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Consider a quantum cat map M associated with a matrix A ∈ Sp (2 n , Z) , which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of M on any nonempty open set in the position–frequency space satisfies a lower bound which is uniform in the semiclassical limit, under two assumptions: (1) there is a unique simple eigenvalue of A of largest absolute value and (2) the characteristic polynomial of A is irreducible over the rationals. This is similar to previous work (Dyatlov and Jin in Acta Math 220(2):297–339, 2018; Dyatlov et al. in J Am Math Soc 35(2):361–465, 2022) on negatively curved surfaces and (Schwartz in The full delocalization of eigenstates for the quantized cat map, 2021) on quantum cat maps with n = 1 , but this paper gives the first results of this type which apply in any dimension. When condition (2) fails we provide a weaker version of the result and discuss relations to existing counterexamples. We also obtain corresponding statements regarding semiclassical measures and damped quantum cat maps. [ABSTRACT FROM AUTHOR]

The spectral radius ρ (A) is the maximum absolute value of the eigenvalues of a matrix A. In this paper, we establish some relationship between the spectral radius of a symmetric matrix and its principal submatrices, i.e., if A is partitioned as a 2 × 2 block matrix A = ( 0 A 12 A 21 A 22 ) , then ρ (A) 2 ≤ ρ 2 2 + θ ⁎ , where θ ⁎ is the largest real root of the equation μ 2 = (x − ν) 2 (ρ 2 2 + x) and ρ 2 = ρ (A 22) , μ = ρ (A 12 A 22 A 21) , ν = ρ (A 12 A 21). Furthermore, the results are used to obtain several upper bounds of the spectral radius of graphs, which strengthen or improve some known results. [ABSTRACT FROM AUTHOR]

Newton-type methods have been successfully applied to solve the absolute value equation Ax − |x| = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix [A − I, A + I] is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs. [ABSTRACT FROM AUTHOR]

In this paper, Mg 2.3 Y 0.1 Ni + x wt.% graphene (x = 1, 3, 5, 7) composite hydrogen storage alloys were fabricated by mechanical ball milling of Mg 2.3 Y 0.1 Ni alloy powder and graphene. The experimental results show that the phases of the composite alloy consist mainly of Mg 2 Ni, Mg, MgNi 2 and Ni 3 Y phases, and graphene tends to be distributed at the edges of the alloy, increasing the phase boundary resulting from the contact between the C-boundary and the Mg 2.3 Y 0.1 Ni alloy, providing more channels for the diffusion of H 2. In which 7 wt.% of graphene is added, the gestation period of the composite alloy completely disappears. And the ball-milled alloy with 3 wt.% graphene at different temperatures has the highest hydrogen uptake in 2 min and the highest hydrogen release in 10 min. At 573 K, the composite alloy has a hydrogen absorption capacity of 3.251 wt.% H 2 in 2 min and reaches 90.21% of the maximum hydrogen absorption, while it is able to release 3.389 wt.% H 2 in 10 min and reaches 99.04% of the maximum hydrogen release. And the composite alloy with 3 wt.% graphene has the smallest dehydrogenation activation energy. The absolute value of the enthalpy change is reduced from 60.1 kJ/mol to 54.8 kJ/mol, and the desorption enthalpy change is reduced from 73.4 kJ/mol to 67.5 kJ/mol. • Addition of graphene increases the phase boundary of the composite alloy. • Graphene lowers the reaction barrier of the alloy with hydrogen. • Graphene improves the kinetics of hydrogen absorption/release of the alloy. • Graphene reduces the thermodynamic stability of composite alloys. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to present new q-parametrized Hermite–Hadamard-like type integral inequalities for functions whose third quantum derivatives in absolute values are s-convex and  (α , m) -convex, respectively. Two new q-integral identities are presented for three time q-differentiable functions. These lemmas are used like basic elements in our proofs, along with several important tools like q-power mean inequality, and q-Holder's inequality. In a special case, a non-trivial example is considered for a specific parameter and this case illustrates the investigated results. We make links between these findings and several previous discoveries from the literature. [ABSTRACT FROM AUTHOR]

Lateral roots, including adventitious roots, are the main component of rapeseed roots with support, absorb, and synthesis functions and their morphological parameters directly affecting the plant's aboveground growth and yield. Root biomass, as a material base for lateral root growth, can be used as a link between plant phenotypes and their physiological processes, as well as to enhance root 3D growth model mechanisms and accuracy. To quantify the relationships between lateral root morphological indices and the corresponding organ biomass for rapeseed, we used two cultivars, NY 22 (conventional) and NZ 1818 (hybrid), and conducted cultivar and fertilizing cylindrical tube experiments during the 2016–2019, with two fertilizer levels, no fertilizer, and 180 kg N ha−1 fertilizer. The lateral root biomass and morphological parameters were determined during the whole growth period. The biomass‐based lateral root morphological parameter models were developed by analyzing the quantitative relationship between the lateral root morphological indices and their corresponding biomass, and the descriptive models were verified with independent experimental data. The results showed that the correlation (r) of simulated and observed values for the lateral root morphological parameters are all greater than 0.9 with significant levels at p < 0.001. The absolute values of the average absolute difference (da) of simulated and observed values for the lateral root length (LLR), lateral root average diameter (ADLR), lateral root surface area (SALR), and lateral root volume (VLR) are −30.408 cm, −0.003 mm, 12.902 cm2, and 0.039 cm3, respectively. The RMSE values are 175.183 cm, 0.010 mm, 59.710 cm2, and 1.513 cm3, respectively. The ratio of da to the average observed values (dap) for the LLR and VLR are all less than 5%, and the ADLR and SALR are all <6%. The models developed in this paper have good performance and reliability for predicting lateral root morphological parameters of rapeseed. The study provides a mechanistic method for linking the rapeseed growth model with the morphological model using corresponding organic biomass and laying a good foundation for establishing a 3D morphological model for rapeseed root system based on biomass. [ABSTRACT FROM AUTHOR]

