2,302 research outputs found
A SURVEY ON -FREENESS
No full textWe say that an integer n is k–free (k 2) if for every
prime p the valuation vp(n) < k. If f : N ! Z, we consider
the enumerating function Sk
f (x) defined as the number of positive
integers n x such that f(n) is k–free. When f is the identity
then Sk
f (x) counts the k–free positive integers up to x. We review
the history of Sk
f (x) in the special cases when f is the identity, the
characteristic function of an arithmetic progression a polynomial,
arithmetic. In each section we present the proof of the simplest
case of the problem in question using exclusively elementary or
standard techniques
Structure-Property Relationships in Heterophasic Thermoplastic Elastomers Filled with Montmorillonite
No full textPolypropylene (PP)/ethylene-propylene rubber (EPR)/Montmorillonite ternary nanocomposites with a phase separated morphology were studied in this work. Wide angle X-ray diffraction (WAXD), small angle X-ray scattering (SAXS), atomic force microscopy (AFM), scanning electron microscopy
(SEM), and transmission electron microscopy (TEM) were used to investigate the samples. One of the aim of this work was to separate the effects of rubber and clay content on the structure, morphology and mechanical properties of the samples. The presence of clay favored the formation
of phase and disrupted the lamellar framework. Clay had moreover a major role in shaping thephase separated morphology of the samples. Atomic Force Microscopy showed that the shearexerted by the clay layers was key for inducing a shish kebab morphology in the polymer matrix.
Rubber content decreased the degree of crystallinity at a crystalline cell level and induced the formation of a double population of lamellar stacks. The mechanical properties of the samples primarily depended on rubber content, and they were secondarily tuned by the effect of clay. This
synergistic effect allowed to obtain composites with increased stiffness, ductility and toughness, oppositely to what is frequently found
Continuity of Yosida Approximants Corresponding to General Duality Mappings
No full textLet X be a real locally uniformly convex Banach space and X∗ be the dual space of X. Let φ: R+ → R+ be a strictly increasing and continuous function such that φ(0) = 0, φ(r) → ∞ as r → ∞, and let Jφ be the duality mapping of X corresponding to φ. We will prove that for every R \u3e 0 and every x0 ∈ X there exists a nondecreasing function ψ = ψ(R, x0): R+ → R+ such that ψ(0) = 0, ψ(r) \u3e 0 for r \u3e 0, and hx ∗ − x ∗ 0, x − x0i ≥ ψ(kx − x0k)kx − x0k for all x satisfying kx − x0k ≤ R and all x ∗ ∈ Jφx and x ∗ 0 ∈ Jφx0. This result extends the previous results of Prüß and Kartsatos who studied the normalized duality mapping J (with φ(r) = r) for uniformly convex and locally uniformly Banach spaces, respectively. As an application, we give a concise proof of the continuity of the Yosida approximants A φ λ and resolvents J φ λ of a maximal monotone operator A: X ⊃ D(A) → 2 X∗ on (0, ∞) × X for an arbitrary φ when X is reflexive and both X and X∗ are locally uniformly convex. We then present an example of pseudomonotone homotopy involving Aφλ on which the Browder degree is invariant. We also discuss examples of positively homogeneous maximal monotone operators to which the theory developed herein is applicable
Ferromagnetism in MnX2 ( X = S, Se) monolayers
No full textUsing density functional theory combined with Monte Carlo (MC) simulations, we show that the two dimensional (2D) MnS2 and MnSe2 sheets are ideal magnetic semiconductors with long-range magnetic ordering and high magnetic moments (3 mu(B) per unit cell), where all the Mn atoms are ferromagnetically coupled, and the Curie temperatures (T-C) estimated for MnS2 and MnSe2 by the MC simulations are 225 and 250 K, respectively, which can be further increased to 330 K and 375 K by applying 5% biaxial tensile strains.Chemistry, PhysicalPhysics, Atomic, Molecular & ChemicalSCI(E)[email protected]
Heavy metal-free, near-infrared colloidal quantum dots for efficient photoelectrochemical hydrogen generation
No full textPhotoelectrochemical (PEC) hydrogen generation based on colloidal quantum dots (QDs) is very promising because of its high solar energy to fuel conversion efficiency and low fabrication costs. However, its commercial development is hindered by various challenges, including the widespread use of toxic heavy metal–based QDs as sensitizers. We report an environmentally friendly, high efficiency PEC device in which the photoanode consists of a mesoporous TiO2 film sensitized with heavy metal-free, near-infrared (NIR) colloidal CuInSexS2−x (CISeS) QDs. To reduce surface-related traps, we grew an ultrathin ZnS shell on the CISeS core QDs by cation exchange. The PEC cell based on this core/shell CISeS/ZnS QDs exhibits suppressed charge recombination and a saturated photocurrent density of ~5.3 mA/cm2 under one sun illumination (AM 1.5 G, 100 mW/cm2). In addition, the as-prepared PEC device shows an outstanding stability, exhibiting a drop of only 23% after 9 h illumination. The success in using such core/shell CISeS/ZnS QDs paves the way to realize environment-friendly, high efficiency and cost-effective PEC devices for hydrogen production
Magnetic properties of phase-separated GaxFe4-xN:Mn in a GaN matrix
No full textDue to their striking magnetic properties, magnetic iron nitride-based (FexN and GayFexN)
compounds are attracting attention as building blocks for high-density magnetic recording write heads
and media.
