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Meteorological Applications
There are various approaches for
CF evaluation in the atmosphere. Perhaps , the strictest of them consists in
calculation of the correlation coefficients (over the time) for each
available pair of aerological stations (they use radiosonds, i.e ...
METHOD OF CORNER TRANSFER MATRIX AND
VACUUM STATES
The product of the transfer matrix
represents the partition function of the N´2N lattice (the right half of the
square lattice), where the boundary spins are fixed in the top, right and
bottom boundaries ...
Method of Inverse Scattering Problem
In this chapter,
method of Inverse Scattering Problem is explained...
METHODS FOR MAGNETOSPHERE AND
NEAR-SPACE PROBLEMS
Mathematical models
are discussed for the two central problems, which are of great importance for
the understanding of the solar wind interaction with the Earth’s
magnetosphere: solar wind flow around magnetosphere and magnetic field reconnection.There...
METHODS OF INTEGRAL TRANSFORMS
The methods of
integral transforms are very efficient to solve and research differential and
integral equations of mathematical physics. These methods consist in the
integration of an equation with some weight function of two arguments that
often result...
METHODS OF NONLINEAR
KINETICS
The Boltzmann equation is the first and most famous nonlinear
kinetic equation introduced by the great Austrian physicist Ludwig Boltzmann in 1872. This equation describes dynamics of a
moderately rarefied gas, taking into account for the two processes...
Methods of Parameter Estimation
Apart from the possibility of not
being able to solve the moment equations explicitly, the sampling
distributions of these estimators are usually hard to find, so one has to
rely on normal approximations ...
METHODS OF REDUCED DESCRIPTION
One of the major
issues raised by the Boltzmann equation was problem
of the reduced description. Equations of hydrodynamics constitute a closed
set of equations for the hydrodynamic field (local density, local momentum,
and local temperature). From the...
Methods of transformation groups
The chapter is
dedicated to a large branch of application of continuous transformation
(symmetries) groups to the problems of mathematical physics. The accents are
made in particular on the applications and development of modern theoretical
group method...
MHD MODELS OF SOLAR WIND FLOW AROUND
THE MAGNETOSPHERE
Magnetohydrodynamics has proved very useful in
describing the behavior of space plasmas, in particular the solar wind flow
around the Earths magnetosphere. The study of the interaction of the solar
wind with the Earth and other planets forms a central object of space
research ...
Miscellaneous Function Spaces
Miscellaneous Function
Spaces are explained in this chapter ...
Mobile Telecommunication
It is customary to distinguish 4
generations of mobile telecommunication systems. The first generation applied
analog modulation, and offered restricted, independent service. The second
generation turned to digital modulation with a wide range of distinct
services. There appeared some early integration of continental size services ...
MODELING
Many of the most
well-known operations research problems can be formulated as (mixed) integer
linear programs. Before both generic (mixed) integer programming models and
generic combinatorial optimization models are introduced, a few examples are
considered ...
Modeling Fuzzy Values
An efficient way of getting suitable
membership functions is the
following procedure, which is based
on the representation theorem that
expresses the equivalence of the
membership function and the set of
all α-cuts of a fuzzy set ...
MODELING IN AUTOMATIC CONTROL (
MATHEMATICAL SYSTEMS THEORY)
As we mentioned in the
introduction to this chapter we want to develop the concepts of mathematical
modeling in the spirit of engineers of automatic control. We have done this
is in our presentation of dynamical systems in mathematics and their use for
modeling ...
Modeling of complex biological systems
Achievements of modern biology
revealed numerous facts on the structure and regulation types of many
intracellular systems. Schemes of processes are composed, chemical structure
and, in most cases, molecular structures of the components of processes are
examined, including the bio-regulators ...
MODELS AND METHODS OF ACTUARIAL
MATHEMATICS
Insurance is a social
mechanism that allows individuals and organizations to compensate economic
losses caused by unfavorable events. Actuarial mathematics is the
mathematical theory of insurance. There exist numerous mathematical models of
insurance ...
MODELS AND METHODS OF ACTUARIAL
MATHEMATICS-CONCLUSION
The actuarial
mathematics is the branch of science which actively develops. It obtains its
new problem settings from insurance practice. Number of investigation
directions is very large. Information on the wide array of problems that were
not covered by the article can be found in works of Borch,
Bowers, Embrechts, Grandell,
Kalashnikov, Panjer, Rotar
and other works ...