Let M n be the space of real matrices of order n. The sign-real spectral radius ξ : M n → R + , introduced in a 1997 paper by S.M. Rump, intervenes for instance in the problem of estimating the componentwise distance to singularity. The function ξ has also a bearing in the analysis of generalized absolute value equations and linear complementarity problems. Although ξ is not a norm, it is at least absolutely homogeneous and continuous. Furthermore, ξ is invariant under transposition, permutation similarity, and a few other linear isomorphisms on M n. A matrix A ∈ M n is called sign-real expansive if ξ (A) ≥ 1. Let Ω n be the set of such matrices. The purpose of this work is to discover new properties of the function ξ and to explore in detail the structure of the set Ω n. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph. The Seidel energy of G , denoted by E s (G) , is the sum of absolute values of all Seidel eigenvalues of G. A complete r -partite graph with n vertices is called r -partite Turán graph, denoted by T (n , r) , if the number of vertices of each part is either ⌊ n r ⌋ or ⌈ n r ⌉. In 2021, Tian et al. proposed a problem that for any edge e of Turán graph T (n , r) with r ≥ 4 , does there exist a sufficiently large integer n 0 such that E s (T (n , r)) < E s (T (n , r) − e) whenever n ≥ n 0 . In this paper, we prove that the Seidel energy of T (n , 5) of order n ≥ 5 is always increased when an edge is deleted. [ABSTRACT FROM AUTHOR]

In this paper, a simple, sensitive, and precise flow injection system was optimized and applied to ascorbic acid determination with a carbon paste electrode modified with the Schiff base copper complex. The modified sensor showed increased sensitivity toward ascorbic acid oxidation with a decrease of oxidation potential by 200 mV. Under optimized flow parameters, working potential, gasket thickness, sample and reaction coil volumes, and flow rate, the developed flow system gave a linear response from 5 to 75 μmol/L of ascorbic acid. The calculated limit of detection was 4.5 μmol/L, calculated as 3σ/s which corresponds to the absolute value of 40 ng for the 50 μL sample coil. The precision for six consecutive injections of 5 and 75 μmol/L ascorbic acid solutions was determined as a relative standard deviation of 5.8 % and 1.5 %, respectively. The flow injection system enabled up to 120 analyses per hour. An optimized flow system was applied to the determination of ascorbic acid in dietary supplements, after simple preparation. [ABSTRACT FROM AUTHOR]

This paper describes penumbra supersonic downflows (PSDs), which can be observed using the Hinode spectropolarimeter. The map obtained from red wing wavelengths at the half of line depth of the Fe I λ 6302 Å line makes it easy to detect these flows. They represent visible fragments of penumbral filaments as they turn sharply before entering the deep layers at the junction of the penumbra and the undisturbed photosphere. The PSD regions observed in this way are a part of the penumbral region where magnetic field lines bend relative to the plane parallel to the spectrometer's aperture and experience polarity reversal of the longitudinal field. The polarity reversal zone is clearly visible on the map constructed from the values of signed net circular polarization (sNCP), i.e., the NCP values multiplied by the sign of the field. The region where the sNCP changes sign is characterized by elevated values of line-of-sight velocities, measured from the center of gravity of the circular polarization absolute value. In most cases, PSDs are observed on the limb side of the penumbra. On the side of the solar disk center, PSDs can be detected by other means, in particular, a map can be constructed from the positions of the centers of gravity of the red lobe in the linear polarization profile. Such a map also clearly shows the moat flow region. [ABSTRACT FROM AUTHOR]

This paper presents an Accounting and Valuation (AV) method within the scope of Integrated Resource Planning (IRP) to analyze social impacts when implementing new energy resources. The method is based on a critical analysis from existing assessments regarding the IRP and its design is based on algorithms that convert qualitative information of social attributes into absolute values. These values feed the subsequent stages of the IRP to select the best energy resource (among available options) to be implemented. The method has been applied and tested as a pilot case in a rural region in Peru. This work provides extremely valuable information for decision-makers to assess, with real and quantitative data, investment decisions regarding energy planning. [ABSTRACT FROM AUTHOR]

A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for it. In addition, we provide a numerical approach using the R language to fit a multivariate folded normal distribution. The accuracy of the estimated mean and variance parameters is then examined. Finally, a real data application to body mass index data are presented. [ABSTRACT FROM AUTHOR]

In the process of coal preparation, large particles are often misplaced into the flotation feedings due to poor classification, and thus bring about negative effects on flotation results. In this paper, batch flotation tests of 0.5–2.5 mm were carried out at different reagent dosage to quantitatively analyze the effect of particle size and density on flotation. Flotation partition curves in corresponding conditions were plotted based on sizing analysis and float-and-sink tests of flotation products. Generalized skew-normal distribution model based on quartile was used to fit the experimental data and the variation rules of separation density, probable error and skewness, etc. with particle size and reagents were obtained, and the density-size partition surface mathematical model was established. The results show that floating ratio decreases with density and particle size. The separation density and probable error both decreases with particle size. The values of skewness were negative and tended to 0 with the decreasing of particle size. As the dosage of reagents increased, the separation density increased, the probable error increased slightly, and the difference of absolute values of skewness decreased. The research results put forward the theoretical instruction of expanding the upper limit of floatable size of particles and improving flotation efficiency. [ABSTRACT FROM AUTHOR]

