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Articles 1291 - 1320 of 10317
Full-Text Articles in Physical Sciences and Mathematics
The Nearest Polyhedral Convex Conic Regions For High-Dimensional Classification, Hakan Çevi̇kalp, Emre Çi̇men, Gürkan Öztürk
The Nearest Polyhedral Convex Conic Regions For High-Dimensional Classification, Hakan Çevi̇kalp, Emre Çi̇men, Gürkan Öztürk
Turkish Journal of Electrical Engineering and Computer Sciences
In the nearest-convex-model type classifiers, each class in the training set is approximated with a convexclass model, and a test sample is assigned to a class based on the shortest distance from the test sample to these classmodels. In this paper, we propose new methods for approximating the distances from test samples to the convex regionsspanned by training samples of classes. To this end, we approximate each class region with a polyhedral convex conicregion by utilizing polyhedral conic functions (PCFs) and its extension, extended PCFs. Then, we derive the necessary formulations for computing the distances from test samples to these …
Analysis Of Shielding Effectiveness By Optimizing Aperture Dimensions Of Arectangular Enclosure With Genetic Algorithm, Sunay Güler, Si̇bel Yeni̇kaya
Analysis Of Shielding Effectiveness By Optimizing Aperture Dimensions Of Arectangular Enclosure With Genetic Algorithm, Sunay Güler, Si̇bel Yeni̇kaya
Turkish Journal of Electrical Engineering and Computer Sciences
Electromagnetic compatibility (EMC) has now become a substantial challenge more than any other time sincethe number of electric vehicles (EV) increased rapidly. The electric driving system in an EV consists of power electroniccomponents supplied by high voltage battery source. They are both source and victim of potential electromagneticinterference (EMI) since fast switching process occurs inside them. Electromagnetic shielding provides a significantprotection against EMI for any electrical and electronic components inside the vehicle. In this paper, analysis of shieldingeffectiveness (SE) by optimizing aperture dimensions of a rectangular enclosure is investigated. Realistic dimensions of theshielding enclosure of an inverter component are employed. …
A Nonlinear Disturbance Observer Scheme For Discrete Time Control Systems, Mehmet Önder Efe, Coşku Kasnakoğlu
A Nonlinear Disturbance Observer Scheme For Discrete Time Control Systems, Mehmet Önder Efe, Coşku Kasnakoğlu
Turkish Journal of Electrical Engineering and Computer Sciences
This paper presents a modification to the original disturbance observer based control (DOBC) scheme byredefining the lowpass filter using a nonlinear element. The proposed technique improves the disturbance predictionperformance for both small and large magnitude disturbance signals. The contribution of the current work is to unfoldthe stability and performance conditions under the proposed modification. A comparative set of simulation studies arediscussed and it is seen that the proposed modification results in smaller disturbance prediction error energy and smallertracking error energy when the plant model is discrete time and uncertain.
Turkish Sign Language Recognition Based On Multistream Data Fusion, Cemi̇l Gündüz, Hüseyi̇n Polat
Turkish Sign Language Recognition Based On Multistream Data Fusion, Cemi̇l Gündüz, Hüseyi̇n Polat
Turkish Journal of Electrical Engineering and Computer Sciences
Sign languages are nonverbal, visual languages that hearing- or speech-impaired people use for communication.Aside from hands, other communication channels such as body posture and facial expressions are also valuable insign languages. As a result of the fact that the gestures in sign languages vary across countries, the significance ofcommunication channels in each sign language also differs. In this study, representing the communication channels usedin Turkish sign language, a total of 8 different data streams-4 RGB, 3 pose, 1 optical flow-were analyzed. Inception3D was used for RGB and optical flow; and LSTM-RNN was used for pose data streams. Experiments were conductedby …
Design Of The Fractional Order Internal Model Controller Using The Swarmintelligence Techniques For The Coupled Tank System, Sateesh Kumar Vavilala, Vinopraba Thirumavalavan, Radhakrishnan Thota, Sivakumaran Natarajan
Design Of The Fractional Order Internal Model Controller Using The Swarmintelligence Techniques For The Coupled Tank System, Sateesh Kumar Vavilala, Vinopraba Thirumavalavan, Radhakrishnan Thota, Sivakumaran Natarajan
Turkish Journal of Electrical Engineering and Computer Sciences