We have recently demonstrated that we can control the aggregation of GaxFe4-xN nanocrystals (NCs)
embedded in a III-nitride matrix. By tuning the growth parameters, and consequently the
stoichiometry of the NCs, we can dictate the magnetic response of the system to be either
ferromagnetic or antiferromagnetic [1,2].
Here we report on the influence of Mn co-doping on the magnetic properties of self-assembled planar
arrays of GaxFe4-xN:Mn NCs embedded in GaN. The samples, fabricated by means of metal organic
vapor phase epitaxy (MOVPE) according to a protocol already reported [1], have all the same
nominal Fe content and differ for the Mn nominal content. The samples are characterized by
transmission electron microscopy and x-ray diffraction. We have measured, by SQUID, hysteresis
loops at different temperatures in the 5-300 K range, the thermal dependence of the magnetization at
different values of the applied magnetic field (in zero-field-cooling and field-cooling modes) and the
field-dependent isothermal and demagnetized remanence, allowing the construction of the Delta_M plots.
In all the investigated samples, the magnetic analysis reveals the presence of a ferromagnetic
component and of a paramagnetic one. The former, assigned to the Ga x Fe 4-x N:Mn NCs, decreases
with increasing the Mn content in the samples, whereas the latter increases and is ascribable to diluted
Fe and/or Mn ions in the GaN matrix. The whole of the results indicates that Mn acts so as to hinder
the formation and/or the growth of the NCs.
The magnetothermal behavior of the samples is well explained considering that magnetically relaxing
NCs coexist with non-relaxing ones. The magnetic moments of the larger NCs are thermally stable
in the spanned temperature range, also due to the fact that dipolar interactions favor the formation of
magnetic aggregates. The magnetic moments of the smaller NCs undergo a superparamagnetic-like
relaxation. We can consider that, at low-temperature, the small NCs are part of the magnetic
aggregates, as their moments are blocked under the action of dipolar interactions that compete with
their magnetic anisotropy. With increasing temperature, the moments of the small NCs relax almost
independently, thus leaving the magnetic aggregates.
[1] A. Navarro-Quezada et al. Appl. Phys. Lett. 101 (2012) 081911
[2] A. Grois et al., Nanotechnol. 25 (2014) 39570
OpenMP solver for rotating spin-1 spin–orbit- and Rabi-coupled Bose–Einstein condensates
No full textWe present OpenMP version of a Fortran program for solving the Gross–Pitaevskii equation for a harmonically trapped three-component rotating spin-1 spinor Bose–Einstein condensate (BEC) in two spatial dimensions with or without spin–orbit (SO) and Rabi couplings. The program uses either Rashba or Dresselhaus SO coupling. We use the split-step Crank–Nicolson discretization scheme for imaginary- and real-time propagation to calculate stationary states and BEC dynamics, respectively. New version program summary: Program title: BEC-GP-SPINOR-ROT-OMP, a program package containing programs spin-SO-rot-imre2d-omp.f90, with util.f90. CPC Library link to program files: https://doi.org/10.17632/j3wr4wn946.2 Licensing provisions: Apache License 2.0 Programming language: OpenMP Fortran 90/95. The program is tested with the GNU, Intel, PGI, and Oracle (former Sun) compilers. Supplementary material: File Supp.pdf gives additional details about the new program version and the underlying physical system. Journal Reference of previous version: Comput. Phys. Commun. 259 (2021) 107657. Does the new version supersede the previous version?: Only partially. The program spin-SO-rot-imre2d-omp.f90 supersedes spin-SO-imre2d-omp.f90, while the one-dimensional program is not part of this package. Nature of problem: The present Open Multi-Processing (OpenMP) Fortran program solves the time-dependent nonlinear partial differential Gross–Pitaevskii (GP) equation for a trapped rotating spinor Bose–Einstein condensate (BEC) in two spatial dimensions. Solution method: We employ the split-step Crank–Nicolson scheme to discretize the time-dependent GP equation in space and time. The discretized equation is then solved by imaginary- or real-time propagation, employing adequately small space and time steps, to yield the solution of stationary and non-stationary problems, respectively. Reason for new version: The BEC is a special form of matter called superfluid. A hallmark of superfluidity is the formation of quantized vortices in a rotating BEC. The present program can be used to study the generation of quantized vortices in a rotating spin-1 trapped BEC and hence should be of general interest to researchers from various