The management of intrusion detection: Configuration,inspection, and investment

This paper analyzes intrusion detection decisions in the presence of multiple alarm types, which differ in occurrence probabilities, damage and investigation costs. Specifically, multi-period optimization models are used to study three critical decisions associated with intrusion detection: (i) Allocation of the investigation budget to different periods and to different alarm types; (ii) Configuration of an intrusion detection system (IDS), i.e. choosing a false alarm rate for a given IDS; and (iii) Allocation of an appropriate amount of the investigation budget in the presence of alternative investment opportunities. Three models that cascade onto each other are presented. We minimize the sum of security costs including damages, due to ignored alarms, the investigation cost and the undetected intrusion cost. We show that it can be optimal to ignore non-critical alarms in order to allocate more of the investigation budget to critical alarms that may occur in the future. We establish that the security costs decrease as the investigation budget increases. Our last model deals with security investments—in the form of an investigation budget. The investigation budget must be increased until the rate of increase in savings in security costs due to the additional budget are equal to the internal rate of return of an organization. These analyses are done with explicit (derived) cost functions, as opposed to implicit (assumed) cost functions. We conclude by providing additional managerial insights and numerical examples.     

On a risk model with claim investigation

In this paper, a queue-based claims investigation mechanism is considered to model an insurer’s claim processing practices. The resulting risk model may be viewed as a first step in developing models with more realistic claim investigation mechanisms. Related to claim investigations, claim settlement delays and time dependent payments have been studied in a ruin context by, e.g. Taylor (1979), Cai and Dickson (2002), and Trufin et al. (2011). However, little has been done on queue-based investigation mechanisms. We first demonstrate the impact of a particular claim investigation system on some common ruin-related quantities when claims arrive according to a compound Poisson process, and investigation times are of a combination of exponential form. Probabilistic interpretations for the defective renewal equation components are also provided. Finally, via numerical examples, we explore various risk management questions related to this problem such as how claim investigation strategies can help an insurer control its activities within its risk appetite.     

Topological degree of condensing multi-valued perturbations of the (S)+-class maps and its applications

Applications of topological characteristics of nonlinear (one-valued and multi-valued) maps are well-known efficient tools for the investigation of solvability for various problems of the theory of differential equations and of optimal control theory. In this paper, a construction of one such characteristic is proposed: this is the degree of condensing multi-valued perturbations of maps of class (S)₊. Principal properties of the characteristic are studied. The considered characteristic is applied for the investigation of a class of controllable systems.     

Investigation of Thermal Convection in an Inclined Narrow Cavity

In order to adapt to the rapid progress in fabricating and utilizing micro electromechanical systems, the investigation of the fluid behaviour in small volumes is of fundamental importance as far as heat and mass transfer are concerned. After the experimental exploration in a small vertical gap with a temperature gradient [1], subsequently the investigation of thermal convection in an inclined narrow cavity is followed experimentally. The gap volume is 6 × 24 × 17 mm³ with a width of 6 mm. Liquid crystal tracer particles are used for measuring the temperature and velocity distribution of the fluid. The measurement results are presented and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pencils of waveguide type and related extremal problems

The variational properties of the spectra of a class of quadratic pencils are investigated. These operator pencils are not strongly damped, which is expressed in a considerable manner in its properties. The obtained results are fundamental in the investigation of two-parameter pencils of waveguide type, which model pencils arising in the theory of regular waveguides. The considerable difficulties, arising at the investigation of pencils of waveguide type, are explained by the fact that they do not generate Rayleigh systems in the entire space, but only on certain of its nonconvex homogeneous sets. These sets occur here as the sets of the admissible vectors of the corresponding extremal problems.Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 80–96, 1990.     

Vibration of a porouse-cellular circular plate

The subject of investigation is a circular porous-cellular plate under uniform pressure. Mechanical properties of the isotropic porous cellular metal vary accross the thickness of the plate. Middle plane of the plate is its symmetry plane. Fields of diseplacements and stresses with respect the nonlinear hypothesis are described. Basing on Hamilton principle three motion equations of the plate are formulated. These equations are approximately solved. The vibration problem is reduced to the second-order differential equation. Numerical investigations are realised for family of plates. Natural frequencies are determined. The obtained results are shown in Figures. To the end of the investigation comparition analyses with respect to homogeneous plates is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On two classes of nonstandard parabolic problems

In this paper the authors continue an investigation of nonstandard parabolic problems. This investigation was motivated by one of the suggested methods for stabilizing ill posed problems for evolution equations. Two different methods are employed—methods which in a sense complement one another.     

Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations

The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community. However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the extension principle. The representation theorem and extension principles as well as algebraic operations form an important part of Atanassov’s IF set theory.     