This study was conducted to provide reference for plant landscaping, optimization of planting structure and rational allocation of species in Cedrus deodcua gardens. [Methods] With three common garden plants in northern China, Trifolium repens L, Poa pralensis L and Trifolium pralense L, as receptors, the effects of four concentrations ( 0.025, 0. 05, 0.075 and 0.10 g/ml) of C. deodara needle extract on seed germination and early seedling growth of the three turf grasses were studied by the Petri dish filter paper method, using a clear water treatment ( 0 g/ml) as control check (CK). Data were subjected to analysis of variance ( ANOVA) and multiple comparisons (Duncan) using SPSS16. 0. [Results] Different concentrations of C. deodcua needle extract had significant inhibitory effects on seed germination, radicle and seedling height growth of T. repens, T. pratense and P. pratensis ( P < 0.05 ), and the inhibitory effects increased with the increase of concentration. When the concentration reached 0. 075 g/ ml, seed germination and seedling growth of T. repens stopped, and radicle and seedling growth of T. pratense and P. pralensis also stopped. When the concentration was equal to 0.10 g/ ml, germination of T. pralense and P. pralensis seeds was inhibited, and the absolute values of allelopathic index was the largest, that is, the inhibitory effects were the largest. And with the increase of concentration, the absolute value of synthetical allelopathic index also increased. The extract of C. deodcua needles contained main allelochemicals leading to the scarcity of understory vegetation. [Conclusions] This study provides a theoretical basis for reasonable garden plant configuration during C. deodara greening and garden landscaping. [ABSTRACT FROM AUTHOR]

Polishing force is a critical process parameter in the polishing process, and its magnitude has a great impact on surface integrity, polishing temperature, and polishing efficiency. At present, there is a lack of research on the polishing force of the abrasive cloth flap wheel (ACFW). In order to more accurately predict the value of polishing force for the ACFW, this paper proposes a modeling method of polishing force for the ACFW based on elastic–plastic contact theory. Firstly, this paper makes the statistical analysis of the protrusion height of abrasive grains (PHAGS) and proposes a calculation method of the contact number of active abrasive grains (CNABGS) for the ACFW based on the probability distribution theory and the flexible polishing principle of the ACFW. Secondly, according to the elastic–plastic contact theory, the interaction process between single abrasive grains and the workpiece is analyzed, and the mean polishing force model of single abrasive grains is developed. Finally, the polishing force model of the ACFW was obtained by combining the calculation method of the CNABGS and the mean polishing force model of the single abrasive grain, and the model was verified by polishing experiments. The experimental results showed that the relative mean percentage error between the measured and predicted values of polishing force was 13.31%, and the maximum value of the absolute error was 0.59, which proved that the polishing force model of the ACFW is reliable and accurate. [ABSTRACT FROM AUTHOR]

Ground contact time (GCT) is one of the most relevant factors when assessing running performance in sports practice. In recent years, inertial measurement units (IMUs) have been widely used to automatically evaluate GCT, since they can be used in field conditions and are friendly and easy to wear devices. In this paper we describe the results of a systematic search, using the Web of Science, to assess what reliable options are available to GCT estimation using inertial sensors. Our analysis reveals that estimation of GCT from the upper body (upper back and upper arm) has rarely been addressed. Proper estimation of GCT from these locations could permit an extension of the analysis of running performance to the public, where users, especially vocational runners, usually wear pockets that are ideal to hold sensing devices fitted with inertial sensors (or even using their own cell phones for that purpose). Therefore, in the second part of the paper, an experimental study is described. Six subjects, both amateur and semi-elite runners, were recruited for the experiments, and ran on a treadmill at different paces to estimate GCT from inertial sensors placed at the foot (for validation purposes), the upper arm, and upper back. Initial and final foot contact events were identified in these signals to estimate the GCT per step, and compared to times estimated from an optical MOCAP (Optitrack), used as the ground truth. We found an average error in GCT estimation of 0.01 s in absolute value using the foot and the upper back IMU, and of 0.05 s using the upper arm IMU. Limits of agreement (LoA, 1.96 times the standard deviation) were [−0.01 s, 0.04 s], [−0.04 s, 0.02 s], and [0.0 s, 0.1 s] using the sensors on the foot, the upper back, and the upper arm, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we first study exponential sums of the form ∑ x ∈ F q ψ (f (x)) χ (g (x)) called hybrid character sums, where f , g are functions over finite field F q , ψ is a nontrivial multiplicative character and χ is a nontrivial additive character of F q. The absolute values or explicit values of them are determined under certain conditions. We then present several constructions of complex codebooks which are also called frames. The proposed codebooks are constructed from Hadamard matrices with binary row selection sequences. The hybrid character sums play an important role in determining the maximum magnitude of the inner products between vectors in these codebooks. It is proved that the magnitude of the inner products between distinct code vectors of each codebook is two-valued, and the maximum magnitude of each codebook asymptotically achieves the Welch bound equality. The constructed codebooks are equivalent to nearly equiangular tight frames and have nice application in compressed sensing matrices. [ABSTRACT FROM AUTHOR]

The clarity evaluation function plays a vital role in the autofocus technique. The accuracy and efficiency of the image clarity evaluation function directly affects the accuracy of autofocus and the speed of focusing. However, classical clarity function values are sensitive to changes in background brightness and changes in object contour length. This paper proposes a normalized absolute values adaptive (NAVA) evaluation function of image clarity. It can eliminate the influence of changes in background brightness and the length of the measured object contour on the image clarity function value. To verify the effectiveness of the NAVA function, several experiments were conducted under conditions of virtual master gear images and actual captured images. For actual captured images, the variation of the evaluation results of the NAVA function is far less than the corresponding variation of the classic clarity function. Compared with classical clarity evaluation functions, the NAVA function can provide normalized absolute clarity values. The correlations between the NAVA function results of image clarity and both the contour length and background brightness of the tested object are weak. The use of the NAVA function in automatic and manual focusing systems can further improve focusing efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a study on the temperature dependent photo-elastic coefficient in single-crystal silicon with (100) and (110) orientations at a wavelength of 1550 nm. The measurement of the photo-elastic coefficient was performed using a polarimetric scheme across a wide temperature range from 5 to 300 K. The experimental setup employed high-sensitivity techniques and incorporated automatic beam path correction, ensuring precise and accurate determination of the coefficient's values. The results show excellent agreement with previous measurements at room temperature, specifically yielding a value of d n / d σ = - 2.463 × 10 - 11 1/Pa for the (100) orientation. Interestingly, there is a significant difference in photo-elasticity between the different crystal orientations of approximately 50 % . The photo-elastic coefficient's absolute value increases by approximately 40% with decreasing temperature down to 5 K. These findings provide valuable insights into the photo-elastic properties of silicon and its behavior under varying mechanical stress, particularly relevant for optomechanical precision experiments like cryogenic gravitational wave detectors and microscale optomechanical quantum sensors. [ABSTRACT FROM AUTHOR]

