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Symmetry in Special and General Relativity

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ISBN: 9783039280940 9783039280957 Year: Pages: 100 DOI: 10.3390/books978-3-03928-095-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2020-01-30 16:39:46
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The development of special and general relativity has relied significantly on ideas of symmetry. Similarly, modern efforts to test these theories have often sought either violations or extensions of the symmetries seen, and symmetry is regularly used a tool in seeking new applications. In this Special Issue of symmetry, we explore some contemporary research related to symmetry in special and general relativity.

Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems

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ISBN: 9783039288793 / 9783039288809 Year: Pages: 118 DOI: 10.3390/books978-3-03928-880-9 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- Economics
Added to DOAB on : 2020-06-09 16:38:57
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This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.

Current Trends in Symmetric Polynomials with their Applications

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ISBN: 9783039216208 9783039216215 Year: Pages: 238 DOI: 10.3390/books978-3-03921-621-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Fubini polynomials --- w-torsion Fubini polynomials --- fermionic p-adic integrals --- symmetric identities --- Chebyshev polynomials --- sums of finite products --- hypergeometric function --- Fubini polynomials --- Euler numbers --- symmetric identities --- elementary method --- computational formula --- two variable q-Berstein polynomial --- two variable q-Berstein operator --- q-Euler number --- q-Euler polynomial --- Fubini polynomials --- Euler numbers --- congruence --- elementary method --- q-Bernoulli numbers --- q-Bernoulli polynomials --- two variable q-Bernstein polynomials --- two variable q-Bernstein operators --- p-adic integral on ?p --- the degenerate gamma function --- the modified degenerate gamma function --- the degenerate Laplace transform --- the modified degenerate Laplace transform --- Fibonacci --- Lucas --- linear form in logarithms --- continued fraction --- reduction method --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Hermite --- generalized Laguerre --- Legendre --- Gegenbauer --- Jacobi --- third-order character --- classical Gauss sums --- rational polynomials --- analytic method --- recursive formula --- fermionic p-adic q-integral on ?p --- q-Euler polynomials --- q-Changhee polynomials --- symmetry group --- Apostol-type Frobenius–Euler polynomials --- three-variable Hermite polynomials --- symmetric identities --- explicit relations --- operational connection --- q-Volkenborn integral on ?p --- Bernoulli numbers and polynomials --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- Changhee polynomials --- Changhee polynomials of type two --- fermionic p-adic integral on ?p --- Chebyshev polynomials of the first, second, third, and fourth kinds --- sums of finite products --- representation --- catalan numbers --- elementary and combinatorial methods --- recursive sequence --- convolution sums --- well-posedness --- stability --- acoustic wave equation --- perfectly matched layer --- Fibonacci polynomials --- Lucas polynomials --- trivariate Fibonacci polynomials --- trivariate Lucas polynomials --- generating functions --- central incomplete Bell polynomials --- central complete Bell polynomials --- central complete Bell numbers --- Legendre polynomials --- Laguerre polynomials --- generalized Laguerre polynomials --- Gegenbauer polynomials --- hypergeometric functions 1F1 and 2F1 --- Euler polynomials --- Bernoulli polynomials --- elementary method --- identity --- congruence --- new sequence --- Catalan numbers --- elementary and combinatorial methods --- congruence --- conjecture --- fluctuation theorem --- thermodynamics of information --- stochastic thermodynamics --- mutual information --- non-equilibrium free energy --- entropy production

Symmetry in Graph Theory

Author:
ISBN: 9783038976585 Year: Pages: 340 DOI: 10.3390/books978-3-03897-659-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Science (General)
Added to DOAB on : 2019-03-21 15:50:41
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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.

