Optimal with respect to accuracy methods for evaluating hypersingular integrals

In this paper we constructed optimal with respect to order quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M), Ω¯ur,γ(Ω,M), Ω=[−1,1]l, l=1,2,…,M=Const, and γ is a real positive number. The functions that belong to classes Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M) have bounded derivatives up to the rth order in domain Ω and derivatives up to the sth order (s=r+⌈γ⌉) in domain Ω∖Γ, Γ=∂Ω. Moduli of derivatives of the vth order (r<v≤s) are power functions of d(x,Γ)−1(1+|lnd(x,Γ)|), where d(x,Γ) is a distance between point x and Γ. The interest in these classes of functions is due to the fact that solutions of singular and hypersingular integral equations are their members. Moreover various physical fields, in particular gravitational and electromagnetic fields belong to these classes as well. We give definitions of optimal with respect to accuracy methods for solving hypersingular integrals. We constructed optimal with respect to order of accuracy quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M).

Differential inequality and non-oscillation of fourth order differential equation

The oscillatory theory of fourth order differential equations has not yet been developed well enough. The results are known only for the case when the coefficients of differential equations are power functions. This fact can be explained by the absence of simple effective methods for studying such higher order equations. In this paper, the authors investigate the oscillatory properties of a class of fourth order differential equations by the variational method. The presented variational method allows to consider any arbitrary functions as coefficients, and our main results depend on their boundary behavior in neighborhoods of zero and infinity. Moreover, this variational method is based on the validity of a certain weighted differential inequality of Hardy type, which is of independent interest. The authors of the article also find two-sided estimates of the least constant for this inequality, which are especially important for their applications to the main results on the oscillatory properties of these differential equations.

Intraspecific Trait Variability Determines Understorey Plant Community Assembly

Increasing evidence points to the major impact of intraspecific variability in species characteristics on community assembly. Contrasting theories predict that high trait variability might either steepening dominance orders or promote diversity. Here, we try to test these predictions with understorey plants in a Polish mixed temperate forest. We focus on four important traits (leaf dry mass LDW, plant height SH, specific leaf area SLA, and number of flowers NF) of the small balsam Impatiens parviflora, the dominant species in this forest system. We relate trait variability to community species richness and abundances, as well as to soil characteristics. The variance – mean relationships of LDW, LH, and NF, but not of SLA, closely followed power functions with slopes > 1.5. Contrary to theory, abundances but not species richness of non-I. parviflora species significantly decreased within increasing variance in I. parviflora trait expression. High trait variability prevailed a higher species richness. Trait variability did not significantly influence species composition and was not significantly correlated with soil characteristics. Our results emphasis the need to study trait variability in terms of appropriate statistical standards as provided by the allometric variance - mean relationship. We argue that an individual based study of local trait variability might return important insights into the composition and assembly of local communities.

A Feasibility Study of Low Cement Content Foamed Concrete Using High Volume of Waste Lime Mud and Fly Ash for Road Embankment

This paper aims to study the feasibility of low cement content foamed concrete using waste lime mud (LM) and fly ash (FA) as mineral additives. The LM/FA ratio was first optimized based on the compressive strength. Isothermal calorimetry test, ESEM, and XRD were used to investigate the role of LM during hydration. Afterward, the optimized LM/FA ratio (1/5) was used to design foamed concrete with various wet densities (600, 700, 800 and 900 kg/m3) and LM–FA dosages (0%, 50%, 60%, 70% and 80%). Flowability measurements and mechanical measurements including compressive strength, flexural strength, splitting strength, elastic modulus, and California bearing ratio were conducted. The results show that the foamed concretes have excellent workability and stability with flowability within 170 and 190 mm. The high alkalinity of LM accelerated the hydration of FA, thereby increasing the early strength. The significant power functions were fitted for the relationships between flexural/splitting and compressive strength with all correlation coefficients (R2) larger with 0.95. The mechanical properties of the foamed concrete increased with the density increasing or LM–FA dosage decreasing. The compressive strength, tensile strength, CBR of all prepared foamed concretes were higher than the minimum requirements of 0.8 and 0.15 MPa and 8%, respectively in the standard.

Queer Intercultural Communication: Sexuality and Intercultural Communication

Queer intercultural communication is the study of sexuality in intercultural communication. It is a critical, interdisciplinary field that explores identity (i.e., race, gender, sexuality, nationality, and class) across political, historical, transnational, and social spheres. Queer intercultural communication is grounded in using an intersectional lens and embodiment, and in understanding the way power functions both systemically and individually. Historically, intercultural communication has lagged in including intersectional works that center on queer and transgender voices, theorizings, and methodologies. Queer intercultural communication has worked to expand the voices that are being centered as a way to theorize about potential and hope. As this work continues, scholarship on sexualities must remain open to broadening discourse, theory, and methodologies that are inclusive of multiple stories that evoke queer possibilities.