In the Alcubierre warp-drive spacetime, we investigate the following scalar curvature invariants: the scalar I, derived from a quadratic contraction of the Weyl tensor, the trace R of the Ricci tensor, and the quadratic r1 and cubic r2 invariants from the trace-adjusted Ricci tensor. In four-dimensional spacetime the trace-adjusted Einstein and Ricci tensors are identical, and their unadjusted traces are oppositely signed yet equal in absolute value. This allows us to express these Ricci invariants using Einstein's curvature tensor, facilitating a direct interpretation of the energy-momentum tensor. We present detailed plots illustrating the distribution of these invariants. Our findings underscore the requirement for four distinct layers of an anisotropic stress-energy tensor to create the warp bubble. Additionally, we delve into the Kretschmann quadratic invariant decomposition. We provide a critical analysis of the work by Mattingly et al., particularly their underrepresentation of curvature invariants in their plots by 8 to 16 orders of magnitude. A comparison is made between the spacetime curvature of the Alcubierre warp-drive and that of a Schwarzschild black hole with a mass equivalent to the planet Saturn. The paper addresses potential misconceptions about the Alcubierre warp-drive due to inaccuracies in representing spacetime curvature changes and clarifies the classification of the Alcubierre spacetime, emphasizing its distinction from class B warped product spacetimes. [ABSTRACT FROM AUTHOR]

This paper presents a method for detecting a crack in simply supported beams by identifying its location and severity (depth). The method is based on the measured natural frequencies for several bending vibration modes of an intact and cracked beam and the Particle Swarm Optimization (PSO). To explain the approach, we calculate the relative frequency shifts (RFS) for eight vibration modes for all possible damage cases. To this aim, we use a mathematical relation deduced in previous research. Next, we monitor the natural frequencies, and in case of arising changes, we calculate the RFSs. We subtract, separately for all modes, the measured RFSs from all calculated RFSs. Considering the absolute values the subtractions achieve, we obtain eight surfaces that achieve elevation zero if the calculated and measured RFSs coincide. The zero-elevation points form curves with different shapes for the different vibration modes. The intersection of these curves, thus the location where all surfaces have zero elevation, indicates the damage location and severity. Adding the elevation values of the eight surfaces point by point, we obtain a new surface that has two points (due to symmetry) with zero elevation. The coordinates of these points indicate the damage parameters. We use the generated surface as an objective function and find the coordinates of the minima involving PSO. Using this method, we accurately identified the damage location and severity. [ABSTRACT FROM AUTHOR]

The global perspective presented here is built on earlier papers discussing the dynamics of the upper branch of the Hadley cell in the two solsticial seasons. The role of the tropics is made explicit in a conceptual model that is presented and evaluated. The fluctuation of deep tropical convection in longitude and time is seen as crucial. The filamentary outflows from such convective events move westward and across the equator deep into the winter hemisphere. The horizontal tilt of the cross-equatorial flow implies a significant upper-tropospheric flux of westerly momentum from the winter tropics to the summer hemisphere. These properties are related to the cross-equatorial propagation of wave activity triggered by deep tropical convection in the summer hemisphere. The filaments carry with them near-equatorial values of absolute vorticity and potential vorticity. After turning anticyclonically, some filaments move eastward and poleward to the equatorial edge of the winter subtropical jet. There is strong evidence they can interact with the eddies on this jet and enhance their poleward westerly momentum flux. In the global perspective, tropical and extratropical systems and the interaction between them are all important for the dynamics of the upper branch of the Hadley cell. significance statement: The Hadley cell is the large-scale overturning in the atmosphere with air in the upper troposphere moving from the equatorial region to near 30° in the winter hemisphere. In the standard view it is midlatitude weather systems that are responsible for removing angular momentum from this upper branch of the Hadley cell. Here it is proposed that tropical systems and their interaction with the midlatitude systems are also important. Insight into the role of the tropics in the dynamics of the Hadley cell can be obtained by considering it as the sum of many events of active deep convection occurring in different longitudes and at different times. [ABSTRACT FROM AUTHOR]

In this paper, we consider the tensor absolute value equations (TAVEs). When one tensor is row diagonal with odd order, we show that the TAVEs can be reduced to an algebraic equation; when it is row diagonal and nonsingular with even order, we prove that the TAVEs is equivalent to a polynomial complementary problem. When no tensor is row diagonal, we formulate the TAVEs equivalently as polynomial optimization problems in two different ways. Each of them can be solved by Lasserre's hierarchy of semideflnite relaxations. The finite convergence properties are also discussed. Numerical experiments show the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, by transforming the vertical linear complementarity problem (VLCP) as a certain absolute value equation, we design a class of modulus-based matrix splitting iteration methods for solving the VLCP. The convergence properties of the proposed methods are discussed in depth. By making use of some numerical experiments, we confirm the efficiency of the proposed methods. Numerical results show that the proposed methods are superior to the classical modulus-based matrix splitting iteration methods. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time and fixed-time bipartite consensus tracking (FFBCT) problems for multi-agent systems (MASs) , in which both cooperative and competition exist. Using Lyapunov stability methods, distributed nonlinear protocols are provided to ensure all agents reach agreement. Its absolute value is the same but it might be different in direction. Besides, the second protocol can make the system reach bipartite consensus in fixed time regardless of the initial state of agents. Moreover, boundaries for settling times are estimated. Some numerical examples are finally presented to prove the validity of our designs. [ABSTRACT FROM AUTHOR]

