Mathematics Commons^™

Phase-Only Digital Encryption, Jonathan Blackledge, Western Govere, Dumisani Sibanda

Articles

Abstract—We study then-dimensional deconvolution prob-lem associated with an impulse response function and an(additive) noise function that are both characterised by thesame phase-only stochastic spectrum. In this case, it is shownthat the deconvolution problem becomes well-posed and has ageneral solution that is both exact and unique, subject to are-normalisation condition relating to the scale of the solution.While the phase-only spectral model considered is of limitedvalue in general (in particular, problems arising in the fieldsof digital signal processing and communications engineering,specifically with regard to the retrieval of information fromnoise), its application to digital cryptography has potential.One of the reasons for this (as …

Sustainable Energy Governance In South Tyrol (Italy): A Probabilistic Bipartite Network Model, Jessica Belest, Laura Secco, Elena Pisani, Alberto Caimo

Articles

At the national scale, almost all of the European countries have already achieved energy transition targets, while at the regional and local scales, there is still some potential to further push sustainable energy transitions. Regions and localities have the support of political, social, and economic actors who make decisions for meeting existing social, environmental and economic needs recognising local specificities.

These actors compose the sustainable energy governance that is fundamental to effectively plan and manage energy resources. In collaborative relationships, these actors share, save, and protect several kinds of resources, thereby making energy transitions deeper and more effective.

This research …

Algebraic Entropies, Hopficity And Co-Hopficity Of Direct Sums Of Abelian Groups, Brendan Goldsmith, Katao Kong

Articles

Necessary and sufficient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopfian and co-Hopfian groups. We obtain sufficient conditions in some situations by placing restrictions on the homomorphisms between the groups. There are clear similarities between the various cases but there is not a simple duality involved.

On The Time Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin Martin

Articles

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes, and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero, we recover the well known integrable three-wave system.

Econophysics And Fractional Calculus: Einstein's Evolution Equation, The Fractal Market Hypothesis, Trend Analysis And Future Price Prediction, Jonathan Blackledge, Derek Kearney, Marc Lamphiere, Raja Rani, Paddy Walsh

Articles

This paper examines a range of results that can be derived from Einstein’s evolution equation focusing on the effect of introducing a Lévy distribution into the evolution equation. In this context, we examine the derivation (derived exclusively from the evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov–Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent and volatility. In this way, we provide a collection of results (which includes the derivation of certain fractional partial …

On The Determination Of The Number Of Positive And Negative Polynomial Zeros And Their Isolation, Emil Prodanov

Articles

A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real co-efficients and degree $n$ can be restricted with significantly better determinacy than that provided by the Descartes' rule of signs and also isolate quite successfully the zeros of the polynomial. The method relies on solving equations of degree smaller than that of the given polynomial. One can determine analytically the exact number of positive and negative zeros of a polynomial of degree up to and including five and also fully isolate the zeros of the polynomial analytically and …

Current Source Density Approaches Improve Spatial Resolution In Event Related Potential Analysis In People With Parkinson's Disease, Conor Fearon, John Butler, Saskia M. Waechter, Isabelle Killane, Richard B. Reilly, Timothy Lynch

Articles

No abstract provided.

Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann

Articles

The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.

Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov

Articles

We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …

When The Intrinsic Algebraic Entropy Is Not Really Intrinsic, Brendan Goldsmith, Luigi Salce

Articles

The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside of this class.

Injective Tensor Products Of Tree Spaces, Milena Venkova, Christopher Boyd, Costas Poulios

Articles

We study tensor products on tree spaces; in particular, we give necessary and sufficient conditions for the n-fold injective tensor product of tree spaces to contain a copy of l_1.

Benjamin-Ono Model Of An Internal Wave Under A Flat Surface, Alan Compelli, Rossen Ivanov

Articles

A two-layer uid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is infinitely deep, with a higher density than the upper layer which is bounded above by a at surface. The uids are incompressible and inviscid. A Hamiltonian formulation for the dynamics in the presence of a depth-varying current is presented and it is shown that an appropriate scaling leads to the integrable Benjamin-Ono equation.