CO-EVOLUTION OF HIGH TECHNOLOGIES AND ARCHITECTONICS OF SOCIETY: TO THE BACKGROUND OF THE PARADIGM

The article deals with a number of cultural and historical forms of implementation of the principle of coevolution of technologies and the semantic organization of society. Using Plato's cosmogony as an example, the use of numerical symbolism as a matrix of the divine creation of the world and the human soul is analyzed. The article analyzes the difference between technologies introduced by ancient Greek philosophers and the philosophy of Taoism in China, based on: 1) on the cultivation of natural processes, and 2) on giving the material substrate any arbitrary shapes. The role of this difference in the endowment of ethical characteristics and power functions of key mythological characters is shown. Using the example of the mythological symbolization of metallurgy and blacksmithing, the features of the archaic perception of complex technological processes are analyzed. On the example of the architectural design of the "Panopticon" by I. Bentham, one of the first social technologies and its role in the transformation of the concept of power and the ways of its implementation is considered. Various forms of realization of the idea of the panopticon with the help of digital information and communication technologies are analyzed.

REPRESENTATION OF THE PAIRED INTERACTION POTENTIAL IN THE FORM OF MULTIDIMENSIONAL RATIONAL SERIES IN JACOBI VARIABLES FOR MANY-BODY PROBLEMS

Scalar power functions of the form x1 + + xN -v Î are in some cases found in physical problems and applications, especially in many-body problems with paired interactions. There are known decompositions for two vectors in three-dimensional space. In this paper, we consider analogous decompositions with any number of N arbitrary M-dimensional vectors in Euclidean space as a product of a multidimensional rational series with respect to spatial variables and hyperspheric functions on the unit sphere SM-1. Such an advantage of expansion arises in three-body problems when solving the Faddeev equation, where it is known that the main problem is the approximate choice of approximation of interaction potentials, in which the t-matrix scattering elements acquired a separable form.

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs for charging the vehicles should be minimized w.r.t. time-dependent electricity costs. A particular challenge investigated in this work is that the maximum power at which a vehicle can be charged is dependent on the current state of charge (SOC) of the vehicle. Such a consideration is particularly relevant in the case of fast charging. Considering this aspect for a discretized time horizon is not trivial, as the maximum charging power of an EV may also change in between time steps. To deal with this issue, we instead consider the energy by which an EV can be charged within a time step. For this purpose, we show how to derive the maximum charging energy in an exact as well as an approximate way. Moreover, we propose two methods for solving the scheduling problem. The first is a cutting plane method utilizing a convex hull of the, in general, nonconcave SOC–power curves. The second method is based on a piecewise linearization of the SOC–energy curve and is effectively solved by branch-and-cut. The proposed approaches are evaluated on benchmark instances, which are partly based on real-world data. To deal with EVs arriving at different times as well as charging costs changing over time, a model-based predictive control strategy is usually applied in such cases. Hence, we also experimentally evaluate the performance of our approaches for such a strategy. The results show that optimally solving problems with general piecewise linear maximum power functions requires high computation times. However, problems with concave, piecewise linear maximum charging power functions can efficiently be dealt with by means of linear programming. Approximating an EV’s maximum charging power with a concave function may result in practically infeasible solutions, due to vehicles potentially not reaching their specified target SOC. However, our results show that this error is negligible in practice.

Quasi-Cauchy quotients and means

Let $$I\subset {\mathbb {R}}$$ I ⊂ R be an interval that is closed under addition, and $$ k\in {\mathbb {N}}$$ k ∈ N , $$k\ge 2\,$$ k ≥ 2 . For a function $$f:I\rightarrow \left( 0,\infty \right) $$ f : I → 0 , ∞ such that $$F\left( x\right) :=\frac{f\left( kx\right) }{ kf\left( x\right) }$$ F x : = f k x k f x is invertible in I, the k-variable function $$ M_{f}:I^{k}\rightarrow I,$$ M f : I k → I , $$\begin{aligned} M_{f}\left( x_{1},\ldots ,x_{k}\right) :=F^{-1}\left( \frac{f\left( x_{1}+\cdots +x_{k}\right) }{f\left( x_{1}\right) +\cdots +f\left( x_{k}\right) } \right) , \end{aligned}$$ M f x 1 , … , x k : = F - 1 f x 1 + ⋯ + x k f x 1 + ⋯ + f x k , is a premean in I, and it is referred to as a quasi Cauchy quotient of the additive type of generator f. Three classes of means of this type generated by the exponential, logarithmic, and power functions, are examined. The suitable quasi Cauchy quotients of the exponential types (for continuous additive, logarithmic, and power functions) are considered. When I is closed under multiplication, the quasi Cauchy quotient means of logarithmic and multiplicative type are studied. The equalities of premeans within each of these classes are discussed and some open problems are proposed.