The energy of a graph is defined as the sum of absolute values of all eigenvalues of its adjacency matrix. For a nonempty graph G , S. Akbari, A. Alazemi, M. Andelić and M.A. Hosseinzadeh proposed a conjecture: The energy of the line graph of G is at least | E (G) | + Δ (G) − 3 , where E (G) is the edge set of G and Δ (G) is the maximum degree of G. In this paper, we give a proof confirming the conjecture, and present a lower bound and an upper bound for the energy of line graphs of regular graphs. [ABSTRACT FROM AUTHOR]

The goal of this paper is to find a formula through which we find all the values of the plithogenic functions. we found this formula and proved it, in addition to providing a definition of the exponential, logarithmic, trigonometric plithogenic function. Also, the absolute value of the plithogenic number was defined. [ABSTRACT FROM AUTHOR]

Jointed rocks under local load are ubiquitous in civil engineering. The instability and failure of jointed rocks are fatal to engineering safety. This paper numerically investigated the effects of loading area and joint angle on the strength dividing points, energy evolution, and crack distribution characteristics of non-persistent jointed rocks. The results demonstrated that the closer the absolute value of joint angle to 45° and the smaller the loading area, the lower the strength dividing points of rocks. The curves of rock joint angle versus total energy at peak and of elastic energy versus amplitude of post-peak abrupt energy change render a W-shape distribution. Meanwhile, compared with joint angle, loading area has more influence on rock energy input. The larger the loading area, the higher the crack fractal dimension, the crack entropy, and the penetration rate. Tensile cracks outnumber shear cracks when jointed rocks are damaged, and shear cracks increases significantly at the post-peak stage. [ABSTRACT FROM AUTHOR]

This paper gives a criterion for the existence of a stationary solution for a class of semilinear stochastic functional differential equations with additive white noise and its global stability. Under the condition that the global Lipschitz constant of nonlinear term f is less than the absolute value of the top Lyapunov exponent for the linear flow Φ with f being monotone or anti-monotone, and the time delay is not very big, we show that the infinite-dimensional stochastic flow possesses a unique globally attracting random equilibrium in the state space of continuous functions, which produces the globally stable stationary solution. Compared to the result of Jiang and Lv (2016) [24] , we remove the assumption of boundedness for f. [ABSTRACT FROM AUTHOR]

In this paper, the representability of the generalized Student's distribution as uniform and normal-scale mixtures is considered. It is also shown that the generalized Burr and the Snedecor–Fisher distributions can be represented as the scale mixtures of uniform, folded normal, exponential, Weibull or Fréchet distributions. New multiplication-type theorems are proven for these and related distributions. The relation between the generalized Student and generalized Burr distribution is studied. It is shown that the Snedecor–Fisher distribution is a special case of the generalized Burr distribution. Based on these mixture representations, some limit theorems are proven for random sums in which the symmetric and asymmetric generalized Student or symmetric and asymmetric two-sided generalized Burr distributions are limit laws. Also, limit theorems are proven for maximum and minimum random sums and absolute values of random sums in which the generalized Burr distributions are limit laws. [ABSTRACT FROM AUTHOR]

In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually using Lyapunov functions. In the application of Lyapunov functions, we need appropriate inequalities for the fractional derivatives of these functions. In this paper, we consider several Riemann–Liouville types of fractional derivatives and prove inequalities for derivatives of convex Lyapunov functions. In particular, we consider the classical Riemann–Liouville fractional derivative, the Riemann–Liouville fractional derivative with respect to a function, the tempered Riemann–Liouville fractional derivative, and the tempered Riemann–Liouville fractional derivative with respect to a function. We discuss their relations and their basic properties, as well as the connection between them. We prove inequalities for Lyapunov functions from a special class, and this special class of functions is similar to the class of convex functions of many variables. Note that, in the literature, the most common Lyapunov functions are the quadratic ones and the absolute value ones, which are included in the studied class. As a result, special cases of our inequalities include Lyapunov functions given by absolute values, quadratic ones, and exponential ones with the above given four types of fractional derivatives. These results are useful in studying types of stability of the solutions of differential equations with the above-mentioned types of fractional derivatives. To illustrate the application of our inequalities, we define Mittag–Leffler stability in time on an interval excluding the initial time point. Several stability criteria are obtained. [ABSTRACT FROM AUTHOR]

Spectral conjugate gradient (SCG) methods are combinations of spectral gradient method and conjugate gradient (CG) methods, which have been well studied in Euclidean space. In this paper, we aim to extend this class of methods to solve optimization problems on Riemannian manifolds. Firstly, we present a Riemannian version of the spectral parameter, which guarantees that the search direction always satisfies the sufficient descent property without the help of any line search strategy. Secondly, we introduce a generic algorithmic framework for the Riemannian SCG methods, in which the selection of the CG parameter is very flexible. Under the Riemannian Wolfe conditions, the global convergence of the proposed algorithmic framework is established whenever the absolute value of the CG parameter is no more than the Riemannian Fletcher–Reeves CG parameter. Finally, some preliminary numerical results are reported and compared with several classical Riemannian CG methods, which show that our new methods are efficient. [ABSTRACT FROM AUTHOR]

A node is a structurally balanced (respectively, unbalanced) node if and only if the absolute value of its corresponding entry in the right eigenvector associated with the zero eigenvalue of the Laplacian matrix is equal to (respectively, is less than) one. The corresponding entry in the right eigenvector is called the algebraic trait for the structurally balanced property of a node. This paper aims to explore the algebraic trait for the structurally balanced property of a node under a signed digraph with a spanning tree by using a geometric-based method. Such a geometric point of view reveals the relationships of the links in a network for structurally balanced and structurally unbalanced nodes. The structurally balanced property of a node is determined by its parent nodes, and the connections between itself and its parent nodes. First of all, a hierarchical structure of its parent nodes is proposed, based on which the Laplacian matrix of the underlying topology can be written as a lower triangular matrix. Then, according to the lower triangular Laplacian matrix, the mathematical expression of the right eigenvector associated with the zero eigenvalue is derived. Based on this, as well as the definition of the structurally balanced node, the algebraic trait for the structurally balanced property of a node is obtained. Finally, a numerical example is provided to verify theoretical results. [ABSTRACT FROM AUTHOR]

