Fourier Inequalities in Lorentz and Lebesgue Spaces

Mapping properties of the Fourier transform between weighted Lebesgue and Lorentz spaces are studied. These are generalizations to Hausdorff-Young and Pitt’s inequalities. The boundedness of the Fourier transform on $R^n$ as a map between Lorentz spaces leads to weighted Lebesgue inequalities for the Fourier transform on $R^n$ . A major part of the work is on Fourier coefficients. Several different sufficient conditions and necessary conditions for the boundedness of Fourier transform on unit circle, viewed as a map between Lorentz $\Lambda$ and $\Gamma$ spaces are established. For a large range of Lorentz indices, necessary and sufficient conditions for boundedness are given. A number of known inequalities for generalized quasi concave functions are generalized and improved as part of the preparation for the proofs of the Fourier series results. The Lorentz space results are used to obtain conditions that guarantee the continuity of the Fourier coefficient map between weighted $L^p$ spaces. Applications to $L\log L$ and Lorentz-Zygmund spaces are also given

On common fixed and periodic points of commuting functions

It is known that two commuting continuous functions on an interval need not have a common fixed point. It is not known if such two functions have a common periodic point. In this paper we first give some results in this direction. We then define a new contractive condition, under which two continuous functions must have a unique common fixed point

A counter example on common periodic points of functions

By a counter example we show that two continuous functions defined on a compact metric space satisfying a certain semi metric need not have a common periodic point

Classification Approaches in Neuroscience: A Geometrical Point of View

Functional magnetic resonance images (fMRI) are brain scan images by MRI machine which are taken functionally cross the time. Several studies have investigated methods analyzing such images (or actually the drawn data from them) and is interestingly growing up. For examples models can predict the behaviours and actions of people based on their brain pattern, which can be useful in many fields. We do the classification study and prediction of fMRI data and we develop some approaches and some modifications on them which have not been used in such classification problems. The proposed approaches were assessed by comparing the classification error rates in a real fMRI data study. In addition, many programming codes for reading from fMRI scans and codes for using classification approaches are provided to manipulate fMRI data in practice. The codes, can be gathered later as a package in R. Also, there is a steadily growing interest in analyzing functional data which can often exploit Riemannian geometry. As a prototypical example of these kind of data, we will consider the functional data rising from an electroencephalography (EEG) signal in Brain-Computer interface (BCI) which translates the brain signals to the commands in the machine. It can be used for people with physical inability and movement problems or even in video games, which has had increased interest. To do that, a classification study on EEG signals has been proposed, while, the data in hand to be classified are matrices. A multiplicative algorithm (MPM), which is a fast and efficient algorithm, was developed to compute the power means for matrices which is the crucial step in our proposed approaches for classification. In addition, some simulation studies were used to examine the performance of MPM against existing algorithms. We will compare the behavior of different power means in terms of accuracy in our classifications, which had not been discovered previously. We will show that it is hard to have a guess to find the optimal power mean to have higher accuracy depending on the multivariate distribution of data available. Then, we also develop an approach, combination of power means, to have the benefit of all to improve the classification performance. All the codes related to the fast MPM algorithms and the codes for manipulating EEG signals in classification are written in MATLAB and can be developed later as a package

Machine Learning And Deep Learning Based Approaches For Detecting Duplicate Bug Reports With Stack Traces

Many large software systems rely on bug tracking systems to record the submitted bug reports and to track and manage bugs. Handling bug reports is known to be a challenging task, especially in software organizations with a large client base, which tend to receive a considerable large number of bug reports a day. Fortunately, not all reported bugs are new; many are similar or identical to previously reported bugs, also called duplicate bug reports. Automatic detection of duplicate bug reports is an important research topic to help reduce the time and effort spent by triaging and development teams on sorting and fixing bugs. This explains the recent increase in attention to this topic as evidenced by the number of tools and algorithms that have been proposed in academia and industry. The objective is to automatically detect duplicate bug reports as soon as they arrive into the system. To do so, existing techniques rely heavily on the nature of bug report data they operate on. This includes both structural information such as OS, product version, time and date of the crash, and stack traces, as well as unstructured information such as bug report summaries and descriptions written in natural language by end users and developers

On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

In recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixed points and a countable set of periodic points

A note on the multiple comparisons of exponential location parameters with several controls under heteroscedasticity

Several researchers have addressed the problem of constructing simultaneous confidence intervals (SCIs) for comparing exponential location parameters with a control or controls under heteroscedasticity when sample sizes are equal or unequal. They usually used simulation-based inference procedures or Lam's technique that leads to conservative SCIs. In this paper, we present a set of SCIs for comparing exponential location parameters with a control, controls and the best control under heteroscedasticity when sample sizes are possibly unequal. Our method is not a simulation-based inference procedure and our results show that the proposed SCIs have some advantages over others

Biocompatibility of Portland Cement Modified with Titanium Oxide and Calcium Chloride in a Rat Model

Introduction: The aim of the present study was to evaluate the biocompatibility of two modified formulations of Portland cement (PC) mixed with either titanium oxide or both titanium oxide and calcium chloride. Methods and Materials: Polyethylene tubes were filled with modified PCs or Angelus MTA as the control; the tubes were then implanted in 28 Wistar rats subcutaneously. One tube was left empty as a negative control in each rat. Histologic samples were taken after 7, 15, 30 and 60 days. Sections were assessed histologically for inflammatory responses and presence of fibrous capsule and granulation tissue formation. Data were analyzed using the Fisher’s exact and Kruskal-Wallis tests. Result: PC mixed with titanium oxide showed the highest mean scores of inflammation compared with others. There was no statistically significant difference in the mean inflammatory grades between all groups in each of the understudy time intervals. Conclusion: The results showed favorable biocompatibility of these modified PC mixed with calcium chloride and titanium oxide.Keywords: Biocompatibility; Mineral Trioxide Aggregate; Portland Cemen

Improved Energy Conversion Process With Coupling Induction Motors And Invastigate Unbalanced Operation With Definition Of The Voltage Unbalance

This paper assesses Voltage unbalance study as one of power quality issues which is especially effected distribution voltages and is noteworthy. however it is possible that voltage in level of producing and transmission be balanced but this voltages in level of distribution can go out of balance and be unbalanced which is because of unbalanced systems, unequal impedances and lack of appropriate and balanced distribution of one phase loads in distribution systems occurs. In this thesis operation of steady state machine conjunction (Induction motor) under unbalanced voltage will be evaluated. Induction motors in small sizes attach as coupled and will be used instead of big sized induction motors, which is proper for improved electromagnetic systems and more efficient energy conversion mechanism in both symmetric and asymmetric states. Two coupled induction motors can have the same or different rates mechanically. This thesis will analyze coupled machinery using symmetric elements and MATLAB software. Definition of unbalance voltage is used by CVUF factor (complex voltage unbalance factor). Induction motors coupling with DC motors (direct current) is analyzed and coupling effect in electromagnetic torque in all system is studied and comparing of unbalanced voltage on standalone and coupled machines is demonstrateed. The purpose of such comparing is finding the best states in balanced and unbalanced working, also this thesis evaluates the effect of induction motors connection as coupling in energy conversion process