The coupled tank system (comprising two tanks) is used in the chemical industries, water treatment plantsetc. Level control of the coupled tank system is a common problem in the process control industry. This work proposes afractional order internal model controller (FOIMC) with a higher order fractional filter for the level control of the coupledtank system. A first order plus delay time (FOPDT) model of the system is used in the controller design. FOIMC hasadvantages like robustness to changes in the system gain and extended stability margins. The proposed higher orderfractional filter makes the controller physically realizable and quickly roll off …
An Efficient Deep Learning Based Fog Removal Model For Multimedia Applications, Gaurav Saxena, Sarita Singh Bhadauria
An Efficient Deep Learning Based Fog Removal Model For Multimedia Applications, Gaurav Saxena, Sarita Singh Bhadauria
Turkish Journal of Electrical Engineering and Computer Sciences
In the present era of technology, several applications such as surveillances systems, security and object recognitions mainly depend on the contents of an image. In this context, the hazy/foggy environment and/or other adverse climatic conditions degrade the image contents that severely influences the result of related applications. The effective haze removal from a single image decides the reliability of these systems. The convolutional neural network (CNN) based techniques are widely used among the available image dehazing methods. However, in CNN based image dehazing techniques, the robustness and accuracy of the learning models are based on the improvement of transmission estimation …
Model-Based Control For Second-Order Piezo Actuator System With Hysteresis Intime-Delay Environment, Saikat Kumar Shome, Sandip Jana, Arpita Mukherjee, Partha Bhattacharjee
Model-Based Control For Second-Order Piezo Actuator System With Hysteresis Intime-Delay Environment, Saikat Kumar Shome, Sandip Jana, Arpita Mukherjee, Partha Bhattacharjee
Turkish Journal of Electrical Engineering and Computer Sciences
Piezo actuated systems are promising solutions for precision positioning applications. In this paper, a piezoelectric actuator is modeled as a second-order system using the Dahl hysteresis model and the system parameters have been identified from experimental data. The modified internal model control (M-IMC) approach is presented, which not only improves control performance but also reduces associated controller hardware resources. System dead time is approximated using first-order Padé expansion and the proposed Smith predictor-based M-IMC for piezoelectric actuators is seen to offer satisfactory stable control response even for plants with large dead time. The control performance of the M-IMC has been …
Determining Overfitting And Underfitting In Generative Adversarial Networksusing Fréchet Distance, Enes Eken
Determining Overfitting And Underfitting In Generative Adversarial Networksusing Fréchet Distance, Enes Eken
Turkish Journal of Electrical Engineering and Computer Sciences
Generative adversarial networks (GANs) can be used in a wide range of applications where drawing samples from a data probability distribution without explicitly representing it is essential. Unlike the deep convolutional neural networks (CNNs) trained for mapping an input to one of the multiple outputs, monitoring the overfitting and underfitting in GANs is not trivial since they are not classifying but generating a data. While training set and validation set accuracy give a direct sense of success in terms of overfitting and underfitting for CNNs during the training process, evaluating the GANs mainly depends on the visual inspection of the …
Obround Trees: Sparsity Enhanced Feedback Motion Planning Of Differential Driverobotic Systems, Mustafa Mert Ankarali
Obround Trees: Sparsity Enhanced Feedback Motion Planning Of Differential Driverobotic Systems, Mustafa Mert Ankarali
Turkish Journal of Electrical Engineering and Computer Sciences
Robot motion planning & control is one of the most critical and prevalent problems in the robotics community. Even though original motion planning algorithms had relied on "open-loop" strategies and policies, researchers and engineers have been focusing on feedback motion planning and control algorithms due to the uncertainties, such as process and sensor noise of autonomous robotic applications. Recently, several studies proposed some robust feedback motion planning strategies based on sparsely connected safe zones. In this class of planning and control policies, local control policy inside a single zone computes and feeds the control actions that can drive the robot …
Novel Ofdm Transmission Scheme Using Generalized Prefix With Subcarrierindex Modulation, Yusuf Acar
Novel Ofdm Transmission Scheme Using Generalized Prefix With Subcarrierindex Modulation, Yusuf Acar