The existing research on gesture classification has mainly focused on larger amplitudes. However, studying subtle movements is essential to achieving precise control of prosthetics or manipulators. This paper proposes a refined recognition method for finger and arm movements. Ten-finger and ten-arm movements were designed for subtle classification, respectively. Features extracted from the time domain, frequency domain, and time-frequency domain included Mean Absolute Value (MAV), Fast Fourier Transform (FFT), and Hilbert-Huang Transform (HHT). The study compares the effects of seven types of feature combinations and uses five classification algorithms to predict results. The combination of "FFT+HHT" yielded better results, and the linear discriminant analysis algorithm achieved better prediction accuracy. This research has significant implications for the precise control of robots or prosthetics and proper rehabilitation in later stages. [ABSTRACT FROM AUTHOR]

We study ground states of attractive Bose gases, which are confined in a harmonic trap V (x) = x 1 2 + Λ x 2 2 ( Λ ≥ 1 ) rotating at the velocity Ω . For any 0 ≤ Ω < Ω ∗ : = 2 , where Ω ∗ is called a critical rotational velocity, it is well known that ground states exist if and only if a < a ∗ for some critical constant 0 < a ∗ < ∞ , where a > 0 denotes the product for the number of particles times the absolute value of the scattering length. In this paper, we consider the critical rotating case, where the rotational velocity Ω = Ω ∗ , to study the existence and non-existence of ground states with respect to a > 0 . As imposed in Remark 2.2 of Lewin et al. (Blow-up profile of rotating 2D focusing bose gases. macroscopic limits of quantum systems, Springer, Berlin, 2018), we also analyze the limiting behavior of ground states as a ↗ a ∗ for the case where Ω = Ω a : = Ω ∗ 1 - C 0 (a ∗ - a) m ↗ Ω ∗ , 0 ≤ m < 1 2 and 0 < C 0 < 1 . [ABSTRACT FROM AUTHOR]

Graceful labeling of a graph G with q edges is assigned the labels for its vertices by some integers from the set {0,1, 2, …, q}, such that no two vertices received the same label, where each edge is assigned the absolute value of the difference between the labels of its end vertices and the resulting edge labeling running from 1 to q inclusive. An edge labeling of a graph G is called vertex anntimagic, if all vertex weights are pairwise distinct, where the vertex weight of a vertex under an edge labeling is the sum of the label of all edges incident with that vertex. In this paper, we address the problem of finding graceful antimagic labelin for split of the star graph k1,n k2,n graph, p2+ kn graph, jellyfish graph jn,n Dragon graph T3,n kite graph (T4,n) and the double comb graph Dcon. [ABSTRACT FROM AUTHOR]

Migration acts as a growth driver for urban agglomerations, posing a difficult methodological task of its statistical accounting as well as further assessment of migration's impact on the economy of agglomerations. The paper analyzes the contribution of migration to the change in population during the intercensal interval 2010-2021 in 20 urban agglomerations of Russia identified as promising centers of economic growth by the Russian Federation Government Decree "On Approval of the Spatial Development Strategy of the Russian Federation for the period until 2025". The study showed that the most underestimated net migration rate was demonstrated by the agglomerations of Krasnodar, distantly followed by Krasnoyarsk and the capitals (Moscow and Saint Petersburg). The leader in terms of the absolute value of unrecorded migration is the Moscow agglomeration. In Nizhny Novgorod and Perm agglomerations, indirect assessment of net migration showed that migration balance was overestimated as per the registered migration data. The identified differences in the volume of net migration between the two sources indicate the unreliability of the data, thus questioning in some urban agglomerations the alignment of the demographic potential with economic development goals. [ABSTRACT FROM AUTHOR]

The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph G is called reciprocal if 1/≥ is an eigenvalue of G whenever λ is an eigenvalue of G. Further, if λ and 1 λ have the same multiplicities, for each eigenvalue λ, then it is called strong reciprocal. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631{633), it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree ∞(G) whose adjacency matrix is non-singular, E(G) λ Δ(G) + ∞(G) and the equality holds if and only if G is a complete graph. Here, we prove the validity of this conjecture for some strong reciprocal graphs. Moreover, we show that if G is a strong reciprocal graph, then E(G) λ Δ(G) + ∞(G) - 1 2. Recently, it has been proved that if G is a reciprocal graph of order n and its spectral radius, ?, is at least 4λmin, where λmin is the smallest absolute value of eigenvalues of G, then E(G) λ n + 1 2. In this paper, we extend this result to almost all strong reciprocal graphs without the mentioned assumption. [ABSTRACT FROM AUTHOR]

The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important applications, including coherent diffraction imaging and audio processing. It is a classical result that for suitable windows any function can, in principle, be uniquely recovered up to a global phase factor from its spectrogram. However, for most practical applications only discrete samples--typically from a lattice--of the spectrogram are available. This raises the question of whether lattice samples of the spectrogram contain sufficient information for determining a function f Є L²(Rd) up to a global phase factor. In the present paper, we answer this question in the negative by providing general nonidentifiability results which lead to a non-uniqueness theory for the sampled STFT phase retrieval problem. Precisely, given any dimension d, any window function g, and any (symplectic or separable) lattice L < Rd, we construct pairs of functions f,h Є L²(Rd) that do not agree up to a global phase factor, but whose spectrograms agree on L. Our techniques are sufficiently flexible to produce counterexamples to unique recoverability under even more stringent assumptions; for example, if the window function is real-valued, the functions f,h can even be chosen to satisfy | f| =| h|. Our results thus reveal the non-existence of a critical sampling density in the absence of phase information, a property which is in stark contrast to uniqueness results in time-frequency analysis. [ABSTRACT FROM AUTHOR]

