bluuebunny/crossref_metadata_2025_split huggingface dataset:
Properties of Dupin Cyclide and Their Application. Part 3: The Problem of Apollonius
Authors: Сальков  , Sal'kov Nikolay 
Published: March 2016

In the first part of work was addressed mainly the
issue of properties under Dupin cyclide, and given some examples
of their applications: three ways of solving the problem of Apollonius using only compass and ruler, using the identified properties of
Dupin cyclid. The second part of work continued with consideration
of the use of property under a lie of Dupin. It is determined that
the focal surface of cyclid of Dupin is degenerated in the lines and
represent curves of the second order. Here under a lie can be defined
conic curve and a sphere whose center lies on the focal curve.
Polyconic conformity these focal curves is revealed. The article
show the formation of the surface of the fourth order on the basis
of defocusing curves of the second order.
In this issue of the journal the reader is invited to consider the
practical application of properties under a lie of Dupin for example
of well known problems with on-voltage. If the first part of the work
was cited only three ways of solving the problem of Apollonius, in
the third part the author considers other possible mates: as at zero
the size of the radius of the circle and the demon is of course great.
All decisions – both known and not really based on properties of
Dupin cyclide. In the course of engineering graphics, introductory
tests, as they say now, drawing on architectural faculties there are
tasks, dedicated to the mating arcs of circles with straight lines,
and circles passing through the points in various combinations.
Therefore, the proposed practical application cannot be considered
far-fetched – it is based on the practical utility of method.
Subject Olympiads As an Indicator of the Quality of Education
Authors: Сальков  , Sal'kov Nikolay 
Published: March 2016

The famous phrase of M.V. Lomonosov: &#34;Mathematics
should be studied for it puts mind in order&#34;. It is quite possible to
rephrase it for descriptive geometry, because geometry is math too.
The invention of microprocessor technology, the advent of the
personal computer, the discovery of the GMR effect (1988), which
dramatically increased the speed and memory capacity of the PC,
are called theSubject olympiads in descriptive geometry are held
in many cities of Russia, including in Moscow. These olympiads,
according to the author of the hundred-Tue, are an indicator of
the quality of teaching in universities. Introduced by the author at
the Moscow State Institute of Public Utilities (MIKHiS), and then
at the Moscow State Academic Art Institute named after V.I. Surikov
course of descriptive geometry, which allows to organize and algorithmization
of the educational process, helped students teams of
both universities without any special additional of preparation to
take a pretty decent place at the Moscow city Olympiads on descriptive
geometry. The structure of the basic course helped to
organize and sturcture lecture material, which, in turn, allowed the
entire amount of information to compress, in principle, by almost
half, and reduce the number of hours of lectures from 32 to 18
without much loss. If current trends to cut a watch from the disciplines
of engineering, it is the doubtless achievement. The use of
this structure led to a positive effect: better memorization of the
material, better absorption, which was identified with the participation
of students who passed the course at the Moscow city Olympiads
on descriptive geometry. The author developed the criterion of
success of the team of students. The article contains the appropriate
tables and charts.
The article does not provide data later than 2013, as Moscow
State Academy of Municipal Economy and Construction was
disbanded in 2014 and included in Moscow State University of
Civil Engineering. From the very beginning, the comparison of the
two approaches in Moscow State Academy of Municipal Economy
and Construction and in Moscow State Academic Art Institute
named after V.I. Surikov was considered: traditional teaching descriptive
geometry and proposed.
Nursing students' knowledge of child abuse and neglect in India
Authors: Poreddi Vijayalakshmi , Pashapu Dharma Reddy , Kathyayani BV , Gandhi SaiLaxmi , El-Arousy Wafaa , Math Suresh Bada 
Published: March 2016

