The inclusive top quark pair (tt<overbar></mml:mover>) production cross-section sigma tt<overbar></mml:mover> has been measured in proton-proton collisions at <mml:msqrt>s</mml:msqrt>=13<mml:mspace width="0.166667em"></mml:mspace>TeV, using 36.1 fb-1 of data collected in 2015-2016 by the ATLAS experiment at the LHC. Using events with an opposite-charge e mu pair and b-tagged jets, the cross-section is measured to be: <disp-formula id="Equ10"><mml:mtable><mml:mtr><mml:mtd columnalign="right">sigma tt<overbar></mml:mover>=826.4 +/- 3.6<mml:mspace width="0.166667em"></mml:mspace>(stat)<mml:mspace width="4pt"></mml:mspace>+/- 11.5<mml:mspace width="0.166667em"></mml:mspace>(syst)<mml:mspace width="4pt"></mml:mspace>+/- 15.7<mml:mspace width="0.166667em"></mml:mspace>(lumi)<mml:mspace width="4pt"></mml:mspace>+/- 1.9<mml:mspace width="0.166667em"></mml:mspace>(beam)<mml:mspace width="0.166667em"></mml:mspace>pb,</mml:mtd></mml:mtr></mml:mtable><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10052_2020_7907_Article_Equ10.gif" position="anchor"></graphic></disp-formula>where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the LHC beam energy, giving a total uncertainty of 2.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. It is used to determine the top quark pole mass via the dependence of the predicted cross-section on mtpole, giving mtpole=173.1-2.1+2.0<mml:mspace width="0.166667em"></mml:mspace>GeV. It is also combined with measurements at <mml:msqrt>s</mml:msqrt><mml:mo>=7<mml:mspace width="0.166667em"></mml:mspace>TeV and <mml:msqrt>s</mml:msqrt><mml:mo>=8<mml:mspace width="0.166667em"></mml:mspace>TeV to derive ratios and double ratios of t<mml:mover accent="true">t<mml:mo stretchy="false"><overbar></mml:mover> and Z cross-sections at different energies. The same event sample is used to measure absolute and normalised differential cross-sections as functions of single-lepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators.
A branching fraction measurement of the B0 -> Ds+</mml:msubsup>pi- decay is presented using proton-proton collision data collected with the LHCb experiment, corresponding to an integrated luminosity of 5.0<mml:mspace width="0.166667em"></mml:mspace>fb-1. The branching fraction is found to be B(B0 -> Ds+</mml:msubsup>pi-)=(19.4 +/- 1.8 +/- 1.3 +/- 1.2)x10-6, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the B0 -> D-pi+, Ds+</mml:msubsup>-> K+K-pi+ and D--> K+pi-pi- branching fractions. This is the most precise single measurement of this quantity to date. As this decay proceeds through a single amplitude involving a b -> u charged-current transition, the result provides information on non-factorisable strong interaction effects and the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element <mml:msub>Vub. Additionally, the collision energy dependence of the hadronisation-fraction ratio <mml:msub>fs/<mml:msub>fd is measured through B<overbar></mml:mover>s0 -> Ds+pi- and B0 -> D-pi <mml:mo>+ decays.
We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov–Bohm operators with two colliding poles moving on an axis of symmetry of the domain.
We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.
The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.
We consider a new Sobolev type function space called the space with multiweighted derivatives. As basis for this space serves some differential operators containing weight functions. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding between the spaces with multiweighted derivatives in different selections of weights.
This Licentiate Thesis consists of four chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we consider and analyze some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we present and prove analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are crucially for the proofs of the main results of this Licentiate Thesis. In Chapter 3 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of spaces. However, with the help of our new embedding theorems we can extend these results to the case of strong degeneration. In Chapter 4 we prove some new estimates for each function in a Tchebychev system. In order to be able to study also compactness of the embeddings from Chapter 3 such estimates are crucial. I plan to study this question in detail in my further PhD studies.