fields. Summary of revisions: Previously we published Fortran [1] and C [2] programs for solving the mean-field GP equation for a BEC, which are now enjoying widespread use. Later we extended these programs to the more complex scenario of dipolar BECs [3], spin-1 spinor BECs [4], and of rotating BECs [5]. The OpenMP [6, 7] and CUDA/MPI [8, 9, 10] versions of these programs, designed to make these faster and more efficient in multi-core computers, are also available. In this paper we present Fortran 90/95 program for solving the GP equation of a two-dimensional (2D) rotating spin-1 spinor BEC with Rashba [11] and Dresselhaus [12] spin–orbit (SO) coupling and Rabi coupling, involving a modification over the same for a spin-1 spinor BEC [4]. A new input parameter OMEG, which represents the angular velocity of rotation Ω of the spin-1 spinor BEC, has been introduced in the program, following Ref. [5]. Besides this new parameter, the execution of the present program follows the same procedure as the 2D program of Ref. [4]. All other input parameters in the two programs are identical and the reader is advised to consult that reference for further details. For some values of input parameters the quantized vortices of a rotating BEC could be arranged in the form of a lattice with a certain spatial symmetry, e.g., triangular or square lattice [5]. In our numerical study, we established recently such a symmetric lattice structure for a Rashba SO-coupled rotating spin-1 BEC in the simplest case, without the Rabi coupling [13]. A Dresselhaus SO-coupled rotating spin-1 BEC should also lead to identical structure, provided the sign of the angular velocity of rotation is changed. For the sake of completeness, in the supplementary material related to this article that can be found online at URL we provide the corresponding GP equations for a rotating spin-1 BEC with some instructive numerical examples. The program package BEC-GP-SPINOR-ROT-OMP contains the programs spin-SO-rot-imre2d-omp.f90 and util.f90 in the directory src, as well as the files makefile and README.md. The makefile allows automated compilation of the program using different supported compilers (GNU, Intel, PGI, Oracle) by a simple make command, as in Ref. [4]. The file README.md contains instructions on how to compile and run the programs. The directory output contains examples of matching outputs of imaginary- and real-time propagation programs in sub-directories with a generic name rotxgamyferro or rotxgamyantiferro, where x denotes the value of the angular velocity of rotation Ω and y denotes the strength of the SO coupling γ for ferromagnetic (c0=482,c2=15) and antiferromagnetic (c0=669,c2=−3.1) cases. The results in imaginary-time sub-directories rot.3gam.5ferro and rot.3gam.5antiferro are calculated using the respective converged imaginary-time wave functions with zero angular velocity. The real-time sub-directories rot.3gam.5ferro and rot.3gam.5polar contain real-time results calculated using the respective converged imaginary-time wave functions as inputs. These sub-directories also contain gnuplot programs fig*.gnu which can be used to generate fig*.eps figure files of component densities. References [1] P. Muruganandam, S. K. Adhikari, Comput. Phys. Commun. 180 (2009) 1888. [2] D. Vudragović, I. Vidanović, A. Balaž, P. Muruganandam, S. K. Adhikari, Comput. Phys. Commun. 183 (2012) 2021. [3] R. Kishor Kumar, L.E. Young-S., D. Vudragović, A. Balaž, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 195 (2015) 117. [4] R. Ravisankar, D. Vudragović, P. Muruganandam, A. Balaž, S. K. Adhikari, Comput. Phys. Commun. 259 (2021) 107657. [5] R. K. Kumar, V. Lončar, P. Muruganandam, S. K. Adhikari, A. Balaž, Comput. Phys. Commun. 240 (2019) 74. [6] L.E. Young-S., D. Vudragović, P. Muruganandam, S.K. Adhikari, A. Balaž, Comput. Phys. Commun. 204 (2016) 209. [7] L. E. Young-S., P. Muruganandam, S. K. Adhikari, V. Lončar, D. Vudragović, A. Balaž, Comput. Phys. Commun. 220 (2017) 503. [8] V. Lončar, A. Balaž, A. Bogojević, S. Škrbić, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 200 (2016) 406. [9] V. Lončar, L.E. Young-S., S. Škrbić, P. Muruganandam, S.K. Adhikari, A. Balaž, Comput. Phys. Commun. 209 (2016) 190. [10] B. Satarić, V. Slavnić, A. Belić, A. Balaž, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 200 (2016) 411. [11] E. I. Rashba, Fiz. Tverd. Tela 2 (1960) 1224; English Transla.: Sov. Phys. Solid State 2 (1960) 1109. [12] G. Dresselhaus, Phys. Rev. 100 (1955) 580. [13] S. K. Adhikari, J. Phys.: Condens. Matter 33 (2021) 065404.Council of Scientific and Industrial Research, IndiaConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Science and Engineering Research BoardDepartment of Physics Bharathidasan University Palkalaiperur CampusInstitute of Physics Belgrade University of Belgrade, Pregrevica 118Instituto de Física Teórica UNESP – Universidade Estadual Paulista, 01.140-70 São PauloInstituto de Física Teórica UNESP – Universidade Estadual Paulista, 01.140-70 São PauloCouncil of Scientific and Industrial Research, India: 03(1422)/18/EMR-IICNPq: 301324/2019-0Science and Engineering Research Board: CRG/2019/00405