Background:Child abuse and neglect are global phenomena. Research on knowledge of and attitudes towards child abuse and neglect among nursing students in India is limited.Aim:To investigate undergraduate nursing students' knowledge of and attitudes towards child abuse and neglect.Methods:A descriptive design was adopted for the study, in which 158 nursing students participated by responding to a standardised questionnaire.Results:The findings revealed that students' knowledge of child abuse and neglect is inadequate, as the total mean (M) score was 13.84±4.35 (M±standard deviation (SD)). The total attitude score of 50.37±6.196 (M±SD) indicated participants' positive attitudes towards prevention of child abuse and neglect. However, there was a negative relation between age and attitudes towards and knowledge of child abuse. Older students scored higher on the total attitude and knowledge scale compared with younger students.Conclusion:The study findings support the hypothesis that nursing education programmes need to improve the curricular content related to the assessment and reporting of suspected child abuse and neglect, and prevention strategies to improve the wellbeing of children. Curricular changes have the potential to provide nurses with an opportunity to reduce the prevalence of child abuse and neglect in India.
Identifying a standardised tool to assess and manage children with idiopathic constipation
Authors: Costigan Ann , Orr Stephanie 
Published: March 2016

Aim To identify a standardised assessment tool that can be used in Ireland to diagnose and treat children with idiopathic constipation, without the need for referral to secondary care. Method The National Institute of Health and Care Excellence (NICE) (2010) guidelines on constipation in children and young people were used as a benchmark tool, which identify keys areas that must be assessed. Seventy-eight patient charts were studied retrospectively to assess whether the key components were undertaken, and 45 patients were deemed suitable for inclusion in an audit due to an idiopathic constipation diagnosis. Results None of the 45 patients received a complete assessment as per the NICE (2010) guidelines. Conclusion A nationwide comprehensive assessment tool to diagnosis and treat idiopathic constipation is needed. The NICE (2010) guidelines should not be used in addition to written information and close follow-up. A document to incorporate all of this called the Poo Passport has been developed.
How to use an ECG machine
Authors: Pace Charlotte 
Published: March 2016

Introduction The electrocardiogram (ECG) can assist monitoring of a wide range of cases, such as emergencies, those undergoing anaesthesia and for critically ill patients. While being a valuable diagnostic tool in veterinary practice, many nurses are apprehensive about using the ECG machine, either due to uncertainty or unfamiliarity of the machine, or being unsure about what to look out for, when in use. This practical and illustrated article gives explanations on how to use the machine and provides examples of the common rhythms and arrhythmias seen in practice.
Understanding Mathematics: Some Key Factors
Authors: Ali Asma Amanat , Reid Norman 
Published: March 2016

<p style="text-align:justify">Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was explored along with a survey of areas of difficulty and student attitudes. This involved looking at student perceptions of their experiences, the nature of the difficulties they have with mathematics and possible reasons for these difficulties. The overall aim is to explore the extent of the effect of working memory and to gain insights so that practical ways forward to enhance mathematics education can be identified. It was found that limited working memory capacity has a very strong influence on performance, confirming other studies. Indeed, if the cognitive load exceeds the capacity of working memory, understanding becomes a casualty, with consequent attitude deterioration. Students need to be able to see that mathematics has a purpose in being able to be applied to real-life situations. However, attempts to develop applications may often generate further working memory overload. Curricula devised by those outside the classroom can sometimes be inappropriate while topics causing the greatest problems at these ages and include areas of geometry, statistics and the applications of mathematics.</p>
Classification of Global and Blow-up Sign-changing Solutions of a Semilinear Heat Equation in the Subcritical Fujita Range : Second-order Diffusion
Authors: Galaktionov Victor A. , Mitidieri Enzo , Pohozaev Stanislav I. 
Published: March 2016

AbstractIt is well known from the seminal paper by Fujita [22] for 1 < p < p0, and Hayakawa [36] for the critical case p = p0, that all the solutions u ≥ 0 of the semilinear heat equationut= Δu + |u|p−1u in ℝN× ℝ+, in the range, (0.1)with arbitrary initial data u0(x) ≥ 0, ≢ 0, blow-up in finite time, while for p > p0there exists a class of sufficiently “small” global in time solutions. This fundamental result from the 1960-70s (see also [39] for related contributions), was a cornerstone of further active blow-up research. Nowadays, similar Fujita-type critical exponents p0, as important characteristics of stability, unstability, and blow-up of solutions, have been calculated for various nonlinear PDEs. The above blow-up conclusion does not include solutions of changing sign, so some of them may remain global even for p ≤ p0. Our goal is a thorough description of blow-up and global in time oscillatory solutions in the subcritical range in (0.1) on the basis of various analytic methods including nonlinear capacity, variational, category, fibering, and invariant manifold techniques. Two countable sets of global solutions of changing sign are shown to exist. Most of them are not radially symmetric in any dimension N ≥ 2 (previously, only radial such solutions in ℝNor in the unit ball B1⊂ℝNwere mostly studied). A countable sequence of critical exponents, at which the whole set of global solutions changes its structure, is detected:, l = 0, 1, 2, ... .. See [47, 48] for earlier interesting contributions on sign changing solutions.
Superposition Operators Between Higher-order Sobolev Spaces and a Multivariate Faà di Bruno Formula: Supercritical Case
Authors: Dinca George , Isaia Florin 
Published: March 2016