This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions.Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we prove some new estimates for each function in a Tchebychev system. In order to be able to study compactness of the embeddings from Chapter 3 such estimates are crucial.In Chapter 3 we rewrite and present some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we rewrite and discuss some analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are not available in the Western literatures in this way and they are crucial for the proofs of the main results in Chapter 4. In Chapter 4 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of the spaces. However, with the help of our new embedding theorems we can extend theseresults to the case of strong degeneration.The main aim of Chapter 5 is to establish boundedness and compactness of the embedding considered in Chapter 4.In Chapter 4 basically only sufficient conditions for boundedness of this embedding were obtained. In Chapter 5 we obtain necessary and sufficient conditions for boundedness and compactness of this embedding and the main results are proved in a different way.
We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n
Using a sample of 1.31x109<mml:mspace width="3.33333pt"></mml:mspace>J/psi events collected with the BESIII detector, we perform a study of J/psi -> gamma KK<overbar></mml:mover>eta '. X(2370) is observed in the KK<overbar></mml:mover>eta ' invariant-mass distribution with a statistical significance of 8.3 sigma. Its resonance parameters are measured to be M=2341.6 +/- 6.5<mml:mspace width="0.166667em"></mml:mspace>(stat.)+/- 5.7<mml:mspace width="0.166667em"></mml:mspace>(syst.)<mml:mspace width="3.33333pt"></mml:mspace>MeV/c2 and Gamma =117 +/- 10<mml:mspace width="0.166667em"></mml:mspace>(stat.)+/- 8<mml:mspace width="0.166667em"></mml:mspace>(syst.)<mml:mspace width="3.33333pt"></mml:mspace>MeV. The product branching fractions for J/psi -> gamma X(2370),X(2370)-> K+K-eta ' and J/psi -> gamma X(2370),X(2370)-> KS0KS0 eta ' are determined to be (1.79 +/- 0.23<mml:mspace width="0.166667em"></mml:mspace>(stat.)+/- 0.65<mml:mspace width="0.166667em"></mml:mspace>(syst.))x10-5 and (1.18 +/- 0.32<mml:mspace width="0.166667em"></mml:mspace>(stat.)+/- 0.39<mml:mspace width="0.166667em"></mml:mspace>(syst.))x10-5, respectively. No evident signal for X(2120) is observed in the KK<overbar></mml:mover>eta ' invariant-mass distribution. The upper limits for the product branching fractions of B(J/psi -> gamma X(2120)-> gamma K+K-eta ') and B(J/psi -> gamma X(2120)-> gamma KS0KS0 eta ') are determined to be 1.49x10<mml:mo>-5 and 6.38<mml:mo>x10<mml:mo>-6 at the 90% confidence level, respectively.
The main result of this paper is that for the har dsphere kernel, the solution of the spatially homogenous Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R3,(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R3), which corresponds to bounded initial entropy.
Abstract—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.
In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .
For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest
We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.
For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.
Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.
In this paper we discuss the Hermite-Hadamard and Fejer inequalities vis-a-vis the convexity concept. In particular, we derive some new theorems and examples where Hermite-Hadamard and Fejer type inequalities are satisfied without the assumptions of convexity or concavity on the actual interval [a,b]
For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved
In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.
In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.
In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.
Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.
Inequalities of the form |u K f|q ≤ C(|ρf|p+|vHf|p), f ≥ 0, are considered, where K is an integral operator of Volterra type and H is the Hardy operator. Under some assumptions on the kernel K we give necessary and sufficient conditions for such an inequality to hold.
