Principal Part Research Articles

Hypersingular integral equation for triple inclined cracks problems in half plane elasticity

Hypersingular integral equation associated with the modified complex potential is formulated to solve the three inclined cracks problems in an elastic half-plane with free traction boundary condition. The modified complex potential possesses two parts; the principal and the complementary parts. The principal part is derived from the original complex potential of the crack problem in an infinite plate. The complementary part eliminates the traction along boundary of half-plane caused by the principal part. The crack opening displacements (COD) is the unknown function and the traction is the right hand terms. The appropriate quadrature formula is adapted to solve the integral equation numerically and the stress intensity factor (SIF) is computed. The behaviour of SIF at crack tips is analysed. Numerical examples show that the SIF increases as the angle of inclined cracks and the distance of cracks from the boundary of half-plane increase. Our results are agreeable with the previous works.

Almost solubility of classes of non-linear integral equations of the first kind on cones

Using convexity properties of the images of completely continuous non-linear integral operators, we describe the closed convex cones lying either in the recessive cone, or in the tangent cone of the closed image of the operator being studied (depending on the nature of the integrand). These cones are determined by the principal part of the asymptotics of the integrand at infinity, independently of the variation of the subordinate part. We discuss applications to the generalized solubility of non-linear integral equations of the first kind.

Boundedness of solutions to a class of coercive systems with Morrey data

We prove global essential boundedness of the weak solutions u∈W01,p(Ω;RN) to the quasilinear system div,(A(x,u,Du))=b(x,u,Du). The principal part A(x,u,Du) of the differential operator is componentwise coercive and supports controlled growths with respect to u and Du, while the lower order term b(x,u,Du) exhibits componentwise controlled gradient growth. The x-behaviour of the nonlinearities is governed in terms of Morrey spaces.

Problematika Pembelajaran Agama Islam Di Sekolah Menengah Kejuruan Negeri 13 Malang

Abstract: Education is the key to the formation of competent human resources in building the nation. Education has a very urgent role to ensure the development and survival of a nation. Education is also a benchmark to advance a nation, and to mirror the personality of its people. The author will choose a location study at Vocational High School 13 Malang, the subject of his research is the principal, vice principal part of the curriculum, Islamic religious education teachers, and students. In this study the authors used three kinds of data collection techniques are methods of observation, interviews, documentation methods. Research findings have been obtained by the authors as follows: Problem in Students in Learning Islamic Education, Problem Educator (Teacher) In the Islamic Religious Education Learning, Problem Management in Islamic Religious Education Learning, Problem curriculum in Islamic Religious Education Learning, Problem Facilities and Infrastructure In Islamic Religious Education Learning,Environmental Problem In Islamic Religious Education Learning

1 IMPLEMENTASI KURIKULUM 2013 DALAM KEGIATAN PEMBELAJARAN PENDIDIKAN AGAMA ISLAM DI SEKOLAH MENENGAH KEJURUAN NEGERI 13 MALANG

Abstract:
 Curriculum 2013 consisting of goals, structure and curriculum, educational
 calendar and syllabus. Islamic religious education, this time religious teachers should be
 aware that there are four trends that will be faced by religion and is a challenge for rel
 igious
 people as follows: internal diversity, diversity of structural, cultural diversity, criticism of
 science. The author will choose a location study at Vocational High School 13 Malang, the
 subject of his research is the principal, vice principal part
 of the curriculum, Islamic religious
 education teachers, and students. In this study the authors used three kinds of data collection
 techniques are methods of observation, interviews, documentation methods. The results of the
 study as follows: 1. Planning
 Islamic Religious Education Learning is a teacher before
 committing learning activities in the classroom should be made syllabus and lesson plans. 2.
 Implementation of Islamic Religious Education Learning is the implementation phase for the
 design drawn up
 plans for teachers. 3. Evaluation of Islamic Religious Education Learning is
 a measuring instrument to measure the achievement of objectives.

Collapse-Limit Input Level of Critical Double Impulse for Damped Bilinear Hysteretic SDOF System With Negative Post-yield Stiffness

The collapse-limit input velocity level of the critical double impulse simulating the principal part of near-fault ground motions is derived for an elastic-plastic structure with viscous damping and P-delta effect. The structural system is modeled by a bilinear hysteretic SDOF system with negative post-yield stiffness reflecting the P-delta effect which plays a key role in the collapse behavior. Since the critical timing of the second impulse in the double impulse has been proven as the zero-restoring force timing after the first impulse for the elastic-plastic SDOF system with viscous damping, that property is used again in this paper. It is shown that the collapse-limit input level of the critical double impulse can be obtained as a function of the post-yield stiffness and the damping ratio by using the energy balance law and the quadratic-function approximation of the damping force-deformation relation. The applicability of the collapse-limit level to actual recorded ground motions is investigated through the time-history response analysis for the stable and collapse models under two actual earthquake ground motions.