Turkish Journal of Electrical Engineering and Computer Sciences
The cyclic prefix (CP) is a prefix technique widely used in orthogonal frequency division multiplexing (OFDM) systems in order to eliminate the intersymbol interference (ISI) caused by the dispersion of wireless channels. However, CP reduces the number of symbols that can be transmitted in one OFDM symbol. Therefore, CP is one of the bottlenecks of OFDM systems limiting their spectral efficiency (SE). This limitation on the SE of the classical CP-based OFDM system is the main motivation for this work to introduce a novel method. In this paper, the design of a new CP structure, which is based on the …
Control Synthesis For Parametric Timed Automata Under Reachability, Ebru Aydin Göl
Control Synthesis For Parametric Timed Automata Under Reachability, Ebru Aydin Göl
Turkish Journal of Electrical Engineering and Computer Sciences
Timed automata is a fundamental modeling formalism for real-time systems. During the design of such real-time systems, often the system information is incomplete, and design choices can vary. These uncertainties can be integrated to the model via parameters and labelled transitions. Then, the design can be completed by tuning the parameters and restricting the transitions via controller synthesis. These problems, namely parameter synthesis and controller synthesis, are studied separately in the literature. Herein, these are combined to generate an automaton satisfying the given specification by both parameter tuning and controller synthesis, thus exploring all design choices. First, it is shown …
A New Approach: Semisupervised Ordinal Classification, Ferda Ünal, Derya Bi̇rant, Özlem Şeker
A New Approach: Semisupervised Ordinal Classification, Ferda Ünal, Derya Bi̇rant, Özlem Şeker
Turkish Journal of Electrical Engineering and Computer Sciences
Semisupervised learning is a type of machine learning technique that constructs a classifier by learning from a small collection of labeled samples and a large collection of unlabeled ones. Although some progress has been made in this research area, the existing semisupervised methods provide a nominal classification task. However, semisupervised learning for ordinal classification is yet to be explored. To bridge the gap, this study combines two concepts ?semisupervised learning? and "ordinal classification" for the categorical class labels for the first time and introduces a new concept of "semisupervised ordinal classification". This paper proposes a new algorithm for semisupervised learning …
Novel Fast Terminal Sliding Mode Controller With Current Constraint Forpermanent-Magnet Synchronous Motor, Yao Fang, Huifang Kong, Daoyuan Ding
Novel Fast Terminal Sliding Mode Controller With Current Constraint Forpermanent-Magnet Synchronous Motor, Yao Fang, Huifang Kong, Daoyuan Ding
Turkish Journal of Electrical Engineering and Computer Sciences
Under the noncascade structure, the balance between q-axis current constraint and dynamic performance in permanent-magnet synchronous motor system has become a critical problem. On the one hand, large transient current is required to provide high torque to achieve fast dynamic performance. On the other hand, current constraint becomes a state constraint problem, instead of governing q-axis reference current in the cascade structure directly. Aiming at this issue, a novel fast terminal sliding mode control (FTSMC)-based controller with current constraint is developed in this paper. The novelty of this scheme is related to the proposed penalty function based on interior point …
Distributed Denial Of Service Attack Detection In Cloud Computing Using Hybridextreme Learning Machine, Gopal Singh Kushwah, Virender Ranga
Distributed Denial Of Service Attack Detection In Cloud Computing Using Hybridextreme Learning Machine, Gopal Singh Kushwah, Virender Ranga
Turkish Journal of Electrical Engineering and Computer Sciences
One of the major security challenges in cloud computing is distributed denial of service (DDoS) attacks. In these attacks, multiple nodes are used to attack the cloud by sending huge traffic. This results in the unavailability of cloud services to legitimate users. In this research paper, a hybrid machine learning-based technique has been proposed to detect these attacks. The proposed technique is implemented by combining the extreme learning machine (ELM) model and the blackhole optimization algorithm. Various experiments have been performed with the help of four benchmark datasets namely, NSL KDD, ISCX IDS 2012, CICIDS2017, and CICDDoS2019, to evaluate the …
A Novel Hybrid Decision-Based Filter And Universal Edge-Based Logical Smoothingadd-On To Remove Impulsive Noise, Rajanbir Singh Ghumaan, Prateek Jeet Singh Sohi, Nikhil Sharma, Bharat Garg