Heavy metal-free, near-infrared colloidal quantum dots for efficient photoelectrochemical hydrogen generation
No full textPhotoelectrochemical (PEC) hydrogen generation based on colloidal quantum dots (QDs) is very promising because of its high solar energy to fuel conversion efficiency and low fabrication costs. However, its commercial development is hindered by various challenges, including the widespread use of toxic heavy metal–based QDs as sensitizers. We report an environmentally friendly, high efficiency PEC device in which the photoanode consists of a mesoporous TiO2 film sensitized with heavy metal-free, near-infrared (NIR) colloidal CuInSexS2−x (CISeS) QDs. To reduce surface-related traps, we grew an ultrathin ZnS shell on the CISeS core QDs by cation exchange. The PEC cell based on this core/shell CISeS/ZnS QDs exhibits suppressed charge recombination and a saturated photocurrent density of ~5.3 mA/cm2 under one sun illumination (AM 1.5 G, 100 mW/cm2). In addition, the as-prepared PEC device shows an outstanding stability, exhibiting a drop of only 23% after 9 h illumination. The success in using such core/shell CISeS/ZnS QDs paves the way to realize environment-friendly, high efficiency and cost-effective PEC devices for hydrogen production
Existence Results for Multivalued Compact Perturbations of -Accretive Operators
No full textLet be a real Banach space with its dual and be a nonempty,
bounded and open subset of with . Let
be an -accretive operator with and , and let be a
compact operator from into with . We prove that if is multivalued and if is single-valued, provided for all and The
surjectivity of is proved if is expansive and is weakly
coercive. Analogous results are given if has compact resolvents and is
continuous and bounded. Various results by Kartsatos, and Kartsatos and Liu are
improved, and a result by Morales is generalized.Comment: The paper needs a significant adjustment because of similar existing
result
Applications of Degree Theories to Nonlinear Operator Equations in Banach Spaces
No full textLet X be a real Banach space and G1, G2 two nonempty, open and bounded subsets of X such that 0 ∈ G2 and G2 ⊂ G1. The problem (∗) T x + Cx = 0 is considered, where T : X ⊃ D(T) → X is an accretive or monotone operator with 0 ∈ D(T) and T(0) = 0, while C : X ⊃ D(C) → X can be, e.g., one of the following types: (a) compact; (b) continuous and bounded with the resolvents of T compact; (c) demicontinuous, bounded and of type (S+) with T positively homogeneous of degree one; (d) quasi-bounded and satisfies a generalized (S+)-condition w.r.t. the operator T, while T is positively homogeneous of degree one. Solutions are sought for the problem (∗) lying in the set D(T + C) ∩ (G1 \ G2). Nontrivial solutions of (∗) exist even when C(0) = 0. The degree theories of Leray and Schauder, Browder, and Skrypnik as well as the degree theory by Kartsatos and Skrypnik for densely defined operators T, C are used. The last three degree theories do not assume any compactness conditions on the operator C. The excision and additivity properties of these degree theories are employed, and the main results are significant extensions or generalizations of previous results by Krasnoselskii, Guo, Ding and Kartsatos involving the relaxation of compactness conditions and/or conditions on the boundedness of the operator T. Moreover, a new degree theory developed by Kartsatos and Skrypnik has been used to prove a similar result for operators of type T + C, where T : X ⊃ D(T) → 2 X∗ is a multi-valued maximal monotone operator, with 0 ∈ D(T) and 0 ∈ T(0), and C : X ⊃ D(C) → X∗ is a densely defined quasi-bounded and finitely continuous operator of type (S˜+). The problem of existence of nonzero solutions for T x + Cx + Gx 3 0 is also considered. Here, T is maximal monotone, C is bounded demicontinuous of type (S+), and G is of class (P). Eigenvalue and invariance of domain results have also been established for the sum L + T + C : G ∩ D(L) → 2 X∗ , where G ⊂ X is open and bounded, L : X ⊃ D(L) → X∗ densely defined linear maximal monotone, T : X → 2X∗ bounded maximal monotone, and C : G → X∗ bounded demicontinuous of type (S+) w. r. t. D(L)
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