In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory Appl 169:705–712, 2016). [ABSTRACT FROM AUTHOR]

Strengthening environmental regulation (Reg) is an important measure to solve energy and environmental problems, then to realize the profit sustainable growth (Gro). Taking 116 listed renewable energy enterprises in China from 2010 to 2019 as samples, this paper uses FE and SYS-GMM models to examine the moderating effect of three types of Reg in the relationship of factor market distortions (Dist) and the Gro. The conclusions are as follows: For the direct impact, capital and labor market distortions (DistK and DistL) hinder the Gro. Specifically, the absolute value of the coefficient of DistK in state-owned enterprises (SOEs) is greater than that of the DistL, which indicates that the inhibitory effect of DistK in SOEs is more significant. For the indirect impact, the coefficients of economic and supervised environmental regulation (RegE and RegS) are positive and significant, and promote the Gro of SOEs and non-SOEs, while legal environmental regulation (RegL) is the opposite, which shows that Reg has significant "cost effect" and "rebound effect". Moreover, Reg has a positive moderating effect, which is mainly reflected in SOEs, and alleviates the inhibitory effect of DistK and DistL on Gro to a certain extent. Finally, this paper puts forward some targeted policy suggestions. [ABSTRACT FROM AUTHOR]

A new class of statistics obtained by ordering the absolute values of the observations arising from absolutely continuous distributions which are symmetrically distributed about zero is introduced in this paper. The statistics generated by the above method are named as absolved order statistics (AOS) of the given sample. The association of the distribution of these statistics with the distribution of order statistics arising from the folded form of the parental density about zero is outlined. The vector of AOS is proved to be a minimal sufficient statistic for the class F θ (1) of all absolutely continuous distributions which are symmetrically distributed about zero. A method of estimation of the scale parameter of any distribution belonging to F θ (1) using AOS is described. Illustration on the advantage of the above method of estimation is described for the distributions such as (i) logistic, (ii) normal, and (iii) double Weibull. A more realistic censoring scheme involving AOS as well is discussed in this paper. We have derived the U-statistic estimator based on AOS for the scale parameter σ of any distribution f (x , σ) ∈ F θ (1) using the best linear unbiased estimate (BLUE) based on AOS of a preliminary sample as kernel. We have illustrated the performance of this estimator with an U-statistic generated from BLUE based on order statistics for each of (i) logistic (ii) normal and (iii) double Weibull distributions. [ABSTRACT FROM AUTHOR]

This paper describes MEM and MEM4PP as new Stata tools and commands. They support the automatic reporting and selection of the best regression and classification models by adding supplemental performance metrics based on statistical post-estimation and custom computation. In particular, MEM provides helpful metrics, such as the maximum acceptable variance inflation factor (maxAcceptVIF) together with the maximum computed variance inflation factor (maxComputVIF) for ordinary least squares (OLS) regression, the maximum absolute value of the correlation coefficient in the predictors' correlation matrix (maxAbsVPMCC), the area under the curve of receiving operator characteristics (AUC-ROC), p and chi-squared of the goodness-of-fit (GOF) test for logit and probit, and also the maximum probability thresholds (maxProbNlogPenultThrsh and maxProbNlogLastThrsh) from Zlotnik and Abraira risk-prediction nomograms (nomolog) for logistic regressions. This new tool also performs the automatic identification of the list of variables if run after most regression commands. After simple successive invocations of MEM (in a.do file acting as a batch file), the collectible results are produced in the console or exported to specially designated files (one.csv for all models in a batch). MEM4PP is MEM's version for parallel processing. It starts from the same batch (the same.do file with its path provided as a parameter) and triggers different instances of Stata to parallelly generate the same results (one.csv for each model in a batch). The paper also includes some examples using real-world data from the World Values Survey (the evidence between 1981 and 2020, version number 1.6). They help us understand how MEM and MEM4PP support the testing of predictor independence, reverse causality checks, the best model selection starting from such metrics, and, ultimately, the replication of all these steps. [ABSTRACT FROM AUTHOR]

The digital beamforming synthetic aperture radar (DBF-SAR) is proposed by scholars as a promising solution to overcome the constraint of the minimum antenna area of the traditional single-channel SAR to achieve high resolution and wide swath (HRWS) by scan-on-receive (SCORE) in the elevation multiple channel. However, the inevitable channel imbalance between the elevation channels of DBF-SAR will degrade the DBF-SAR image quality. In this paper, we present a method to estimate the sampling time delay error, amplitude error and phase error based on the external calibration data. For the sampling time delay deviation, we adopt to calculate the statistical average of the position deviation of several external calibration points in the reference channel image with that of the error channel image. To avoid noise interference, we image the DBF-SAR original echo-carrying amplitude information to obtain the amplitude error between channels by dividing the absolute values of the complex image data of the error channel. Due to the phase error between channels, the image contrast will decrease. Therefore, the problem of estimating the phase error can be transformed into the problem of maximizing the image contrast. So, in this paper, we use the gradient descent method to optimally estimate the phase error. Finally, the effectiveness of the method is verified by the simulation of airborne measured data and simulation data. [ABSTRACT FROM AUTHOR]