Integral Transforms and Operational Calculus

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ISBN: 9783039216185 9783039216192 Year: Pages: 510 DOI: 10.3390/books978-3-03921-619-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

Keywords

highly oscillatory --- convolution quadrature rule --- volterra integral equation --- Bessel kernel --- convergence --- higher order Schwarzian derivatives --- Janowski star-like function --- Janowski convex function --- bound on derivatives --- tangent numbers --- tangent polynomials --- Carlitz-type q-tangent numbers --- Carlitz-type q-tangent polynomials --- (p,q)-analogue of tangent numbers and polynomials --- (p,q)-analogue of tangent zeta function --- symmetric identities --- zeros --- Lommel functions --- univalent functions --- starlike functions --- convex functions --- inclusion relationships --- analytic function --- Hankel determinant --- exponential function --- upper bound --- nonlinear boundary value problems --- fractional-order differential equations --- Riemann-Stieltjes functional integral --- Liouville-Caputo fractional derivative --- infinite-point boundary conditions --- advanced and deviated arguments --- existence of at least one solution --- Fredholm integral equation --- Schauder fixed point theorem --- Hölder condition --- generalized Kuramoto–Sivashinsky equation --- modified Kudryashov method --- exact solutions --- Maple graphs --- analytic function --- Hadamard product (convolution) --- partial sum --- Srivastava–Tomovski generalization of Mittag–Leffler function --- subordination --- differential equation --- differential inclusion --- Liouville–Caputo-type fractional derivative --- fractional integral --- existence --- fixed point --- Bernoulli spiral --- Grandi curves --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- orthogonality property --- symmetric --- encryption --- password --- hash --- cryptography --- PBKDF --- q–Bleimann–Butzer–Hahn operators --- (p,q)-integers --- (p,q)-Bernstein operators --- (p,q)-Bleimann–Butzer–Hahn operators --- modulus of continuity --- rate of approximation --- K-functional --- Hurwitz-Lerch zeta function --- generalized functions --- analytic number theory --- ?-generalized Hurwitz-Lerch zeta functions --- derivative properties --- series representation --- basic hypergeometric functions --- generating functions --- q-polynomials --- analytic functions --- Mittag–Leffler functions --- starlike functions --- convex functions --- Hardy space --- vibrating string equation --- initial conditions --- spectral decomposition --- regular solution --- the uniqueness of the solution --- the existence of a solution --- analytic --- ?-convex function --- starlike function --- strongly-starlike function --- subordination --- q -Sheffer–Appell polynomials --- generating relations --- determinant definition --- recurrence relation --- q -Hermite–Bernoulli polynomials --- q -Hermite–Euler polynomials --- q -Hermite–Genocchi polynomials --- Volterra integral equations --- highly oscillatory Bessel kernel --- Hermite interpolation --- direct Hermite collocation method --- piecewise Hermite collocation method --- differential operator --- q-hypergeometric functions --- meromorphic function --- Mittag–Leffler function --- Hadamard product --- differential subordination --- starlike functions --- Bell numbers --- radius estimate --- (p, q)-integers --- Dunkl analogue --- generating functions --- generalization of exponential function --- Szász operator --- modulus of continuity --- function spaces and their duals --- distributions --- tempered distributions --- Schwartz testing function space --- generalized functions --- distribution space --- wavelet transform of generalized functions --- Fourier transform --- analytic function --- subordination --- Dziok–Srivastava operator --- nonlinear boundary value problem --- nonlocal --- multi-point --- multi-strip --- existence --- Ulam stability --- functions of bounded boundary and bounded radius rotations --- subordination --- functions with positive real part --- uniformly starlike and convex functions --- analytic functions --- univalent functions --- starlike and q-starlike functions --- q-derivative (or q-difference) operator --- sufficient conditions --- distortion theorems --- Janowski functions --- analytic number theory --- ?-generalized Hurwitz–Lerch zeta functions --- derivative properties --- recurrence relations --- integral representations --- Mellin transform --- natural transform --- Adomian decomposition method --- Caputo fractional derivative --- generalized mittag-leffler function --- analytic functions --- Hadamard product --- starlike functions --- q-derivative (or q-difference) operator --- Hankel determinant --- q-starlike functions --- fuzzy volterra integro-differential equations --- fuzzy general linear method --- fuzzy differential equations --- generalized Hukuhara differentiability --- spectrum symmetry --- DCT --- MFCC --- audio features --- anuran calls --- analytic functions --- convex functions --- starlike functions --- strongly convex functions --- strongly starlike functions --- uniformly convex functions --- Struve functions --- truncated-exponential polynomials --- monomiality principle --- generating functions --- Apostol-type polynomials and Apostol-type numbers --- Bernoulli, Euler and Genocchi polynomials --- Bernoulli, Euler, and Genocchi numbers --- operational methods --- summation formulas --- symmetric identities --- Euler numbers and polynomials --- q-Euler numbers and polynomials --- Hurwitz-Euler eta function --- multiple Hurwitz-Euler eta function --- higher order q-Euler numbers and polynomials --- (p, q)-Euler numbers and polynomials of higher order --- symmetric identities --- symmetry of the zero