Borcherds lifts of harmonic Maass forms and modular integrals

We extend Borcherds' singular theta lift in signature $(1,2)$ to harmonic Maass forms of weight $1/2$ whose non-holomorphic part is allowed to be of exponential growth at $i\infty$. We determine the singularities of the lift and compute its Fourier expansion. It turns out that the lift is continuous but not differentiable along certain geodesics in the upper half-plane corresponding to the non-holomorphic principal part of the input. As an application, we obtain a generalization to higher level of the weight $2$ modular integral of Duke, Imamoglu and T\'oth. Further, we construct automorphic products associated to harmonic Maass forms.

Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits

Abstract Let j ⁢ ( z ) {j(z)} be the modular j-invariant function. Let τ be an algebraic number in the complex upper half plane ℍ {\mathbb{H}} . It was proved by Schneider and Siegel that if τ is not a CM point, i.e., [ ℚ ( τ ) : ℚ ] ≠ 2 {[\mathbb{Q}(\tau):\mathbb{Q}]\neq 2} , then j ⁢ ( τ ) {j(\tau)} is transcendental. Let f be a harmonic weak Maass form of weight 0 on Γ 0 ⁢ ( N ) {\Gamma_{0}(N)} . In this paper, we consider an extension of the results of Schneider and Siegel to a family of values of f on Hecke orbits of τ. For a positive integer m, let T m {T_{m}} denote the m-th Hecke operator. Suppose that the coefficients of the principal part of f at the cusp i ⁢ ∞ {i\infty} are algebraic, and that f has its poles only at cusps equivalent to i ⁢ ∞ {i\infty} . We prove, under a mild assumption on f, that, for any fixed τ, if N is a prime such that N ≥ 23 {N\geq 23} and N ∉ { 23 , 29 , 31 , 41 , 47 , 59 , 71 } {N\notin\{23,29,31,41,47,59,71\}} , then f ( T m . τ ) {f(T_{m}.\tau)} are transcendental for infinitely many positive integers m prime to N.

Medium and long-term power quantity check and adjustment method based on power quantity margin

Medium and long-term power trade is increasing, and the adjustable margin of power grid is reducing. Therefore, medium and long-term power quantity security check is necessary. Firstly, a power quantity margin model is constructed, and power quantity constraints and the future state grid model are considered. The power quantity limits of principal parts such as unit and line section are calculated, and quantity adjustment method is given.Then the medium and long-term power quantity check and adjustment are realized through the correlation coefficient matrix. Finally, the actual provincial power grid is taken as an example to verify the effectiveness of the proposed model and method. Through the calculation of the quantity margin by power, the verification of medium and long-term transactions and the control of the safety margin of the power grid are realized.

Theory of Integral Equations for Axisymmetric Scattering by a Disk

A theory of integral equations for radial currents in the axisymmetric problem of scattering by a disk is constructed. The theory relies on the extraction of the principal part of a continuously invertible operator and on the proof of its positive definiteness. Existences and uniqueness theorems are obtained for the problem. An orthonormal basis is constructed for the energy space of the positive definite operator. Each element of the basis on the boundary behaves in the same manner as the unknown function. The structure of the matrix of the integral operator in this basis is studied. It is found that the principal part has an identity matrix, while the matrix of the next operator is tridiagonal.

Room‐Temperature Ni Interaction with Deformation‐Induced Defects in Si: A DLTS Study

The deep‐level (DL) spectrum of plastically deformed n‐type Si and its modification due to interaction with the mobile Ni species are investigated by the deep‐level transient spectroscopy (DLTS) technique. The used geometry of plastic deformation makes it possible to separate the DL centers associated with the dislocations themselves or with dislocation traces, the quasi‐2D defects left by moving dislocations. It is shown that the chemomechanical polishing at room temperature in a Ni‐contaminated slurry results in the appearance of additional DL centers; the principal part of the novel centers forms due to nickel interaction with the dislocation trails. The DLTS signatures of the nickel‐related defects in our plastically deformed samples are similar to those for the nickel‐silicide precipitates.