This PhD thesis is devoted to investigate weighted differential Hardy inequalities and Hardy-type inequalities with the kernel when the kernel has an integrable singularity, and also the additivity of the estimate of a Hardy type operator with a kernel.The thesis consists of seven papers (Papers 1, 2, 3, 4, 5, 6, 7) and an introduction where a review on the subject of the thesis is given. In Paper 1 weighted differential Hardy type inequalities are investigated on the set of compactly supported smooth functions, where necessary and sufficient conditions on the weight functions are established for which this inequality and two-sided estimates for the best constant hold. In Papers 2, 3, 4 a more general class of -order fractional integrationoperators are considered including the well-known classical Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard operators. Here 0 < < 1. In Papers 2 and 3 the boundedness and compactness of two classes of such operators are investigated namely of Weyl and Riemann-Liouville type, respectively, in weighted Lebesgue spaces for 1 < p ≤ q < 1 and 0 < q < p < ∞. As applications some new results for the fractional integration operators of Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard are given and discussed.In Paper 4 the Riemann-Liouville type operator with variable upper limit is considered. The main results are proved by using a localization method equipped with the upper limit function and the kernel of the operator. In Papers 5 and 6 the Hardy operator with kernel is considered, where the kernel has a logarithmic singularity. The criteria of the boundedness and compactness of the operator in weighted Lebesgue spaces are given for 1 < p ≤ q < ∞ and 0 < q < p < ∞, respectively. In Paper 7 we investigated the weighted additive estimates for integral operators K+ and K¯ defined by
K+ ƒ(x) := ∫ k(x,s) ƒ(s)ds, K¯ ƒ(x) := ∫ k(x,s)ƒ(s)ds.
It is assumed that the kernel k of the operators K+and K- belongs to the general Oinarov class. We derived the criteria for the validity of these addittive estimates when 1 ≤ p≤ q < ∞
We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.
We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1
Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1
The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.
We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.
In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.
In times of regional geopolitical turmoil – why do some investment portfolios, equity funds, perform better than others? Is it simply luck, the effects of systematic risk or do factors such as investment styles and managerial skills play a significant part in the performance of a fund?
As financial markets often reflect the macro environment, much of the previous year’s fluctuations of Eastern European stocks can be seen to derive from a number of geopolitical events; from the 2013 summer clashes between the Turkish police and opposing parties to the current issue concerning Russia and Ukraine. Needless to say, these events have affected return on equity in their regions and created a distressed environment for investors and equity fund managers investing in Eastern Europe.
This thesis aims to explore how the aforementioned macroeconomic events impact the market and thus the portfolios of asset managers. The thesis also intends to provide aspects of eventual investment strategies that are more preferable than others under such circumstances, in order to mitigate the subsequent risks.
A stochastic process or sometimes called random process is the counterpart to a deterministic process in theory. A stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. In this case, Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. However, in discrete time, a stochastic process amounts to a sequence of random variables known as a time series. Over the past decades, the problems of synergetic are concerned with the study of macroscopic quantitative changes of systems belonging to various disciplines such as natural science, physical science and electrical engineering. When such transition from one state to another take place, fluctuations i.e. (random process) may play an important role. Fluctuations in its sense are very common in a large number of fields and nearly every system is subjected to complicated external or internal influences that are often termed noise or fluctuations. Fokker-Planck equation has turned out to provide a powerful tool with which the effects of fluctuation or noise close to transition points can be adequately be treated. For this reason, in this thesis work analytical and numerical methods of solving Fokker-Planck equation, its derivation and some of its applications will be carefully treated. Emphasis will be on both for one variable and N- dimensional cases.
The Galerkin method is studied for solving the boundary integral equations associated with the Laplace operator on nonsmooth domains. Convergence is established with a condition on the meshsize, which involves the local curvature on certain approximating domains. Error estimates are also proved, and the results are generalized to systems of equations.
In the setting of the integers, Granville, Harper and Soundararajan showed that the upper bound in Halasz's Theorem can be improved for smoothly supported functions. We derive the analogous result for Halasz's Theorem in F-q[t], and then consider the converse question of when the general upper bound in this version of Halasz's Theorem is actually attained.
This work examines positive solutions of systems of inequalities ±∆pu ≥ ρ(x)f (u), in Ω, where p = (p1, ..., pk), pi > 1 and ∆p is the diagonal-matrix diag(∆p1 , ..., ∆pk ), ∆pi is the pi-Laplace operator, Ω is an arbitrary domain (bounded or not) in RN (N ≥ 2), u = (u1, ..., uk)T and f = (f1, ..., fk)T are vector-valued functions and ρ(x) is a nonnegative function in Ω which is locally bounded. Using a maximum principle-based argument we provide explicit estimates on positive solutions u at each point x ∈ Ω, and as applications we find Liouville type results in unbounded domains such as RN, exterior domains or generally unbounded domains with the property that supx∈Ω dist(x, ∂Ω) = ∞, for various nonlinearities f and weights ρ. We also give explicit upper bounds on extremal parameters of related nonlinear multi-parameter eigenvalue problems in bounded domains.
