We construct injective hulls and projective covers in categories of generalized uniform hypergraphs which generalizes the constructions in the category of quivers and the category of undirected graphs. While the constructions are not functorial, they are “sub-functorial”, meaning they are subobjects of functorial injective and projective refinements.
In this study, the multiple knapsack problems (MKP) with uncertainty model is introduced. The uncertainty represents the capacities of the knapsack. A possibility degree of interval number is used to convert the uncertain capacities to deterministic capacities. Some basic stability notions in parametric multiple knapsack are defined. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind. A numerical example (case study) is introduced to present the suggested approach.
We present a special B-spline tight frame and use it to introduce our numerical approximation method. We apply our method to investigate Gibbs effects and illustrate some features of the associated framelet expansion. It is shown that Gibbs effects occurs in the framelet expansion of a function with a jump discontinuity at 0 for certain classes of framelets. Numerical results are obtained regarding the behavior of the Gibbs effects. We present the results by expanding functions using the quasi-ane system. This system is generated by the B-spline tight framelets with a specific number of generators. We show numerically the existence of Gibbs effects in the truncated expansion of a given function by using some tight framelet representation.
Finite-state automaton is a machine that processes input strings and produces output indicating whether the input string is accepted or not. It is an acceptor recognizer for input specification. A finite-state automaton is an input/output device that accepts strings as input and produces binary numbers 0s and 1s.
Two automata are equivalent if they generate the same or similar output for each input string. That is to say, two automata are equivalent if and only if they have the same computing powers. In this paper, we develop an algorithm that can be used to determine if two automata are equivalent. Such automaton could be an non-deterministic finite automata (NFA) that is converted to deterministic finite automata (DFA) or a DFA that is minimized into another DFA (minimized DFA) which are equivalent in the sense that they have the same computing power and can therefore be used to compute the same regular expression. Examples of the use of the algorithms are provided and their results show that they are equivalent in all respects. From the examples, it is clearly seen that each pair of automaton accept the same language, hence they are said to be equivalent. The proposed algorithm performs better in terms of time and space complexities when compared with existing algorithms because it runs faster and occupies less space in the computer’s memory.
Computer Mathematics is a developing branch of the computer engineering. This area has a mathematical background on which this work centers its development. We started with basic set definitions but placed on emphasis on sets of real numbers. In developing this we used the idea of the transformed set operations on specific real number sets to generate a reasonable result which undoubtedly is very much useful in the circuit networking Mathematical arguments were implored and the basic results verified and displayed using the Truth Table as contained in the body of the work.