Designing Cognition Model of Knowledge Effect on Employees’ Creativity (Case Study: Police Engineering Administration)

Today, knowledge sharing has determinant role in promotion of various industries and organizations as an element of knowledge management. According to daily incremental importance of knowledge as the most critical resource for competitive advantage, organizations try to find effective ways of knowledge sharing among employees. Knowledge sharing is considered as an important and principal part of knowledge management, and creative employees are promoter and dynamic force of organizational activities. Methodology: This research tries to design a model to make relationship between knowledge sharing and employees’ creativity. Therefore, related factors were identified to perceive knowledge sharing and also employees’ creativity, and some data was obtained using questionnaire. In order to study the relationship among variables and their effects on each other, structural equation model (SEM) was used by Lisrel software. Results: Results of this research show the positive and direct effect of knowledge sharing on employees’ creativity. Conclusion: Technological conditions have an important role in knowledge sharing, and managers of IRI police engineering administration must have always mention that more focus on technological conditions increase knowledge sharing in IRI police engineering administration.

The Dirichlet problem for singular elliptic equations with general nonlinearities

In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\begin{cases} \displaystyle - \Delta_{1} u = h(u)f & \text{in}\, \Omega,\newline u\geq 0& \text{in}\ \Omega, \newline u=0 & \text{on}\ \partial \Omega, \end{cases} $$ where, $\Delta_{1} $ is the $1$-laplace operator, $\Omega$ is a bounded open subset of $\mathbb{R}^N$ with Lipschitz boundary, $h(s)$ is a continuous function which may become singular at $s=0^{+}$, and $f$ is a nonnegative datum in $L^{N,\infty}(\Omega)$ with suitable small norm. Uniqueness of solutions is also shown provided $h$ is decreasing and $f>0$. As a by-product of our method a general theory for the same problem involving the $p$-laplacian as principal part, which is missed in the literature, is established. The main assumptions we use are also further discussed in order to show their optimality.

Normal Form Coordinates for the KdV Equation Having Expansions in Terms of Pseudodifferential Operators

Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the KdV equation on the torus having the following two main properties: (1) up to a remainder term, which is smoothing to any given order, the coordinate transformation is a pseudodifferential operator of order 0 with principal part given by the Fourier transform and (2) the pullback of the KdV Hamiltonian is in normal form up to order three and the corresponding Hamiltonian vector field admits an expansion in terms of a paradifferential operator. Such coordinates are a key ingredient for studying the stability of finite gap solutions of the KdV equation under small, quasi-linear perturbations.

BMS characters and modular invariance

We construct the characters for the highest weight representations of the 3d Bondi-Metzner-Sachs (BMS3) algebra. We reproduce our character formula by looking at singular limits from 2d CFT characters and find that our answers are identical to the characters obtained for the very different induced representations. We offer an algebraic explanation to this arising from an automorphism in the parent 2d CFT. We then use the characters to construct the partition function and show how to use BMS modular transformations to obtain a density of primary states. The entropy thus obtained accounts for the principal part of the entropy obtained from the BMS-Cardy formula. This suggests that BMS primaries capture most of the entropy of Flat Space Cosmologies, which are the flatspace analogues of BTZ black holes in AdS3.

Review: brain neurobiology of gambling disorder based on rodent models.

Different literature reviews of gambling disorder (GD) neurobiology have been focused on human studies, others have focused on rodents, and others combined human and rodent studies. The main question of this review was: which are the main neurotransmitters systems and brain structures relevant for GD based on recent rodent studies? This work aims to review the experimental findings regarding the rodent´s neurobiology of GD. A search in the Pub Med database was set (October 2012–October 2017) and 162 references were obtained. After screening, 121 references were excluded, and only 41 references remained from the initial output. More, other 25 references were added to complement (introduction section, neuroanatomical descriptions) the principal part of the work. At the end, a total of 66 references remained for the review. The main conclusions are: 1) according to studies that used noninvasive methods for drug administration, some of the neurotransmitters and receptors involved in behaviors related to GD are: muscarinic, N-methyl-D-aspartate (NMDA), cannabinoid receptor 1 (CB1), cannabinoid receptor 2 (CB2), dopamine 2 receptor (D2), dopamine 3 receptor (D3), and dopamine 4 receptor (D4); 2) moreover, there are other neurotransmitters and receptors involved in GD based on studies that use invasive methods of drug administration (eg, brain microinjection); example of these are: serotonin 1A receptor (5-HT1A), noradrenaline receptors, gamma-aminobutyric acid receptor A (GABAA), and gamma-aminobutyric acid receptor B (GABAB); 3) different brain structures are relevant to behaviors linked to GD, like: amygdala (including basolateral amygdala (BLA)), anterior cingulate cortex (ACC), hippocampus, infralimbic area, insular cortex (anterior and rostral agranular), nucleus accumbens (NAc), olfactory tubercle (island of Calleja), orbitofrontal cortex (OFC), medial prefrontal cortex (mPFC), prefrontal cortex (PFC) – subcortical network, striatum (ventral) and the subthalamic nucleus (STN); and 4) the search for GD treatments should consider this diversity of receptor/neurotransmitter systems and brain areas.