Differential Geometry

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ISBN: 9783039218004 9783039218011 Year: Pages: 166 DOI: 10.3390/books978-3-03921-801-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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Abstract

The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and trans-Sasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both well-known geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.

Keywords

Euclidean submanifold --- position vector field --- concurrent vector field --- concircular vector field --- rectifying submanifold --- T-submanifolds --- constant ratio submanifolds --- Ricci soliton --- Kähler–Einstein metrics --- compact complex surfaces --- pinching of the curvatures --- statistical manifolds --- Hessian manifolds --- Hessian sectional curvature --- scalar curvature --- Ricci curvature --- Minkowski plane --- Minkowskian length --- Minkowskian angle --- Minkowskian pseudo-angle --- L2-harmonic forms --- Hodge–Laplacian --- manifold with singularity --- L2-Stokes theorem --- capacity --- k-th generalized Tanaka–Webster connection --- non-flat complex space form --- real hypersurface --- lie derivative --- shape operator --- conical surface --- developable surface --- generalized 1-type Gauss map --- cylindrical hypersurface --- inextensible flow --- lightlike surface --- ruled surface --- Darboux frame --- C-Bochner tensor --- generalized normalized ?-Casorati curvature --- Sasakian manifold --- slant --- invariant --- anti-invariant --- trans-Sasakian 3-manifold --- Reeb flow symmetry --- Ricci operator --- Sasakian statistical manifold --- conjugate connection --- Casorati curvature --- framed rectifying curves --- singular points --- framed helices --- centrodes --- circular rectifying curves --- statistical structure --- affine hypersurface --- affine sphere --- conjugate symmetric statistical structure --- sectional ?-curvature --- complete connection --- symplectic curves --- circular helices --- symplectic curvatures --- Frenet frame

Engineering Mathematics in Ship Design

Authors: --- ---
ISBN: 9783039218042 9783039218059 Year: Pages: 168 DOI: 10.3390/books978-3-03921-805-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: General and Civil Engineering --- Technology (General)
Added to DOAB on : 2020-01-30 16:39:46
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Engineering mathematics is a branch of applied mathematics where mathematical methods and techniques are implemented for solving problems related to the engineering and industry. It also represents a multidisciplinary approach where theoretical and practical aspects are deeply merged with the aim at obtaining optimized solutions. In line with that, the present Special Issue, 'Engineering Mathematics in Ship Design', is focused, in particular, with the use of this sort of engineering science in the design of ships and vessels. Articles are welcome when applied science or computation science in ship design represent the core of the discussion.