Abstract
This paper is a continuation of the work begun in [6] on superposition operators, (Ngu) (x) = g(u(x)), between two arbitrary Sobolev spaces. Sufficient conditions which ensure the well-definedness, the continuity and the validity of the higher-order chain rule for such operators are given in the supercritical case (see Remark 1.1). As a consequence of these properties, it is proved that Ng (Wm,p (Ω) ∩ W0
k,p (Ω)) ⊂ W0
l,q (Ω).
The Topology of a Subspace of the Legendrian Curves on a Closed Contact 3-Manifold
Authors: Maalaoui Ali , Martino Vittorio 
Published: March 2016

Abstract
In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.
Concentrating Bound States for Kirchhoff Type Problems in ℝ3 Involving Critical Sobolev Exponents
Authors: He Yi , Li Gongbao , Peng Shuangjie 
Published: March 2016

Abstract
We study the concentration and multiplicity of weak solutions to the Kirchhoff type equation with critical Sobolev growth,

where ε is a small positive parameter and a, b > 0 are constants, f ∈ C1(ℝ+,ℝ) is subcritical, V : ℝ3 → ℝ is a locally Hölder continuous function. We first prove that for ε0 > 0 sufficiently small, the above problem has a weak solution uε with exponential decay at infinity. Moreover, uε concentrates around a local minimum point of V in Λ as ε → 0. With minimax theorems and Ljusternik-Schnirelmann theory, we also obtain multiple solutions by employing the topological construction of the set where the potential V(z) attains its minimum.
Effect of a Gradient Term on the Solvability of the Heat Equation with a Supercritical Reaction with Respect to the Hardy Potential
Authors: Abdellaoui Boumediene , Attar Ahmed , Merchán Susana , Peral Ireneo 
Published: March 2016

Abstract
In this paper we consider the following nonlinear parabolic problem

where Ω ⊂ ℝN, N > 2, is a bounded domain with 0 ∈ Ω and 1 < p < 3. The main goal of this work is to analyze the influence of the gradient term in order to obtain the existence of a positive solution for the largest class of data ( f, u0) and for all λ > 0.
Fat Handles and Phase Portraits of Non Singular Morse-Smale Flows on S3 with Unknotted Saddle Orbits
Authors: Campos B. , Vindel P. 
Published: March 2016

Abstract
In this paper we build Non-singular Morse-Smale flows on S3 with unknotted and unlinked saddle orbits by identifying fat round handles along their boundaries. This way of building the flows enables to get their phase portraits. We also show that the presence of heteroclinic trajectories imposes an order in the round handle decomposition of these flows; this order is total for NMS flows composed of one repulsive, one attractive and n unknotted saddle orbits, for n ≥ 1.
Liouville Theorem for a Fourth Order Hénon Equation
Authors: Cowan Craig 
Published: March 2016

Abstract
We examine the following fourth order Hénon equation
Δ2u = |x|αup in ℝN,
where 0 < α. Define the Hardy-Sobolev exponent . We show that in dimension N = 5 there are no positive bounded classical solutions provided 1 < p < p4(α).
Approximation Results for a General Class of Kantorovich Type Operators
Authors: Vinti Gianluca , Zampogni Luca 
Published: March 2016

