相关论文: Non-traditional intervals and their use. Which one…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations,…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
We prove averaging theorems for ordinary differential equations and retarded functional differential equations. Our assumptions are weaker than those required in the results of the existing literature. Usually, we require that the…
A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…
It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet…
The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…
Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…
We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.