Advances in Mechanical Systems Dynamics

Authors: --- ---
ISBN: 9783039281886 9783039281893 Year: Pages: 236 DOI: 10.3390/books978-3-03928-189-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mechanical Engineering --- General and Civil Engineering --- Technology (General)
Added to DOAB on : 2020-04-07 23:07:08
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Modern dynamics was established many centuries ago by Galileo and Newton before the beginning of the industrial era. Presently, we are in the presence of the fourth industrial revolution, and mechanical systems are increasingly being integrated with electronic, electrical, and fluidic systems. This trend is present not only in the industrial environment, which will soon be characterized by the cyber-physical systems of industry 4.0, but also in other environments like mobility, health and bio-engineering, food and natural resources, safety, and sustainable living. In this context, purely mechanical systems with quasi-static behavior will become less common and the state-of-the-art will soon be represented by integrated mechanical systems, which need accurate dynamic models to predict their behavior. Therefore, mechanical system dynamics are going to play an increasingly central role. Significant research efforts are needed to improve the identification of the mechanical properties of systems in order to develop models that take non-linearity into account, and to develop efficient simulation tools. This Special Issue aims at disseminating the latest research achievements, findings, and ideas in mechanical systems dynamics, with particular emphasis on applications that are strongly integrated with other systems and require a multi-physical approach.

Noether's Theorem and Symmetry

Authors: ---
ISBN: 9783039282340 9783039282357 Year: Pages: 186 DOI: 10.3390/books978-3-03928-235-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Law
Added to DOAB on : 2020-04-07 23:07:08
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In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.

Possible Scenarios for Homochirality on Earth

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ISBN: 9783039217229 9783039217236 Year: Pages: 318 DOI: 10.3390/books978-3-03921-723-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General)
Added to DOAB on : 2019-12-09 11:49:16
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In 1978, Fred Hoyle proposed that interstellar comets carrying several viruses landed on Earth as part of the panspermia hypotheses. With respect to life, the origin of homochirality on Earth has been the greatest mystery because life cannot exist without molecular asymmetry. Many scientists have proposed several possible hypotheses to answer this long-standing L-D question. Previously, Martin Gardner raised the question about mirror symmetry and broken mirror symmetry in terms of the homochirality question in his monographs (1964 and 1990). Possible scenarios for the L-D issue can be categorized into (i) Earth and exoterrestrial origins, (ii) by-chance and necessity mechanisms, and (iii) mirror-symmetrical and non-mirror-symmetrical forces as physical and chemical origins. These scenarios should involve further great amplification mechanisms, enabling a pure L- or D-world.

Keywords

chirogenesis --- enantiomorphism --- nepheline --- magmatic flow --- etch figures --- origin of life --- biological homochirality --- deracemization --- super-high-velocity impact --- plasma reactor --- absolute asymmetric synthesis --- amino acids --- origin of life --- amino acid handedness --- nucleus–molecular coupling --- chirality --- circularly polarized luminescence --- circular dichroism --- symmetry breaking --- parity violation --- weak neutral current --- tunneling --- Z0 boson --- homochirality --- precision measurement --- homochirality --- circularly polarized light --- asymmetric reaction --- polymer --- ?-strand --- hidden chirality --- two-fold helix --- multi-point approximation --- tilt-chirality --- high dimensional chirality --- spin polarized electrons --- homochirality --- magnetism --- prebiotic --- environmental chirality --- C1- and C2-symmetric catalysts --- chiral field (memory) --- racemic field --- Viedma ripening effect --- Wallach’s rule --- heat capacity --- metal-organic framework --- triethylenediamine (DABCO) molecules --- racemate --- Salam hypothesis --- homochirality --- parity violation --- neutrinos --- gravitation --- enantiomer self-disproportionation --- SDE --- achiral stationary phase --- homochiral and heterochiral aggregates --- chiral separation --- chirality --- genesis of life chirality --- asymmetric autocatalysis --- homochirality --- chirality --- asymmetric synthesis --- Soai reaction --- biological homochirality --- enantioselective reaction --- autocatalysis --- origin of life --- replicators --- bioorganic homochirality --- circularly polarized photon --- spin-polarized lepton --- parity violation in the weak interaction --- symmetry breaking --- assemblies --- supramolecular chirality --- homochirality --- self-assembly --- vortex --- lipid --- supramolecular assembly --- symmetry breaking --- homochirality

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english (15)

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2020 (8)

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