Abstract
We introduce and study a family of integral operators in the Kantorovich sense acting on functions defined on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform convergence and in the setting of Orlicz spaces with respect to the modular convergence. Moreover, we show how our theory applies to several classes of integral and discrete operators, as sampling, convolution and Mellin type operators in the Kantorovich sense, thus obtaining a simultaneous approach for discrete and integral operators. Further, we obtain general convergence results in particular cases of Orlicz spaces, as Lp−spaces, interpolation spaces and exponential spaces. Finally we construct some concrete examples of our operators and we show some graphical representations.
A Jumping Problem for Some Singular Semilinear Elliptic Equations
Authors: Canino Annamaria , Grandinetti Mascia , Sciunzi Berardino 
Published: March 2016

Abstract
We consider a jumping problem for singular semilinear elliptic equations. Existence of two distinct solutions is proved via a truncation argument and exploiting minimax methods to prove the existence of solutions to the truncated problem. In the final step, to pass to the limit, a refined analysis about the behavior of the solutions is required, because of the singular nature of the problem.
Spinorial Yamabe Type Equations on S3 via Conley Index
Authors: Isobe Takeshi 
Published: March 2016

Abstract
In this paper, we consider the existence of solutions to spinorial Yamabe type equations on S3 with a prescribed function H. We give a new condition about H under which at least one non-trivial solution exists. It is proved by a method based on Conley index theory applied to a reduced functional defined on a certain finite dimensional non-compact manifold. Our proof is also applicable to similar equations on Sm for all m ≥ 2.
A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space
Authors: Liu Zhao , Dai Wei 
Published: March 2016

Abstract
In this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝn
+:

where for i = 1, 2. First, we show that, under some mild growth conditions, (0.1) is equivalent to the IE system

where

is the Green’s function in ℝn
+ with the same Dirichlet boundary conditions. Then, inspired by the work [12] of Y. Fang and W. Chen on the Dirichlet problem for (−Δ)mu = up in ℝn
+, we use method of moving planes in integral forms to prove the nonexistence of nontrivial nonnegative solutions for IE system (0.2), and as a consequence, we derive the nonexistence of nontrivial nonnegative classical solutions for problem (0.1).
Maxwell’s Equations in Anisotropic Media and Carnot Groups as Variational Limits
Authors: Baldi Annalisa , Franchi Bruno 
Published: March 2016

Abstract
Let G be a free Carnot group (i.e. a connected simply connected nilpotent stratified free Lie group) of step 2. In this paper, we prove that the variational functional generated by “intrinsic” Maxwell’s equations in G is the Γ-limit of a sequence of classical (i.e. Euclidean) variational functionals associated with strongly anisotropic dielectric permittivity and magnetic permeability in the Euclidean space.
Existence of Heteroclinic Solutions for a Pseudo-relativistic Allen-Cahn Type Equation
Authors: Ambrosio Vincenzo 
Published: March 2016

Abstract
We study the existence and uniqueness of heteroclinic solutions to non-linear Allen-Cahn equation

where G is a double-well potential. We investigate such a problem using variational methods after transforming the problem to an elliptic equation with a nonlinear Neumann boundary conditions.
A Linking/S1-equivariant Variational Argument in the Space of Dual Legendrian Curves and the Proof of the Weinstein Conjecture on S3 ”in the Large”
Authors: Bahri Abbas 
Published: March 2016