Van Der Waals Universe With Adiabatic Matter Creation, Emil Prodanov, Rossen Ivanov

Articles

A FRWL cosmological model with perfect fluid comprising of van der Waals gas and dust has been studied in the context of dynamical analysis of a three-component autonomous non-linear dynamical system for the particle number density $n$, the Hubble parameter $H$, and the temperature $T$. Perfect fluid isentropic particle creation at rate proportional to an integer power $\alpha$ of $H$ has been incorporated. The existence of a global first integral allows the determination of the temperature evolution law and hence the reduction of the dynamical system to a two-component one. Special attention is paid to the cases of $\alpha = …

Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

Articles

Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups G_R ≃ D_h. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the G_R-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with D_h symmetries are presented.

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

Does It Take Three To Dance The Tango? Organizational Design, Triadic Structures And Boundary Spanning Across Subunits, Stefano Tasselli, Alberto Caimo

Articles

In this paper, we investigate the processes of boundary spanning across subunits within organizational networks. We hypothesize that patterns of advice across organizational subunits are explained by different triadic mechanisms depending on the organizational design of the intra-organizational network. In organizational networks characterized by flat hierarchy, we found triadic cyclic closure to be positively associated to boundary spanning across subunits; but when the network reflects an organizational structure with formal hierarchical differentiation among members, then we found triadic transitive closure to be associated to boundary spanning across subunits. We test these predictions in two empirical studies consisting of two organizational …

On The Cosmological Models With Matter Creation, Emil M. Prodanov, Rossen Ivanov

Articles

The matter creation model of Prigogine--Géhéniau--Gunzig--Nardone is revisited in terms of a redefined creation pressure which does not lead to irreversible adiabatic evolution at constant specific entropy. With the resulting freedom to choose a particular gas process, a flat FRWL cosmological model is proposed based on three input characteristics: (i) a perfect fluid comprising of an ideal gas, (ii) a quasi-adiabatic polytropic process, and (iii) a particular rate of particle creation. Such model leads to the description of the late-time acceleration of the expanding Universe with a natural transition from decelerating to accelerating regime. Only the Friedmann equations and the …

On The Time-Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin I. Martin

Articles

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume a constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero we recover the well known integrable three-wave system.

On The Reidemeister Spectrum Of An Abelian Group, Brendan Goldsmith, Fatemeh Karimi, Noel White

Articles

The Reidemeister number of an automorphism ϕ of an Abelian group G is calculated by determining the cardinality of the quotient group G/(ϕ − 1G)(G), and the Reidemeister spectrum of G is precisely the set of Reidemeister numbers of the automorphisms of G. In this work we determine the full spectrum of several types of group, paying particular attention to groups of torsion-free rank 1 and to direct sums and products. We show how to make use of strong realization results for Abelian groups to exhibit many groups where the Reidemeister number is infinite for all automorphisms; such groups then …

Vacuum Polarization For Varying Quantum Scalar Field Parameters In Schwarzschild–Anti–De Sitter Spacetime, Cormac Breen, Peter Taylor

Articles

Equipped with new powerful and efficient methods for computing quantum expectation values in static-spherically symmetric spacetimes in arbitrary dimensions, we perform an in-depth investigation of how the quantum vacuum polarization varies with the parameters in the theory. In particular, we compute and compare the vacuum polarization for a quantum scalar field in the Schwarzschild–anti–de Sitter black hole spacetime for a range of values of the field mass and field coupling constant as well as the black hole mass and number of spacetime dimensions. In addition, a new approximation for the vacuum polarization in asymptotically anti–de Sitter black hole spacetimes is …

Investigating Secondary Students Beliefs About Mathematical Problem-Solving, Mark Prendergast, Cormac Breen, Aibhin Bray, Fiona Faulkner, Brian Carroll, Dominic Quinn

Articles

Many studies over the past thirty years have highlighted the important role of students’ beliefs for successful problem solving in mathematics. Given the recent emphasis afforded to problem solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing thirty item (five scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief …

Cognitive Load Reduces The Effects Of Optic Flow On Gait And 2 Electrocortical Dynamics During Treadmill Walking 3, Brenda Malcolm, John J. Foxe, John Butler, Sophie Molholm, Pierfilippo De Sanctis