Numerical study of helicopter blade–vortex mechanism of interaction using the potential flow theory

The blade–vortex interaction (BVI) phenomenon plays a key role in the rotorcraft aerodynamics. Numerical investigations of BVI using classical CFD approaches are computationally expensive. In the present research we propose a numerical approach, based on the potential flow theory, for the numerical investigation of helicopter blade–vortex mechanism of interaction. This approach overcomes the computational expenses posed by the CFD techniques. The influence of vertical miss distance, angle of attack, airfoil camber, and vortex strength on the helicopter blade–vortex mechanism of interaction is subject of investigation. The study reveals that the magnitude of the aerodynamic coefficients decreases with the increase of vertical miss distance and angle of attack, and the decrease of vortex strength and core size.     

On the geometry of the (2n+1)-webs in 2n-dimensional affinely connected spaces A2n

An approach for the investigation of the geometry of (2n+1) -webs in 2n-dimensional affinely connected spaces A_2n by means of the prolonged differentiation is given in [1] Using this approach in the present paper some properties of (2n+1)-webs in A_2n are studied. Necessary and sufficient conditions under which the generalized affinor of Hess of a (2n+1)-web is covariantly constant are found. The space A_2n, containing a (2n+1)-web with a constant covariant generalized affinor of Hess, is determined. Conditions for geodesicity of the lines of a given (2n+1)-web in A_2n in terms of its tensor are found, also.The present investigation is partially supported by the Ministry of Science and Higher Education of People's Republic of Bulgaria under grant 1021.     

On the asymptotic stability of differential equations with “maxima”

Differential equations with “maxima” are considered. Effective sufficient as well as necessary and sufficient conditions for asymptotic stability of the trivial solution are found. The present investigation is supported by the Ministry of Culture, Science, and Education of People’s Republic of Bulgaria under Grant 61.     

A computational study of solution approaches for the resource constrained elementary shortest path problem

We present the results of a computational investigation of solution approaches for the resource constrained elementary shortest path problem ( $\mathcal{RCESPP}$ ). In particular, the best known algorithms are tested on several problem instances taken from literature. The main aims are to provide a detailed state of the art and to evaluate methods that turn out to be the most promising for solving the problem under investigation. This work represents the first attempt to computationally compare solution approaches for the $\mathcal{RCESPP}$ .     

Glass-reinforced plastic high-pressure tanks

The design and fabrication of lens-shaped tanks are described. The results of an investigation of the deformation and strength of the tanks are presented together with the data of cyclic tests.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 149–152, January–February, 1970.     

Investigation of the specific heat of polymers

The results of an investigation of the specific heat of a series of polymers on the temperature interval 223–383°K are presented.     

“Almost quasistationary” approximation for the problem of solidification front stability

“Almost quasistationary” approximation is suggested for the investigation of the problem of solidification front stability. It is appropriate for the initial stage of the process when sizes of particles are sufficiently small. The cases of “sphere like” and “cylinder-like” nuclei are considered. Capillary forces are taken into account.     

Quadrature Domains and p-Laplacian Growth

The classical Hele–Shaw (Laplacian-growth) problem is generalised to power-law fluids (satisfying the p-Laplace equation) and a number of results are established that are analogous to some of those involving null-quadrature domains in the former. The results are formal, but suggest a number of avenues warranting rigorous investigation; some of these are formulated as conjectures or open problems. Submitted: May 31, 2008. Accepted: July 20, 2008.     

Extremes of characteristic functions of a Sturm-Liouville operator

The inverse spectral problems for one-dimensional Shrödinger-type differential operators are known to be closely related to investigation of some particular classes of entire or meromorphic functions.     

Creep of polyethylene terephthalate with variable stresses under conditions of uniaxial extension

The results from experimental and theoretical investigation of the creep of polyethylene terephthalate film during stepwise varying stresses under conditions of uniaxial extension are given.Izhevsk Mechanical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 929–933, September–October, 1972.     

Shear strength and laws of shear deformation of some cross-linked resins

The authors present the results of an experimental investigation and comparison with theory of certain laws of shear deformation and shear strength for rigid cross-linked resins. The possibility of describing the state of strain of homogeneous isotropic polymers by means of the generalized nonlinear Maxwell equation is considered. The results of an investigation of thin-walled tubular specimens of three cross-linked polymers based on epoxy resins and one linear polymer are offered as a check on the corresponding theoretical relations. The agreement between the theoretical and experimental results is perfectly satisfactory. Experimental values of the high-elastic constants in shear and tension have been determined. It is shown that the theoretical and experimental relations coincide with satisfactory accuracy. Certain experimental data on the comparative conditions of failure in shear and tension are presented.Mekhanika Polimerov, Vol. 2, No. 2, pp. 214–228, 1966