An approximation of problems of optimal control on the coefficients of elliptic convection-diffusion equations with an imperfect contact matching condition

We consider nonlinear optimization problems for processes described by non-self-adjoint elliptic equations of convection-diffusion problems with an imperfect contact matching conditions. These are the problems with a jump of the coefficients and of the solution on the interface; the jump of the solution is proportional to the normal component of the flux. Variable coefficients multiplying the highest and the lowest derivatives in the equation and the coefficients by nonlinear terms in the equations of state are used as controls. Finite difference approximations of optimization problems are constructed and investigated. For the approximation of state equations we propose a new ``modified difference scheme'' in which the variable grid coefficients in the principal part of the difference operator are computed using method other than traditionally applied in the theory of difference schemes. The problem's correctness is investigated. The accuracy estimation of difference approximations with respect to the state are obtained. Convergence rate of approximations with respect to cost functional is estimated, too. Weak convergence with respect to control is proved. The presence of a non-self-adjoint operator causes certain difficulties in constructing and studying approximations of differential equations describing discontinuous states of controlled processes, in particular, in proving the difference approximations well-posedness, and in studying the relationship between the original optimal control problem and the approximate mesh problem. The approximations are regularized. The obtained results will be heavily used later in solving problems associated with the development of effective methods for the numerical solution to the constructed finite-dimensional mesh optimal control problems and their computer implementation.

Multigrid for second‐order ADN elliptic systems

SummaryThis paper theoretically examines a multigrid strategy for solving systems of elliptic partial differential equations (PDEs) introduced in the work of Lee. Unlike most multigrid solvers that are constructed directly from the whole system operator, this strategy builds the solver using a factorization of the system operator. This factorization is composed of an algebraic coupling term and a diagonal (decoupled) differential operator. Exploiting the factorization, this approach can produce decoupled systems on the coarse levels. The corresponding coarse‐grid operators are in fact the Galerkin variational coarsening of the diagonal differential operator. Thus, rather than performing delicate coarse‐grid selection and interpolation weight procedures on the original strongly coupled system as often done, these procedures are isolated to the diagonal differential operator. To establish the theoretical results, however, we assume that these systems of PDEs are elliptic in the Agmon–Douglis–Nirenberg (ADN) sense and apply the factorization and multigrid only to the principal part of the system of PDEs. Two‐grid error bounds are established for the iteration applied to the complete system of PDEs. Numerical results are presented to illustrate the effectiveness of this strategy and to expose factors that affect the convergence of the methods derived from this strategy.

Harmonic maps and wild Teichmüller spaces

We use meromorphic quadratic differentials with higher order poles to parametrize the Teichmüller space of crowned hyperbolic surfaces. Such a surface is obtained on uniformizing a compact Riemann surface with marked points on its boundary components, and has noncompact ends with boundary cusps. This extends Wolf’s parametrization of the Teichmüller space of a closed surface using holomorphic quadratic differentials. Our proof involves showing the existence of a harmonic map from a punctured Riemann surface to a crowned hyperbolic surface, with prescribed principal parts of its Hopf differential which determine the geometry of the map near the punctures.

Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains

The dynamical stability of solitary lattice waves in non-integrable FPUT chains is a long-standing open problem and has been solved so far only in a certain asymptotic regime, namely by Friesecke and Pego for the KdV limit, in which the waves propagate with near sonic speed, have large wave length, and carry low energy. In this paper we derive a similar result in a complementary asymptotic regime related to fast and strongly localized waves with high energy. In particular, we show that the spectrum of the linearized FPUT operator contains asymptotically no unstable eigenvalues except for the neutral ones that stem from the shift symmetry and the spatial discreteness. This ensures that high-energy waves are linearly stable in some orbital sense, and the corresponding nonlinear stability is granted by the general, non-asymptotic part of the seminal Friesecke-Pego result and the extension by Mizumachi. Our analytical work splits into two principal parts. First we refine two-scale techniques that relate high-energy waves to a nonlinear asymptotic shape ODE and provide accurate approximation formulas. In this way we establish the existence, local uniqueness, smooth parameter dependence, and exponential localization of fast lattice waves for a wide class of interaction potentials with algebraic singularity. Afterwards we study the crucial eigenvalue problem in exponentially weighted spaces, so that there is no unstable essential spectrum. Our key argument is that all proper eigenfunctions can asymptotically be linked to the unique bounded and normalized solution of the linearized shape ODE, and this finally enables us to disprove the existence of unstable eigenfunctions in the symplectic complement of the neutral ones.