scholarly journals A Time-Homogeneous Diffusion Model with Tax

2013 ◽  
Vol 50 (1) ◽  
pp. 195-207 ◽  
Author(s):  
Bin Li ◽  
Qihe Tang ◽  
Xiaowen Zhou
Keyword(s):  
Lower Bound ◽  
Diffusion Process ◽  
Necessary Condition ◽  
Present Value ◽  
Ruin Theory ◽  
Exit Problem ◽  
Explicit Formulae ◽  
Exit Probabilities ◽  
Tax Payments ◽  
Sufficient And Necessary Condition

We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probability with the default threshold equal to the lower bound are solved as immediate corollaries. A sufficient and necessary condition for the tax identity in ruin theory is discovered.

A Time-Homogeneous Diffusion Model with Tax

2013 ◽  
Vol 50 (01) ◽  
pp. 195-207 ◽  
Author(s):  
Bin Li ◽  
Qihe Tang ◽  
Xiaowen Zhou
Keyword(s):  
Lower Bound ◽  
Diffusion Process ◽  
Necessary Condition ◽  
Present Value ◽  
Ruin Theory ◽  
Exit Problem ◽  
Explicit Formulae ◽  
Exit Probabilities ◽  
Tax Payments ◽  
Sufficient And Necessary Condition

We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probability with the default threshold equal to the lower bound are solved as immediate corollaries. A sufficient and necessary condition for the tax identity in ruin theory is discovered.

scholarly journals Analytical expressions of copositivity for fourth-order symmetric tensors

2020 ◽  
pp. 1-22 ◽  
Author(s):  
Yisheng Song ◽  
Liqun Qi
Keyword(s):  
Lower Bound ◽  
Fourth Order ◽  
Scalar Potential ◽  
Sufficient Conditions ◽  
Scalar Fields ◽  
Positive Definiteness ◽  
Necessary Condition ◽  
Symmetric Tensors ◽  
Scalar Potentials ◽  
Sufficient And Necessary Condition

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are fourth-order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of fourth-order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for fourth-order 2-dimensional symmetric tensors. For fourth-order 3-dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) copositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for fourth-order 2-dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for fourth-order 2-dimensional symmetric tensors. Finally, these results may be applied to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.

Some bounds on the minimum number of queries required for quantum channel perfect discrimination

2012 ◽  
Vol 12 (1&2) ◽  
pp. 138-148
Author(s):  
Cheng Lu ◽  
Jianxin Chen ◽  
Runyao Duan
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Quantum Channel ◽  
Necessary Condition ◽  
Quantum Channels ◽  
Sequential Scheme ◽  
Minimum Number ◽  
Perfect Discrimination ◽  
Sufficient And Necessary Condition

We prove a lower bound on the $q$-maximal fidelities between two quantum channels $\E_0$ and $\E_1$ and an upper bound on the $q$-maximal fidelities between a quantum channel $\E$ and an identity $\I$. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguishability between $\E$ and $\I$ and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating $\E$ and $\I$. Interestingly, in the $2$-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in \cite{DFY09}, we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating $\E$ and $I$ over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels $\E_0$ and $\E_1$ in sequential scheme and over all possible discrimination schemes respectively.

ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH σf = 22n + 2n+3(n ≥ 3)

2014 ◽  
Vol 25 (03) ◽  
pp. 343-353 ◽  
Author(s):  
YU ZHOU ◽  
LIN WANG ◽  
WEIQIONG WANG ◽  
XINFENG DONG ◽  
XIAONI DU
Keyword(s):  
Lower Bound ◽  
Boolean Function ◽  
Lower Bounds ◽  
Boolean Functions ◽  
Sum Of Squares ◽  
Necessary Condition ◽  
Resilient Function ◽  
The Absolute ◽  
Global Avalanche Characteristics ◽  
Sufficient And Necessary Condition

The Global Avalanche Characteristics (including the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Son et al. (1998) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function. In this paper, we give a sufficient and necessary condition on a balanced Boolean function reaching the lower bound on the sum-of-squares indicator. We also analyze whether these balanced Boolean functions exist, and if they reach the lower bounds on the sum-of-squares indicator or not. Our result implies that there does not exist a balanced Boolean function with n-variable for odd n(n ≥ 5). We conclude that there does not exist a m(m ≥ 1)-resilient function reaching the lower bound on the sum-of-squares indicator with n-variable for n ≥ 7.