A Novel Hybrid Decision-Based Filter And Universal Edge-Based Logical Smoothingadd-On To Remove Impulsive Noise, Rajanbir Singh Ghumaan, Prateek Jeet Singh Sohi, Nikhil Sharma, Bharat Garg
Turkish Journal of Electrical Engineering and Computer Sciences
This paper presents a novel hybrid filter along with a universal extension to remove salt and pepper noise even at a very high noise density. The proposed filter initially specifies a threshold and then denoises the image using a combination of linear, nonlinear, and probabilistic techniques. Furthermore, to improve the quality, a universal add-on is presented which uses edge detection and smoothening techniques to brush out fine details from the restored image. To evaluate the efficacy, the proposed and existing filtering techniques are implemented in MATLAB and simulated with benchmark images. The simulation results show that the proposed filter is …
Shapeshifter: A Morphable Microprocessor For Low Power, Nazli Tokatli, İsa Ahmet Güney, Sercan Sari, Merve Güney, Uğur Nezi̇r, Gürhan Küçük
Shapeshifter: A Morphable Microprocessor For Low Power, Nazli Tokatli, İsa Ahmet Güney, Sercan Sari, Merve Güney, Uğur Nezi̇r, Gürhan Küçük
Turkish Journal of Electrical Engineering and Computer Sciences
A composite core contains large and small heterogeneous microengines. The most important property of composite cores is their ability to select the most proper microengine for running applications to save power without sacrificing too much performance. To achieve this, a composite core tries to predict the performance of the passive microengine by collecting various processor statistics from the active microengine at runtime. In the method proposed in the literature, the microengine, which is more ideal for running the rest of the application, is determined by a migrationdecision circuitry that is bound to collected statistics and complex functions, which are run …
Clustering Ensemble Selection Based On The Extended Jaccard Measure, Hajar Khalili, Mohsen Rabbani, Ebrahim Akbari
Clustering Ensemble Selection Based On The Extended Jaccard Measure, Hajar Khalili, Mohsen Rabbani, Ebrahim Akbari
Turkish Journal of Electrical Engineering and Computer Sciences
Clustering ensemble selection has shown high efficiency in the improvement of the quality of clustering solutions. This technique comprises two important metrics: diversity and quality. It has been empirically proved that ensembles of higher effectiveness can be achieved through taking into consideration the diversity and quality simultaneously. However, the relationships between these two metrics in base clusterings have remained uncertain. This paper suggests a new hierarchical selection algorithm using a diversity/quality measure based on the Jaccard similarity measure. In the proposed algorithm, the selection of the subsets of the clustering partitions is done based on their diversity measures. The proposed …
Deriving Weak Deflection Angle By Black Holes Or Wormholes Usinggauss-Bonnet Theorem, Yashmitha Kumaran, Ali̇ Övgün
Deriving Weak Deflection Angle By Black Holes Or Wormholes Usinggauss-Bonnet Theorem, Yashmitha Kumaran, Ali̇ Övgün
Turkish Journal of Physics
In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on nonasymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of …
The Hydrothermal Synthesis Of Blue-Emitting Boron-Doped Cqds And Its Application For Improving The Photovoltaic Parameters Of Organic Solar Cell, Tuğbahan Yilmaz
The Hydrothermal Synthesis Of Blue-Emitting Boron-Doped Cqds And Its Application For Improving The Photovoltaic Parameters Of Organic Solar Cell, Tuğbahan Yilmaz
Turkish Journal of Chemistry
In this work, boron-doped CQDs (B-CQDs) were synthesized by using boric acid, urea, and citric acid via hydrothermal method to use as a novel additive material for poly(3-hexylthiophene-2,5-diyl) (P3HT):[6,6]-phenyl-C61-butyric acid methyl ester (PCBM) based organic solar cells. The OSCs with an inverted device structure were fabricated on titanium dioxide (TiO2) thin film. It was showed the crystallinity, morphological and optical properties of P3HT:PCBM films improved after B-CQDs additive. The best performance was obtained to be a 39.65% of FF, a 546 mV of Voc, an 8.606 mA cm-2 of Jsc after 3 vol.% B-CQDs addition in P3HT:PCBM blend. The power …
Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak
Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak
Turkish Journal of Mathematics
In this study, we consider the domains of the minimal and maximal operators generated of singular differential-expression-type Sturm-Liouville and obtain all self-adjoint extensions of the operator in terms of boundary conditions.