MODELS FOR CONTROL
There is an expression
that is popular because it is appealing: Optimal control. This is the dream
of everybody, to control the process in an optimal way! Technically speaking,
optimal control can be regarded as a mathematical chapter in a very old
discipline: The calculus of variations ...
MODELS FOR DESCRIPTION AND PREDICTION
Fortunately there are also
circumstances where data are available. Consider for instance the basin of
some river, which has the tendency to overflow. The problem is to predict
overflows a few hours before they occur ...
Models for Parasite Populations
Chronologically speaking, the
tropical helminth infections provided the next step
in the genesis of epidemic theory. Early work by Kostitzin
in 1934 was followed thirty years later by Macdonald's study of schistosomiasis and a flourishing of activity in the
seventies and eighties ...
Models for Vector-Born Infections
Independently from Hamer, it was Ronald Ross who in 1911 introduced the mass
action idea in continuous time in his study of the transmission of malaria.
Ross' work in subsequent years qualifies him as the true founding father of
modern epidemic theory ...
Models for Water Storage
Water storage problems were first
treated by A. Hazen in 1914, when he studied the discharge of thirteen
American rivers. This work was extended by C.E. Sudler
in 1927. Both these authors used graphical methods. In a pioneering study
carried out during 1938-1956, the British engineer H.E ...
Models
of regional agricultural development, location and water USE WITH REGARD TO
NON-POINT SOURCE POLLUTION.
Water use optimization in national
and regional economies as well as within the agricultural sector is generally
directed by economic criteria such as maximum output per unit cost.
Specifically, criteria of maximum output of an item typical of the
specialized agricultural region are used ...
MODELS OF SOLAR RADIATION
Life on earth is supported by the
sun. The sun provides the earth with light, heat, and energy, which is used
by plants to synthesize products necessary for life and consumed as
foodstuffs by practically all other organisms ...
Models with Structure
The infection that sparked off a
tremendous increase in epidemic modeling activity in the 1980s was HIV. The
effect has been that in the past ten years more different infections of
humans and animals have been studied with more realistic models than ever
before ...
MODERN BIOMETRY
Biometry is a discipline
devoted to the mathematical and statistical aspects of biology. The benefits
to mankind of biometrical developmentsranging from
their applications in agriculture, and in animal and plant sciences, to those
in medical science, an...
MONTE CARLO OPTIMIZATION
Another type of numerical problem
which can be solved via Monte Carlo
is the problem of optimization in
the following form: find the optimum of a function ...
More Consistent with Psychological
Evidence
Kahneman
and Tversky
postulated that individuals make choices to optimize a value function which
is S-shaped with the inflection point corresponding to the reference point.
They note that the reference point is readily manipulated, and showed how
prospect theory with an S-shaped ...
Multiple Correlation
This chapter explains
the multiple correlation ...
Multiple Criteria Decision Making -
Vector Optimization
In vector optimization the focus
typically lies on an interactive exploration of the efficient set, rather
than on building a complete preference model of the decision maker ...
Multiple Integrals.
This chapter deals
with multipe integrals.The
multiple integral on a more complicated domain could be reduced to iterated
integrals by a suitable division ...
Multiple Regression
This chapter explains
multiple regression ...
MULTIPLE-CRITERIA DECISION MAKING
This chapter deals
with decision making processes governed by multiple criteria. In order to
concentrate on this aspect of decision making, the focus lies on
deterministic approaches, at the expense of consideration of the problems of
risk and uncertain...
Multistate Population Models
Multistate
models have two or more living
states that intercommunicate, i.e. where a decrement from one state is an increment
to another. Such models date back to the early twentieth century, but did not
come into common use in demography until the 1970s
...
Multivariate
data, Imprecise vectors, and combination of Imprecise SAMPLES.
For the mathematical description
of vector-valued imprecise observations one can use so-called imprecise
vectors which are described by corresponding vector-characterizing functions ...
Multivariate Location and Scatter
The statistics most commonly used
to flag leverage points have traditionally been the diagonal elements hiiof the hat matrix, which is
well known in the context of regression ...
Multivariate Regression
Multivariate regression models are
useful when response variables are correlated and depend on sets of predictor
variables. As described above the relationship between one dependent
(response) variable and a single independent (predictor) variable can be
measured by a linear regression analysis ...
Mutiple Criteria Decision Making -
Value Function Approach
The value function approach is
essentially based on the assumption of the existence of a function v: Y ,
assigning real numbers to all feasible outcomes y Y
that represent the decision makers preferences
...
