that generates a uniformly bounded holomorphic semigroup. Suppose that ε > 0 and T > 0 are two given constants. The backward parabolic equation of finding a function u : [ 0 , T ] → X satisfying u t + A ⁢ u = 0 , 0 < t < T , ∥ u ⁢ (T) - φ ∥ ⩽ ε , for φ in X, is regularized by the generalized Sobolev equation u α ⁢ t + A α ⁢ u α = 0 , 0 < t < T , u α ⁢ (T) = φ , where 0 < α < 1 and A α = A ⁢ (I + α ⁢ A b ) - 1 with b ⩾ 1 . Error estimates of the method with respect to the noise level are proved. [ABSTRACT FROM AUTHOR]

In this article, we provide results on the existence and compactness of the set of solutions for a class of initial-value problem representing a first-order random impulsive differential equation. The key tool to achieve our goal is based on an alternative nonlinear Leary-Schauder type theorem in the settings of generalized Banach spaces. [ABSTRACT FROM AUTHOR]

We introduced the q-Picard, the q-Picard-Cauchy, the q-Gauss-Weierstrass, and the q-truncated Picard singular integrals. Using the last three mentioned integrals, the orders of approximation for functions from a generalized Holder space were determined, both in the Lp-norm and in the generalized Holder-norm. [ABSTRACT FROM AUTHOR]

Commercial electrical steels, Fe-Si alloys with < 4 wt.% Si, are inexpensive and efficient materials for electrical power conversion. Further efficiency improvements require increasing the silicon concentration to 6 wt.%, at which point the material becomes brittle and difficult to form by conventional rolling and sheet fabrication methods. Additive manufacturing stands to overcome challenges with commercial manufacturing techniques by leveraging near-net-shape fabrication. The wide array of process conditions provides additive manufacturing with increased flexibility, enabling control over the microstructure and mechanical properties. This work explores the microstructures and magnetic properties of ring-shaped Fe-Si alloys produced using concentric and cross-hatch tool paths on a laser-directed energy deposition additive manufacturing system. Concentric-built samples exhibit elongated grain structures while cross-hatch-built samples comprise lower aspect ratio grain structures. Thermal finite element analysis simulations model the stress conditions produced by the different scan path geometries. Microhardness measurements probe the mechanical properties as a function of anneal temperature, providing a qualitative understanding of the intergranular defect density. Soft magnetic properties measured under quasistatic and AC conditions show frequency- and microstructure-dependent coercivity and permeability. Finally, analysis of the core loss quantifies how the build strategies and thermal treatments influence efficiency in electrical power conversion applications. Understanding the influences of scan path geometry and thermal treatment provides a pathway towards application of additively manufactured soft magnetic materials. [ABSTRACT FROM AUTHOR]