scholarly journals General tax Structures and the Lévy Insurance Risk Model

2009 ◽  
Vol 46 (04) ◽  
pp. 1146-1156 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Xiaowen Zhou
Keyword(s):  
Net Present Value ◽  
Risk Model ◽  
General Structure ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Present Value ◽  
Scale Functions ◽  
Exit Problem ◽  
Tax Payments ◽  
Insurance Risk Model

In the spirit of Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) we consider a Lévy insurance risk model with tax payments of a more general structure than in the aforementioned papers, which was also considered in Albrecher, Borst, Boxma, and Resing (2009). In terms of scale functions, we establish three fundamental identities of interest which have stimulated a large volume of actuarial research in recent years. That is to say, the two-sided exit problem, the net present value of tax paid until ruin, as well as a generalized version of the Gerber–Shiu function. The method we appeal to differs from Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) in that we appeal predominantly to excursion theory.

scholarly journals A SUFFICIENT AND NECESSARY CONDITION FOR SUPERDENSE CODING OF QUANTUM STATES

2008 ◽  
Vol 06 (05) ◽  
pp. 1115-1125 ◽  
Author(s):  
DAOWEN QIU
Keyword(s):  
Lower Bound ◽  
Success Probability ◽  
Quantum States ◽  
Entangled States ◽  
Necessary Condition ◽  
Entangled State ◽  
Maximally Entangled State ◽  
High Success Probability ◽  
Sufficient And Necessary Condition ◽  
Arbitrary Quantum

Recently, Harrow et al. [Phys. Rev. Lett.92 (2004) 187901] gave a method for preparing an arbitrary quantum state with high success probability by physically transmitting some qubits, and by consuming a maximally entangled state, together with exhausting some shared random bits. In this paper, we discover that some states are impossible to be perfectly prepared by Alice and Bob initially sharing some entangled states. In particular, we present a sufficient and necessary condition for the states being enabled to be exactly prepared with probability equal to unity, in terms of the initial entangled states (maybe nonmaximally). In contrast, if the initially shared entanglement is maximal, then the probabilities for preparing these quantum states are smaller than unity. Furthermore, the lower bound on the probability for preparing some states are derived.

scholarly journals General tax Structures and the Lévy Insurance Risk Model

2009 ◽  
Vol 46 (4) ◽  
pp. 1146-1156 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Xiaowen Zhou
Keyword(s):  
Net Present Value ◽  
Risk Model ◽  
General Structure ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Present Value ◽  
Scale Functions ◽  
Exit Problem ◽  
Tax Payments ◽  
Insurance Risk Model

In the spirit of Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) we consider a Lévy insurance risk model with tax payments of a more general structure than in the aforementioned papers, which was also considered in Albrecher, Borst, Boxma, and Resing (2009). In terms of scale functions, we establish three fundamental identities of interest which have stimulated a large volume of actuarial research in recent years. That is to say, the two-sided exit problem, the net present value of tax paid until ruin, as well as a generalized version of the Gerber–Shiu function. The method we appeal to differs from Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) in that we appeal predominantly to excursion theory.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals Research on the Relationship between Shared Leadership and Individual Creativity-Qualitative Comparative Analysis on the Basis of Clear Set

2021 ◽  
Vol 13 (10) ◽  
pp. 5445
Author(s):  
Muyun Sun ◽  
Jigan Wang ◽  
Ting Wen
Keyword(s):  
Comparative Analysis ◽  
Environmental Factors ◽  
Shared Leadership ◽  
Management Practices ◽  
Qualitative Comparative Analysis ◽  
Necessary Condition ◽  
The Individual ◽  
The Impact ◽  
The Relationship ◽  
Sufficient And Necessary Condition

Creativity is the key to obtaining and maintaining competitiveness of modern organizations, and it has attracted much attention from academic circles and management practices. Shared leadership is believed to effectively influence team output. However, research on the impact of individual creativity is still in its infancy. This study adopts the qualitative comparative analysis method, taking 1584 individuals as the research objects, underpinned by a questionnaire-based survey. It investigates the influence of the team’s shared leadership network elements and organizational environmental factors on the individual creativity. We have found that there are six combination of conditions of shared leadership and organizational environmental factors constituting sufficient combination of conditions to increase or decrease individual creativity. Moreover, we have noticed that the low network density of shared leadership is a sufficient and necessary condition of reducing individual creativity. Our results also provide management suggestions for practical activities during the team management.

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