In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.
This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X-u,X-xi(t) =X(t) is given by X(t) = phi(t) + integral(t)(0) b (t, s, X(s), u(s)) ds + integral(t)(0) sigma (t, s, X(s), u(s)) dB(s) + integral(t )(0)h (t, s) d xi(s). Here dB(s) denotes the Brownian motion Ito type differential, xi denotes the singular control (singular in time t with respect to Lebesgue measure) and u denotes the regular control (absolutely continuous with respect to Lebesgue measure). Such systems may for example be used to model harvesting of populations with memory, where X(t) represents the population density at time t, and the singular control process xi represents the harvesting effort rate. The total income from the harvesting is represented by J(u, xi) = E[integral(T)(0) f(0)(t, X(t), u(t))dt + integral(T)(0) f(1)(t, X(t))d xi(t) + g(X(T))], for the given functions f(0), f(1) and g, where T > 0 is a constant denoting the terminal time of the harvesting. Note that it is important to allow the controls to be singular, because in some cases the optimal controls are of this type. Using Hida-Malliavin calculus, we prove sufficient conditions and necessary conditions of optimality of controls. As a consequence, we obtain a new type of backward stochastic Volterra integral equations with singular drift. Finally, to illustrate our results, we apply them to discuss optimal harvesting problems with possibly density dependent prices.
We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor ν = 2/3. The emergent Entangled Pauli Principle (EPP), introduced in Phys. Rev. B 98, 161118(R) (2018) and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M-clustering property within any given number of Landau levels, that is, wave functions with Mth-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M = 3 case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of Phys. Rev. X 1, 021015 (2011) to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.
As a result of a more globalized and industrial world, sustainability issues in terms of the environment and society has become an everyday heading in the financial world. The fact that companies should work actively towards sustainability and accountability is today a necessity rather than a choice. The purpose of this study is to research responsible investment (RI) and portfolio performance. To examine this relationship the study focuses on ESG where its dimensions will be included jointly through optimization, discussion and conclusion. The report outlines how ESG can be integrated into the investment process, but the weight of the study addresses the discussion of a portfolio's performance at the inclusion of ESG. Methods used are Modern Portfolio Theory (MPT) combined with the implementation of ESG according to "best-in-class". The results of the study lead towards the conclusion that ESG in addition to its positive effects, provided an accurate assessment, on sustainability also is financially arguable for investors.
ireless Communication is one of the fields of Telecommunications which is growing with the tremendous speed. With the passage of time wireless communication devices are becoming more and more common. It is not only the technology of business but now people are using it to perform their daily tasks, be it for calling, shopping, checking their emails or transfer their money. Wireless communication devices include cellular phones, cordless phones and satellite phones, smart phones like Personal Digital Assistants (PDA), two way pagers, and lots of their devices are on their way to improve this wireless world. In order to establish two way communications, a wireless link may be using radio waves or Infrared light. The Wireless communication technologies have become increasingly popular in our everyday life. The hand held devices like Personal Digital Assistants (PDA) allow the users to access calendars, mails, addresses, phone number lists and the internet. Personal digital assistants (PDA) and smart phones can store large amounts of data and connect to a broad spectrum of networks, making them as important and sensitive computing platforms as laptop PCs when it comes to an organization’s security plan. Today’s mobile devices offer many benefits to enterprises. Mobile phones, hand held computers and other wireless systems are becoming a tempting target for virus writers. Mobile devices are the new frontier for viruses, spam and other potential security threats. Most viruses, Trojans and worms have already been created that exploit vulnerabilities. With an increasing amount of information being sent through wireless channels, new threats are opening up. Viruses have been growing fast as handsets increasingly resemble small computers that connect with each other and the internet. Hackers have also discovered that many corporate wireless local area networks (WLAN) in major cities were not properly secured. Mobile phone operators say that it is only a matter of time before the wireless world is hit by the same sorts of viruses and worms that attack computer software.