Necessary Optimality Conditions
This paper gives an
overview over basic mathematical settings used to tackle problems with an
infinite number of free variables or constraints.
NON UNIFORM RANDOM VARIATE GENERATION
In this chapter we assume that a
uniform (0,1) random number generator called
rndis given. The aim of this chapter is to
present methods and algorithms which transform sequences of random numbers ...
NON UNIFORM RANDOM VARIATE GENERATION -
OTHER METHODS
This method, due to Kinderman and Monahan (see Devroye-1986), was used to
simulate various particular distributions. The following theorem (see
Vaduva-1993) gives a general form of the method ...
NONCONVEX VARIATIONAL PROBLEMS
This note is concerned
with nonconvex problems of the calculus of
variations. First, the notion of minimizer is
introduced through simple examples. The direct method of
finding a minimizer and its limitations in the nonconvex case are then explained. We...
Non-life Insurance
Let X denote an insurance risk,
that is, the aggregate amount of claims to be covered by an insurance policy.
Determining a premium for this policy is setting a price for covering this
risk. We consider X as a random variable. The pure premium of X is the
expected value of X ...
NONLINEAR FLUX BOUNDARY CONDITIONS
This chapter explains
the nonlinear flux boundary conditions. ...
NONLINEAR PROGRAMMING
Nonlinear programming
is a direct extension of linear programming, when we replace linear model
functions by nonlinear ones. Numerical algorithms and computer programs are widely
applicable and commercially available as black box software. However, to
...
NONLINEAR
PROGRAMMING-Optimization Algorithms
Historically all
methods for constrained nonlinear programming originated either from linear
programming, or from unconstrained optimization. Since linear programming
techniques are supposed to be well known (see Linear Programming), we present
a brief...
Nonsmooth Problems
Nonsmooth
optimization problems
are problems, where either the cost functional J or the functions describing
the constraints are not smooth in the mathematical sense, that means, it lacks
differentiability properties to an extent that the behavior of solution
methods is affected ...
Non-Zero-Sum Games
In zero-sum games the interests of
the two players are diametrically opposed. This is no longer the case for
general non-cooperative games, and many interest structures are possible. We
illustrate this with a few classical examples.Pure
coordination games are the exact opposite of zero-sum games, in that the
interests of the players coincide ...
NTU Games - Basic Model and Definitions
The interpretation of such an
NTU-game (N, V) is that V(S) is the set of feasible payoff (utility) vectors
for the coalition S if that coalition forms ...
NTU Games - The Bargaining Set
The bargaining set is, in fact, a
common name for various solution concepts that share similar ideas of so
called objections and counter objections. Generally, a bargaining set is
bigger than the core and thus, excludes fewer points as being not acceptable ...
NTU-GAMES
Nontransferable
utility (NTU) games derive from many economic situations. A classical example
is an exchange economy. By pooling and redistributing their initial
endowments, coalitions can reach certain payoff (utility) distributions that
constitute the...
Numerical Algorithms
The main element of
the computational experiment triad model-algorithm- program is a
constructed computational algorithm, which allows us to research an applied
mathematical model with the necessary completeness. The development of
numerical methods is...
NUMERICAL
ALGORITHMS FOR INVERSE AND ILL-POSED PROBLEMS
This paper is devoted
to inverse and ill-posed problems and numerical algorithms for their
solution. Inverse and ill-posed problems arise in science, engineering, medicine,
ecology, etc. Development of the theory of inverse and ill-posed problems is
...
NUMERICAL ANALYSIS AND COMPUTATION
The study of physical
phenomena usually requires mathematical modeling. For the computer solution
the exact mathematical model has to be approximated by a suitable numerical
model. By far the most frequently used numerical models take the form of a
line...
Numerical Examples
We illustrate our
topic with a very classical shock tube problem - the Sod problem. Many other
cases are available, see [35] for example. The
conditions are described in Table 1. The problem is a pure Riemann problem.
In Figures 7, 8 and 9, we have ...
NUMERICAL FLUX BOUNDARY CONDITIONS
In this section, we
focus on the problem of the numerical boundary conditions....
NUMERICAL INTEGRATION
The principal
statements of problems for computation of definite and multiple integrals by
means of quadrature and cubature formulae are
presented and the most interesting and often used results of the theory of quadrature formulae are considered. A ...
Numerical Methods
Numerical modeling is
the main method for examining the processes of formation and variability of
circulations in oceans and seas. Simulation of the general ocean and sea
dynamics has several specific features. The problem is described by a
complicated...
