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In this paper, the calculus of functions with values in L-spaces is developed. We then consider nonlinear integral equations of Fredholm and Volterra types for functions with values in L-spaces. Such class of equations includes set-valued integral equations, fuzzy integral equations, and many others. We prove theorems of existence and uniqueness of the solutions of such equations and investigate data dependence of their solutions.

The purpose of this paper is to introduce the Picard–Ishikawa hybrid iterative process. This new iterative process can be seen as a hybrid of Picard and Ishikawa iterative processes. It is our purpose in this paper to show that this new hybrid iterative process converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, Noor, Picard–Mann and Picard–Krasnoselskii iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points. Efemeride, Baia Mare, 2002). We establish data dependence and stability results for our newly developed iterative process. Moreover, we apply our newly developed iterative process in finding the solution of delay differential equations.

In this article we have considered a fractional order impulsive integro-differential equation (IDE) in Caputo’s sense for the unique solution and data dependence results. We take help of the Banach fixed point theory and basic literature of fractional calculus. The results are examined with the help of an expressive numerical example for an application of the results.

In this paper, we study convergence and data dependence of SP and normal-S iterative methods for the class of almost contraction mappings under some mild conditions. The validity of these theoretical results is confirmed with numerical examples. It has been observed that a special case of SP iterative method, namely normal-S iterative method, performs better and so the latter is implemented in the stable inversion of nonlinear discrete time dynamical systems to yield convergence results when Picard iterative method diverges. This is also illustrated with a numerical example. Our work extends and improves upon many results existing in the literature.

In this paper, we will prove some fixed point results for multi-valued almost pseudo-contractions in some generalized metric spaces. Data dependence theorems and some applications to multi-valued coincidence problems are also given.

The power of data dependence testing techniques of a parallelizing compiler is its essence to transform and optimize programs. Numerous techniques were proposed in the past, and it is, however, still a challenging problem to evaluate the relative power of these techniques to better understand the data dependence testing problem. In the past, either empirical studies or experimental evaluation results are published to compare these data dependence testing techniques, being not able to convince the research community completely. In this paper, we show a theoretical study on this issue, comparing the power on disproving dependences of existing techniques by proving theorems in a proposed formal system K-DT. Besides, we also present the upper bounds of these techniques and introduce their minimum complete sets. To the best of our knowledge, K-DT is the first formal system used to compare the power of data dependence testing techniques, and this paper is the first work to show the upper bounds and minimum complete sets of data dependence testing techniques.

We study a weaker and more natural notion of stability called weak $$w^{2}$$ -stability to get an insight in the corresponding results obtained by Maruster and Maruster (J Comput Appl Math 276:110–116, 2015) and Wang (J Comput Appl Math 285:226–229, 2015). A data dependence result for fixed points of strongly demicontractive operators is also established. Some illustrative examples are given to validate results obtained herein.

In this paper, we propose some fixed point results for a new type of contractive multivalued operators in the setting of \(\mathcal {H}^+\)-metric spaces which are further applied to get results on data dependence and well-posed multivalued problems. By doing this, our work generalizes Nadler’s, Kikkawa and Suzuki’s, and some other fixed point theorems. The theorems provided allow upgrading of Pathak and Shahzad’s and Popescu’s results which is shown by an example. A homotopy result is presented at the end as an application of our main theorem.

In the present paper, we introduce new types of Presic operators. These operators generalize the well-known Istraţescu mappings, known as convex contractions. Also, we study the existence and uniqueness of fixed points for this type of operators and the convergence of one-step sequence toward the unique fixed point. Also, data dependence results are presented. Finally, some examples are given, suggesting that the above mappings are proper generalizations of convex contractions of second order.

Computationally expensive programs spend most of their time in the execution of DO-loops [1,2]. Therefore, an efficient approach for exploiting potential parallelism is to concentrate on the parallelism available in loops in ordinary programs and has a considerable effect on the speedup [3,4]. Through some loop transformations using a dependence distance in single loops [6,10], a loop can be splitted into partial loops to be executed in parallel without violating data dependence relations, that is, the size of distance can be used as a reduction factor [6], which is the number of iterations that can be executed in parallel. In the case of non-constant distance such that it varies between different instances of the dependence, it is much more difficult to maximize the degree of parallelism from a loop. Partitioning of loops requires efficient and exact data dependence analysis. A precise dependence analysis helps in identifying dependent/independent iterations of a loop. And it is important that appropriate dependence analysis be applied to exploit maximum parallelism within loops. We can consider some tests that examine the dependence of onedimensional subscripted variables— the separability test, the GCD test and the Banerjee test [8,11]. In general, the GCD test is applied first because of its simplicity, even if it is an approximate test. Next, for the case that the gcd test is true, the separability test is attempted again, and through this exact

We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.

An OpenMP approach was proposed to parallelize the sequential molecular dynamics (MD) code on shared memory machines. When a code is converted from the sequential form to the parallel form, data dependence is a main problem. A traditional sequential molecular dynamics code is anatomized to find the data dependence segments in it, and the two different methods, i. e., recover method and backward mapping method were used to eliminate those data dependencies in order to realize the parallelization of this sequential MD code. The performance of the parallelized MD code was analyzed by using some performance analysis tools. The results of the test show that the computing size of this code increases sharply form 1 million atoms before parallelization to 20 million atoms after parallelization, and the wall clock during computing is reduced largely. Some hot-spots in this code are found and optimized by improved algorithm. The efficiency of parallel computing is 30% higher than that of before, and the calculation time is saved and larger scale calculation problems are solved.