Articles

While navigating complex environments the brain must continuously adapt to both external demands such as fluctuating sensory inputs, as well as internal demands, such as engagement in a cognitively demanding task. Previous studies have demonstrated changes in behavior and gait with increased sensory and cognitive load, but the underlying cortical mechanisms remain largely unknown. Here, in a Mobile Brain/Body Imaging (MoBI) approach sixteen young adults walked on a treadmill with high-density EEG while 3D motion capture tracked kinematics of the head and feet. Visual load was manipulated with the presentation of optic flow with and without continuous mediolateral perturbations. The …

General Dissipative Materials For Simple Histories, John Murrough Golden, G. Amendola, M. Fabrizio

Articles

A material with memory typically has a set of many free energy functionals associated with it, all members of which yield the same constitutive relations. An alternative interpretation of this set is explored in the present work. Explicit formulae are derived for the free energy and total dissipation of an arbitrary material in the cases of step function and sinusoidal/exponential histories. Expressions for the fraction of stored and dissipated energy are deduced. Also, various formulae are given for discrete spectrum materials. For materials with relaxation function containing one decaying exponential, the associated Day functional is the physical free energy. For …

Menstrual Cycle And The Temporal Discrimination Threshold, Eavan M. Mc Govern, Emer O'Connor, Ines Beiser, Laura Williams, John Butler, Brendan Quinlivan, Shruti Narasimham, Rebecca Beck, Richard B. Reilly, Sean O'Riordan, Michael Hutchinson

Articles

The temporal discrimination threshold (TDT) is a proposed pre-clinical biomarker (endophenotype) for adult onset isolated focal dystonia (AOIFD). Age- and sex-related effects on temporal discrimination demonstrate that women, before the age of 40 years, have faster temporal discrimination than men but their TDTs worsen with age at almost three times the rate of men. Thus after 40 years the TDT in women is progressively worse than in men. AOIFD is an increasingly female-predominant disorder after the age of 40; it is not clear whether this age-related sexually-dimorphic difference observed for both the TDT and sex ratio at disease onset in …

Discriminants Of Polynomials In The Archimedean And Non-Archimedean Metrics, Vasili Bernick, Natalia Budarina, Hugh O'Donnell

Articles

An upper bound for the number of cubic polynomials which have small discriminant in terms of the Euclidean and p-adic metrics simultaneously is obtained.

Direct Immunoassays And Their Performance: Theoretical Modelling Of The Effects Of Antibody Orientation And Associated Kinetics, Dana Mackey, Eilis Kelly, Robert Nooney, Richard O'Kennedy

Articles

The orientation and activity of antibodies immobilized on solid surfaces are of direct relevance to many immunosensing applications. We therefore investigate a mathematical model which estimates the fraction of antibodies which are available for reaction in a randomly adsorbed sample. Numerical simulations are presented which highlight the separate effects of antibody orientation, accessibility and loss of binding ability on the amount of captured antigen. The assay response can then be expressed as a function of total antibody density and used for optimizing the surface coverage strategy under various conditions.

Dynamical Analysis Of An N−H−T Cosmological Quintessence Real Gas Model With A General Equation Of State, Emil Prodanov, Rossen Ivanov

Articles

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter, and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. …

Distribution Of Zeros Of Nondegenerate Functions On Short Cuttings Ii, Vasili Ivanovich Bernik, Natalia Viktorovna Budarina, Artyom Vadimovich Lunevich, Hugh O’Donnell

Articles

No abstract provided.

Catalogue Of Extreme Wave Events In Ireland: Revised And Updated For 14 680 Bp To 2017, Laura Cooke, Emiliano Renzi, John M. Dudley, Colm Clancy, FréDéRic Dias

Articles

This paper aims to extend and update the survey of extreme wave events in Ireland that was previously carried out by O’Brien et al. (2013). The original catalogue high- lighted the frequency of such events dating back as far as the turn of the last ice age and as recent as 2012. Ireland’s marine territory extends far beyond its coastline and is one of the largest seabed territories in Europe. It is therefore not surprising that extreme waves have continued to occur reg- ularly since 2012, particularly considering the severity of weather during the winters of 2013–2014 and 2015–2016. In …

Reply To "Comment On 'Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence"', Rossen Ivanov, Emil Prodanov

Articles

No abstract provided.