NUMERICAL METHODS FOR INTEGRAL
EQUATIONS
This chapter presents
a review of direct and iterative numerical methods for solving linear and
nonlinear integral equations of the second kind...
NUMERICAL
METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMIC SYSTEMS.
Approximate methods of
solution of Cauchy problem for systems of ordinary differential equations,
including delay differential equations, are described. Principal methods of
local and global error estimation as well as the inequalities for accuracy
...
NUMERICAL METHODS FOR WEATHER
FORECASTING PROBLEMS
This paper presents
the basic aspects of numerical methods for weather forecasting problems. The
spectrum of models and some additional questions near this problem are
described. The parameterization schemes for models and also the use of
numerical ...
Numerical
Model of Global Transport and Transformations of MultICOMPONENT GASEOUS
POLLUTANTS AND AEROSOLS.
Let us consider the
numerical model of global transport of multicomponent
gaseous species and aerosols in the troposphere of the Northern Hemisphere. The
model is formulated for the spherical earth in the coordinate system , where is the longitude, is...
NUMERICAL MODELING OF CLIMATIC
VARIABILITY AND CLIMATE CHANGES
As it was mentioned
above, the investigations of climatic variability and climate changes can be
broken down into three components, which differ by the time-scales as with
respect to the mechanisms regulating these processes....
Numerical Quadrature Formulas
The definition of the order of
accuracy of a numerical integration formula is the following:A numerical integration formula is of order k if
it is exact for polynomials of degree ≤ k...
Numerical Results
The numerical
algorithm for solving the problem of the pollutant transport is based on the
splitting method. The problem is split according to physical processes and
sufficiently small time steps using a scheme
consisting of four stages as follows...
Numerical
Schemes for 1-D Problems
Coming back to the
Euler equation, the idea is to limit the gradient in the
variables. The characteristic variables give the most accurate
results, the physical variable enable to control the sign of the
reconstructed density and pressure as well as ..
NUMERICAL SIMULATION OF BIOSPHERE
DYNAMICS
Numerical simulation
of biosphere processes is the part of a wider scientific activity, which
could be called global dynamics. Effective prevention of global crises is
impossible without a sufficiently accurate forecast of the future state of
the ...
NUMERICAL SIMULATION OF CLIMATE
PROBLEMS
Evaluation of the
impact of climatic variability and climate changes on the development of
societies around the world is one of the important challenge
of science and international policy. This fact necessitates the implementation
of a number of program...
Numerical Solution Based on the Maximum
Principle
According to the procedure
outlined in Section 2.2, the optimal control can be determined from the
solution of the associated boundary value problem,
...
One-Person Decision Making
Testing rationality experimentally
in one-person games mainly involves testing (the axioms of) utility theory.
There is probably no need to prove that human players will be unable to solve
optimization tasks involving complex combinatory factors unaided ...
One-step Methods
The most widespread methods of
numerical solution of ODEs are those which
represent solution in form of a table of approximate values of sought
function y(t) ...
Operations
Research and Information Systems: The Implementation ISSUE
.
In the first three
sections we discussed many basic aspects of operations research, and the
following sections were devoted to two ingredients of OR/MS: models and
mathematics. Mathematics of OR is a technical approach, with the development
of a theory...
Operations
Research: Scientific Decision-Making and the Role of MODELING.
Management in its
function as problem solver or decision-maker transforms information into
actions in order to redesign or control organizational systems for which it
has responsibility. Thus decision-making or planning can be conceptualized as
an input...
Operator Algebra
By an operator algebra we usually
mean an algebra consisting of operators closed under the adjoint
operation, i.e ...
Operator Theory
Operator theory
studies individual operators, and it is very diverse. Some selected topics
are briefly outlined in the following...
OPERATOR THEORY AND OPERATOR ALGEBRA
A Hilbert space is a Banach space whose norm comes from an inner product, and
it is the most natural infinite-dimensional generalization of the Euclidean
space. Operators on a Hilbert space appear in many places, and may be viewed
as matrices of ...
Optimal Control Problems
In control theory, one
considers a system whose state can be influenced by some action, the control.
Accordingly, the system is called a control system. A problem of optimal
control arises if one wants to choose a control which is optimal with respect
to some predefined goal ...
Optimal
Design in Linear Models Under a Given Covariance Structure.
A typical example is the
observation of a random process having a known covariance function
(expressing e.g. the seasonal or other fluctuations) but with an unknown mean
(expressing e.g. the trend) ...
Optimal Shape Design
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