A traditional approach to solving the problem of local compaction of a horizontal microcode is described. In accordance with this approach any linear segment of the source microcode is made to correspond to a unique data dependence graph. A notion of the data exchange between the microoperations is introduced. Based on this notion, a model is developed that demonstrates that a given linear segment is, generally, associated with a set of semantically equivalent data dependence graphs, which differ from one another by the order of the execution of the exchanges on shared static resources. An optimization combinatorial problem on the permutation of the exchanges of a linear segment is formulated. Conditions for the existence of an admissible solution are studied, and a method for finding it is developed. A new space of solutions for the local compaction problem is obtained through the use of a new data dependence graph, which is, in a sense, better than the original one.

Traditional data dependence testing algorithms have become very accurate and efficient for simple subscript expressions, but they cannot handle symbolic expressions because of the complexity of data-flow and lack of the semantic information of variables in programs. In this paper, a range-based testing and query approach, called DDTQ, is proposed to eliminate data dependence between array references with symbolic subscripts. DDTQ firstly extracts data dependence information from the symbolic subscripts, a testing algorithm is then used to disprove the dependence based on the ranges of expressions. The assumed dependence that cannot be handled by the disprover will be converted into simple questions by a question engine so that the compiler can solve them by user interaction in a friendly way. The experiment on perfect benchmarks indicates that DDTQ is effective in improving the parallelizing capability of the compiler.

JAPS is an automatic parallelizing system based on JAVA running on NOW. It implements the automatic process from dependence analysis to parallel execution. The current version of JAPS can exploit functional parallelism and the detection of data parallelism will be incorporated in the new version, which is underway. The framework and key techniques of JAPS are presented. Specific topics discussed are task partitioning, summary information collection, data dependence analysis, pre-scheduling and dynamic scheduling, etc.

In this paper, we prove that the convergence of a new iteration and S-iteration can be used to approximate the fixed points of contractive-like operators. We also prove some data dependence results for these new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature. MSC:47H10.

Precise value-based data dependence analysis for scalars is useful for advanced compiler optimizations. The new method presented here for flow and output dependence uses Factored Use and Def chains (FUD chains), our interpretation and extension of Static Single Assignment. It is precise with respect to conditional control flow and dependence vectors. Our method detects dependences which are independent with respect to arbitrary loop nesting, as well as loop-carried dependences. A loop-carried dependence is further classified as being carried from the previous iteration, with distance 1, or from any previous iteration, with direction

Curare, the program restructurer described in this paper automatically transforms a sequential Lisp program into an equivalent concurrent program that runs on a multiprocessor. Data dependences constrain the program's concurrent execution because, in general, two conflicting statements cannot execute in a different order without affecting the program's result. Not all dependences are essential to produce the program's result.Curare attempts to transform the program so it computes its result with fewer conflicts. An optimized program will execute with less synchronization and more concurrency. Curare then examines loops in a program to find those that are unconstrained or lightly constrained by dependences. By necessity,Curare treats recursive functions as loops and does not limit itself to explicit program loops. Recursive functions offer several advantages over explicit loops since they provide a convenient framework for inserting locks and handling the dynamic behavior of symbolic programs. Loops that are suitable for concurrent execution are changed to execute on a set of concurrent server processes. These servers execute single loop iterations and therefore need to be extremely inexpensive to invoke. Restructured programs execute significantly faster than the original sequential programs. This improvement is large enough to attract programmers to a multiprocessor, particularly since it requires little effort on their part.

We prove a convergence result and a data dependence for Ishikawa iteration when applied to contraction-like operators. An example is given, in which instead of computing the fixed point of an operator, we approximate the operator with a contractive-like one. For which it is possible to compute the fixed point, and therefore to approximate the fixed point of the initial operator.

The existence, uniqueness, differentiability and data dependence of solutions of initial-boundary value problems in classical elastodynamics are treated by applying the theory of first-order symmetric hyperbolic systems. Sharp results on the differentiability of solutions are obtained in terms of body force, initial data and boundary conditions.

Current analytic methods including time and frequency domain approaches are often inadequate to fully characterize FBA. Because of its episodic nature and changing character with gestation, FBA does not lend itself to rigorous statistical analysis. To overcome this problem, we have developed an analytic approach which assumes that the activity occurs quasi-randomly during most of gestation, identifies episodes of activity (breathing) and non-activity (apnea) and characterizes the data within these epochs in a straightforward manner. Using a minicomputer, coded human ultrasonic or baboon tracheal fluid pressure data are digitized, pre-processed for removal of artefacts and breath detection. The distribution of detected breaths is used to identify epochs of FBA and to characterize each epoch with appropriate parameters, including duration, # of breaths, mean fetal breathing rate (FBR), FBR variability and mean breathing amplitude. Tabular and graphical outputs provide epoch by epoch results and summary statistics for a complete study. This approach offers several advantages: 1) data dependence making no assumptions about periodicities or character of breath-activity, 2) focus on the activities of interest while filtering out inherent variability and 3) systematic data reduction and application of standard statistical techniques to multiple recordings from any number of subjects.