Abstract
Let α be a contact form on S3, let ξ be its Reeb vector-field and let v be a non-singular vector-field in ker α. Let Cβ be the space of curves x on S3 such ẋ = aξ + bv, ȧ = 0, a ≩ 0. Let L+, respectively L−, be the set of curves in Cβ such that b ≥ 0, respectively b ≤ 0. Let, for x ∈ Cβ, J(x) = ∫0
1 αx(ẋ)dt. The framework of the present paper has been introduced previously in eg [3].
We establish in this paper that some cycles (an infinite number of them, indexed by odd integers, tending to ∞) in the S 1-equivariant homology of Cβ, relative to L+ ∪ L− and to some specially designed ”bottom set”, see section 4, are achieved in the Morse complex of (J,Cβ) by unions of unstable manifolds of critical points (at infinity)which must include periodic orbits of ξ; ie unions of unstable manifolds of critical points at infinity alone cannot achieve these cycles. At the odd indexes (2k−1) = 1+(2k−2), 1 for the linking, (2k−2) for the S1-equivariance, we find that the equivariant contributions of a critical point at infinity to L+ and to L− are fundamentally asymmetric when compared to those of a periodic orbit [5]. The topological argument of existence of a periodic orbit for ξ turns out therefore to be surprisingly close, in spirit, to the linking/equivariant argument of P. Rabinowitz in [12]; e.g. the definition of the ”bottom sets” of section 4 can be related in part to the linking part in the argument of [12]. The objects and the frameworks are strikingly different, but the original proof of [12] can be recognized in our proof, which uses degree theory, the Fadell-Rabinowitz index [8] and the fact that πn+1(Sn) = Z2, n ≥ 3. We need of course to prove, in our framework, that these topological classes cannot be achieved by critical points at infinity only, periodic orbits of ξ excluded, and this is the fundamental difficulty.
The arguments hold under the basic assumption that no periodic orbit of index 1 connects L+ and L−. It therefore follows from the present work that either a periodic orbit of index 1 connects L+ and L− (as is probably the case for all three dimensional over-twisted [8] contact forms, see the work of H. Hofer [10], the periodic orbit found in [10] should be of index 1 in the present framework); or (with a flavor of exclusion in either/or) a linking/ equivariant variational argument a la P. Rabinowitz [12] can be put to work. Existence of (possibly multiple) periodic orbits of ξ, maybe of high Morse index, follows then.
Therefore, to a certain extent, the present result runs, especially in the case of threedimensional over-twisted [8] contact forms, against the existence of non-trivial algebraic invariants defined by the periodic orbits of ξ and independent of what ker α and/or α are.
Solitary Waves for a Class of Quasilinear Schrödinger Equations Involving Vanishing Potentials
Authors: Marcos do Ó João , Gloss Elisandra , Santana Cláudia 
Published: March 2016

Abstract
In this paper we study the existence of weak positive solutions for the following class of quasilinear Schrödinger equations
−Δu + V(x)u − [Δ(u2)]u = h(u) in ℝN,
where h satisfies some “mountain-pass” type assumptions and V is a nonnegative continuous function. We are interested specially in the case where the potential V is neither bounded away from zero, nor bounded from above. We give a special attention to the case when V may eventually vanish at infinity. Our arguments are based on penalization techniques, variational methods and Moser iteration scheme.
Nonlinear Parametric Robin Problems with Combined Nonlinearities
Authors: Papageorgiou Nikolaos S. , Rădulescu Vicenţiu D. 
Published: March 2016

Abstract
We consider a nonlinear parametric Robin problem driven by the p-Laplacian. We assume that the reaction exhibits a concave term near the origin. First we prove a multiplicity theorem producing three solutions with sign information (positive, negative and nodal) without imposing any growth condition near ±∞ on the reaction. Then, for problems with subcritical reaction, we produce two more solutions of constant sign, for a total of five solutions. For the semilinear problem (that is, for p = 2), we generate a sixth solution but without any sign information. Our approach is variational, coupled with truncation, perturbation and comparison techniques and with Morse theory.
Best Constants for Adams’ Inequalities with the Exact Growth Condition in ℝn
Authors: Lu Guozhen , Tang Hanli , Zhu Maochun 
Published: March 2016

Abstract
In this paper, we establish the following sharp Adams inequality with exact growth condition in the entire space ℝn (n ≥ 3): There exists a constant C(n) > 0 such that for all with ,

,
where . This extends the main result in [27] when n = 4 to all dimensions n ≥ 3. A crucial technical lemma we need is Lemma 4.2 for all p > 1 (corresponding to the Adams inequality for all n ≥ 3) whose proof is quite involved. As an application, we obtain the best constant for Ozawa’s inequality of Adams type in the Sobolev space : For any α < βn, there exists a constant C(α, n) > 0 such that for all satisfying , we have . Moreover, if α ≥ βn then the inequality cannot hold with a uniform constant C(α, n).
Discrete Hardy-type Inequalities
Authors: Liao Zhong-Wei 
Published: March 2016

Abstract
This paper studies the Hardy-type inequalities on the discrete intervals. Firstly, two variational formulas for the optimal constants are introduced. Based on these formulas, an approximating procedure and the known basic estimates of the optimal constants are deduced. Thirdly, as the main innovation of this paper, an improved factor for the upper estimates is presented, which is smaller than the known one and is the best possible. Finally, some comparison results are included for comparing the optimal constants on different intervals.