No shale-rock physical model has been established in the observation coordinate system. To this end, this paper carried out anisotropic wave velocity tests on shale rock and compared the Thomsen, Daley, and Berryman solutions to characterize anisotropic acoustic wave velocity. Finally, the Daley solution was selected. Based on basic rock physical models, such as SCA and DEM methods, and combined with the Daley solution, an anisotropic shalerock physical model was established in the observation coordinate system and applied in Well B1 in the Luzhou area, Sichuan Basin. Our research conclusions were as follows: 1. for the samples from the same core, the P-wave velocities in three directions were in the order VP11 >VP45 >VP33, shear-wave velocity VS11 was the largest, but VS33 and VS45 did not follow the law of Vs33 >Vs45 for some samples; 2. the Daley solution, which not only considers the accuracy requirements but also has a complete expression of P-, SV-, and SH-waves, is most suitable for characterization of anisotropic wave velocity in this study area; 3. the rock physical model constructed in the observation coordinate system has high accuracy, in which the absolute value of the relative error of the P-wave slowness was between 0% and 5.05% (0.55% on average), and that of shear-wave slowness was between 0% and 6.05% (0.59% on average); 4. the acoustic waves recorded in Well B1 in the observation coordinate system were very different from those in the constitutive coordinate system. The relative difference of the P-wave was between 6.76% and 30.84% (14.68% on average), and that of the S-wave was between 7.00% and 23.44% (13.99% on average). The acoustic slowness measured in the observation coordinate system, such as in a deviated well or a horizontal well section, must be converted to the constitutive coordinate system before it can be used in subsequent engineering applications; 5. the anisotropic shale-rock physical model built in the observation coordinate system proposed in this paper can provide basic data and guidance for subsequent pore pressure prediction, geomechanical modeling, and fracturing stimulation design for deviated and horizontal wells. [ABSTRACT FROM AUTHOR]

Process steam is an important product in the industrial sector but the traditional steam boiler will lead to tremendous fossil fuel consumption and carbon emissions. The non-concentrating solar collectors have a huge potential for process steam generation but their application potential has not been fully explored. In this paper, a high-efficient evacuated flat plate solar collector used for direct steam generation is proposed. Its thermal performance in both direct steam generation mode and pressurization water mode is presented via experiment test and a validated numerical model. The results indicate that the direct steam generation mode can obtain a 10% enhancement (absolute value) of the thermal efficiency compared with the pressurization water mode. The thermal radiant losses of the solar collector can be suppressed and the heat transfer coefficient of the working fluid can also be elevated. Furthermore, a dual-mode evacuated flat plate solar system is proposed to produce thermal energy for space heating in the heating season and generate steam in the non-heating season, thereby solving the solar seasonal mismatch problem for the traditional solar thermal heating system. The comparison with the state-of-the-art study manifests that the dual-mode system proposed in this paper has better performance all year round. [Display omitted] [ABSTRACT FROM AUTHOR]

The object of research in the paper is the process of fluid transfer through the pore space of the reservoir rock. In this paper, using an expert method, the shortcomings of the Ukrainian methodology for assessing the reservoir properties of the reservoir were highlighted. In particular, the sources of uncertainty accumulation in determining the absolute values of the reservoir’s filtration parameters have been identified. The existing problem is that the algorithms of actions, which are the basis of the Ukrainian method of assessing reservoir properties, introduce a significant degree of uncertainty into the assessment results. In order to reduce uncertainty, the introduction of the concept of a representative elemental volume is considered when conducting laboratory research and the construction of a three-dimensional digital model of this elementary volume. It is suggested to improve the Ukrainian method of assessing the collector properties of the deposit based on current Western research. It was established that the standard methods of assessing the reservoir properties of the deposit are a source of accumulation of uncertainty in the development of technological documentation for the development of the deposit. The work is aimed at the development of an improved methodology for assessing the collector properties of the deposit. It is proposed to add to the action algorithm the stage of determining the representative volume of the sample, building its three-dimensional model, and digitizing it. At the final stage, the connectivity of the pores inside the sample is determined using the Minkowski function to improve the quality of the project documentation for the development of deposits. Guidelines have been developed to improve standard methods for assessing the collector properties of the deposit. The use of an improved methodology for assessing the reservoir properties of the deposit leads to a significantly lower degree of uncertainty and helps to form a more reliable picture of the operation of the reservoir at the design stage of its development. The presented study will be useful for the engineering personnel of foreign contractor companies, as it justifies the need to collect additional core material and sets the quality criteria of the information obtained about the collector properties of the deposit. [ABSTRACT FROM AUTHOR]

The stress state of a fault plane influences the mode of sliding and characteristics of slide behaviour. Existing researchers have mainly focused on studying the effect of shear stiffness on fault behaviour under the constant normal load (CNL) boundary conditions. However, the impact of the normal stiffness effect of deep faults on fault sliding stability and seismic source parameters remains uncertain. Addressing the issue, this paper conducts friction tests on granite-simulated faults under the constant normal stiffness (CNS) boundary conditions. It analyzes the impact of normal stiffness on the mechanical behaviour of fault sliding. The results of this paper demonstrate the following findings: (1) Under both normal boundary conditions, various sliding modes occur, including creep-slip, chaotic stick-slip, regular inclusion chaotic stick-slip, and regular stick-slip. (2) The normal stiffness effect reduces the duration of creep-slip and chaotic stick-slip behaviour and decreases the frequency of regular inclusion chaotic stick-slip behaviour. (3) Shear stress and normal stress of the regular stick-slip mode exhibit periodic changes under the CNS boundary conditions. (4) Compared to the CNL boundary conditions, the CNS boundary conditions show a larger shear stress drop and a positive correlation between the normal stress drop and normal stiffness. (5) The CNS boundary conditions result in larger shear stiffness, the absolute value of stick-slip stiffness, characteristic sliding displacement, and fracture energy compared to the relevant seismic source parameters of the CNL boundary conditions. These parameters display positive correlations with normal stiffness. The stick-slip period and normal stiffness initially decrease and then increase, while the normal displacement drop and normal stiffness display a negative correlation trend. These analyses provide comprehensive insights into the mechanical characteristics of fault-slip behaviour and can contribute to improving models and predictions related to fault-sliding behaviour and seismic activity. • We discover a new fault-slip pattern known as regular inclusion chaotic stick-slip. • The normal stiffness effect shortens the duration of fault-slip behaviour. • Under CNS condition, the shear and normal stress exhibit synchronous changes. • The values of seismic source parameters tend to be larger for the CNS condition. [ABSTRACT FROM AUTHOR]