We discuss the Dirichlet problem for p-harmonic functions on a network. We show that every continuous function on the p-Royden boundary is p-resolutive and that the set of regular boundary points coincides with the p-harmonic boundary. Also we prove that the p-Dirichlet solution is left continuous with respect to p.

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We explore an NP-complete set such that the problem of breaking a cryptographic scheme reduces to the complete set, where the reduction can be given in a straightforward form like the reduction from the graph isomorphism to the subgraph isomorphism. We construct such NP-complete sets Π_DL and Π_IF for the discrete logarithm problem modulo a prime and the integer factoring problem, respectively. We also show that the decision version of Diffie-Hellman problem reduces directly to Π_DL with respect to the polynomial-time many-one reducibility. These are the first complete sets that have direct reductions from significant cryptographic primitives.

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In this article, we optimize a growth condition such that an analytic function being almost integer-valued at integers turns out to be a polynomial. Our argument relies on a computational optimization combined with Diophantine approximations on lattices.

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We consider the initial value problem for wave equations with weighted nonlinear terms in one space dimension. Under the assumption that the initial data and nonlinearity are odd functions, we are able to show global existence of small amplitude solutions. We also prove that symmetric assumptions on the initial data are necessary to obtain the global solution, by showing a blow-up result.

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An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced before. The square of the Hamiltonian turns out to be an operator without, essentially, the ``coin register,'' and hence it can be compared with the one-dimensional continuous-time quantum walk. It is shown that, under a limit with respect to a parameter, which expresses the magnitude of the diagonal components of the unitary matrix defining the discrete-time quantum walks, the one-dimensional continuous-time quantum walk is obtained from operators defined through the Hamiltonians of the one-dimensional discrete-time quantum walks. Thus, this result can be regarded, in one-dimension, as a partial answer to a problem proposed by Ambainis.

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In this paper, we provide sufficient conditions for constructing univalent analytic functions in the unit disk |z|<1. We motivate our results through several examples and compare with the previously known coefficient conditions. Finally as an application, we present an interesting theorem involving Gaussian hypergeometric function.

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This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detection and enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of the conventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stop filter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied to arbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptive mechanism with the help of the frequency transformation and its block diagram representation. In addition, we prove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, we demonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields much better signal-to-noise ratio (SNR) improvement than the conventional low-order filters.

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Distributed Denial of Service (DDoS) attacks exhaust victim's bandwidth or services. Traditional architecture of Internet is vulnerable to DDoS attacks and an ongoing cycle of attack & defense is observed. A recent attack report of year 2013 –- `Quarter 1' from Prolexic Technologies identifies that 1.75 percent increase in total number of DDoS attacks has been recorded as compared to similar attacks of previous year's last quarter. In this paper, different types and techniques of DDoS attacks and their countermeasures are surveyed. The significance of this paper is the coverage of many aspects of countering DDoS attacks including new research on the topic. We survey different papers describing methods of defense against DDoS attacks based on entropy variations, traffic anomaly parameters, neural networks, device level defense, botnet flux identifications, application layer DDoS defense and countermeasures in wireless networks, CCN & cloud computing environments. We also discuss some traditional methods of defense such as traceback and packet filtering techniques, so that readers can identify major differences between traditional and current techniques of defense against DDoS attacks. We identify that application layer DDoS attacks possess the ability to produce greater impact on the victim as they are driven by legitimate-like traffic, making it quite difficult to identify and distinguish from legitimate requests. The need of improved defense against such attacks is therefore more demanding in research. The study conducted in this paper can be helpful for readers and researchers to recognize better techniques of defense in current times against DDoS attacks and contribute with more research on this topic in the light of future challenges identified in this paper.

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The normal-ordered form of the composition of the exponential of a quadratic annihilation operator and its adjoint is derived by means of a new method based on quantum white noise calculus. Our method consists of two steps: (i) to derive a system of differential equations consisting of quantum white noise derivatives and Wick products; and (ii) to solve explicitly the system of differential equations.

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