Fuzzy relation equations are becoming extremely important in order to investigate the optimal solution of the inverse problem even though there is a restrictive condition for the availability of the solution of such inverse problems. We discussed the methods for finding the optimal (maximum and minimum) solution of inverse problem of fuzzy relation equation of the form $R \circ Q = T$ where for both cases R and Q are kept unknown interchangeably using different operators (e.g. alpha, sigma etc.). The aim of this study is to make an in-depth finding of best project among the host of projects, depending upon different factors (e.g. capital cost, risk management etc.) in the field of civil engineering. On the way to accomplish this aim, two linguistic variables are introduced to deal with the uncertainty factor which appears in civil engineering problems. Alpha-composition is used to compute the solution of fuzzy relation equation. Then the evaluation of the projects is orchestrated by defuzzifying the obtained results. The importance of adhering to such synopsis, in the field of civil engineering, is demonstrated by an example.
To protect our health and environment from pollution, among others regulatory agencies in the European Union (EU) and legislation from the U.S. Environmental Protection Agency (EPA) has required that pollutants produced by diesel engines - such as nitrogen oxides (NOx), hydrocarbons (HC) and particulate matter (PM) - be reduced. The key emission reduction and control technologies available for NOx control on Diesel engines are combination of Exhaust Gas Recirculation (EGR) and Selective Catalytic Reduction (SCR). SCR addresses emission reduction through the use of Diesel Exhuast Fluid (DEF), which has a trade-name AdBlue. Which is 32.5% high purity urea and 67.5% deionized water, Adblue in the hot exhaust gas decomposes into ammonia (NH3) which then reacts with surface of the catalyst to produce harmless nitrogen(N2) and water (H20). Highest NOx conversion ratios while avoiding ammonia slip is achieved by Efficient SCR and accurate Urea Dosing System it’s therefore critical we model and simulate the UDS in order to analyze and gain holistic understanding of the UDS dynamic behavior. The process of Modeling and Simulating of Urea Dosing System is a result of a compromise between two opposing trends. Firstly, one needs to use as much mathematical models as it takes to correctly describe the fundamental principles of fluid dynamics such as, (1) mass is conserved (2), Newton’s second law and (3) energy is conserved, secondly the model needs to be as simple as possible, in order to express a simple and useful picture of real systems. Numerical model for the simulation of Urea Dosing System is implemented in GT Suite® environment, it is complete UDS Model (Hydraulic circuit and Dosing Unit) and it stands out for its ease of use and simulation fastness, The UDS model has been developed and validated using as reference Hilite Airless Dosing System at the ATC Lab, results provided by the model allow to analyze the UDS pump operation, as well the complete system, showing the trend of some important parameters which are difficult to measure such as viscosity, density, Reynolds number and giving plenty of useful information to understand the influence of the main design parameters of the pump, such as volumetric efficiency, speed and flow relations.
The variational capacity cap(p) in Euclidean spaces is known to enjoy the density dichotomy at large scales, namely that for every E subset of R-n, infx is an element of R(n)cap(p)(E boolean AND B(x, r), B(x, 2r))/cap(p)(B(x, r), B(x, 2r)) is either zero or tends to 1 as r -amp;gt; infinity. We prove that this property still holds in unbounded complete geodesic metric spaces equipped with a doubling measure supporting a p-Poincare inequality, but that it can fail in nongeodesic metric spaces and also for the Sobolev capacity in R-n. It turns out that the shape of balls impacts the validity of the density dichotomy. Even in more general metric spaces, we construct families of sets, such as John domains, for which the density dichotomy holds. Our arguments include an exact formula for the variational capacity of superlevel sets for capacitary potentials and a quantitative approximation from inside of the variational capacity.