Validation Of Hplc Method For The Determination Of Chemical And Radiochemical Purity Of A 68ga-Labelled Euk-Sub-Kf-(3-Iodo-Y-) Dotaga, Ayşe Uğur, Şükrü Gökhan Elçi̇, Doğangün Yüksel
Validation Of Hplc Method For The Determination Of Chemical And Radiochemical Purity Of A 68ga-Labelled Euk-Sub-Kf-(3-Iodo-Y-) Dotaga, Ayşe Uğur, Şükrü Gökhan Elçi̇, Doğangün Yüksel
Turkish Journal of Chemistry
The prostate-specific membrane antigen (PSMA) represents an ideal biomarker for molecular imaging. Various PSMA-targeted radioligands are available for prostate cancer imaging. In this study, labeling of PSMA I&T with 68Ga, as well as validation of the radiochemical purity of the synthesis product by reverse phase radio high-performance liquid chromatography (HPLC) method are intended. Since the standard procedure for the quality control (QC) was not available, definition of chemical and radiochemical purity of 68Ga-PSMA I&T was carried out according to the Q2 (R1) ICH guideline. The standard QC tests were analyzed with Scintomics 8100 radio-HPLC system equipped with a radioactivity detector. …
Integrated 3d-Qsar, Molecular Docking, And Molecular Dynamics Simulation Studies On 1,2,3-Triazole Based Derivatives For Designing New Acetylcholinesterase Inhibitors, Khalil El Khatabi, Ilham Aanouz, Reda El-Mernissi, Atul Kumar Singh, Mohammed Aziz Ajana, Tahar Lakhlifi, Shashank Kumar, Mohammed Bouachrine
Integrated 3d-Qsar, Molecular Docking, And Molecular Dynamics Simulation Studies On 1,2,3-Triazole Based Derivatives For Designing New Acetylcholinesterase Inhibitors, Khalil El Khatabi, Ilham Aanouz, Reda El-Mernissi, Atul Kumar Singh, Mohammed Aziz Ajana, Tahar Lakhlifi, Shashank Kumar, Mohammed Bouachrine
Turkish Journal of Chemistry
Alzheimer's disease (AD) is a multifactorial and polygenic disease. It is the most prevalent reason for dementia in the aging population. A dataset of twenty-six 1,2,3-triazole-based derivatives previously synthetized and evaluated for acetylcholinesterase inhibitory activity were subjected to the three-dimensional quantitative structure-activity relationship (3D-QSAR) study. Good predictability was achieved for comparative molecular field analysis (CoMFA) (Q2 = 0.604, R2 = 0.863, rext2 = 0.701) and comparative molecular similarity indices analysis (CoMSIA) (Q2 = 0.606, R2 = 0.854, rext2 = 0.647). The molecular features characteristics provided by the 3D-QSAR contour plots were quite useful for designing and improving the activity of …
Recent Developments In $\Delta$-Casorati Curvature Invariants, Bang-Yen Chen
Recent Developments In $\Delta$-Casorati Curvature Invariants, Bang-Yen Chen
Turkish Journal of Mathematics
The theory of $\delta$-invariants, initiated by the author in the early 1990s, is a challenging topic in modern differential geometry, having a lot of applications. In the spirit of $\delta$-invariants, Decu et al. (2007) initiated the study of $\delta$-Casorati curvatures. Since then there are many interesting results on $\delta$-Casorati curvatures obtained by many authors. In this article we provide a comprehensive survey on recent developments in $\delta$-Casorati curvatures done during the last decade.
Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep
Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep
Turkish Journal of Mathematics
A star edge coloring of a graph $G$ is a proper edge coloring such that there is no bicolored path or cycle of length four. The minimum number of colors needed for a graph $G$ to admit a star edge coloring is called the star chromatic index and it is denoted by $\chi_s^{'}(G)$. In this paper, we consider graphs of maximum degree $\Delta \geq 4$ and show that if the maximum average degree of a graph is less than $\frac{14}{5}$ then $\chi_s^{'}(G) \leq 2\Delta + 1$.
An Extension Of Maximum Principle With Some Applications, Ali Parsian
An Extension Of Maximum Principle With Some Applications, Ali Parsian
Turkish Journal of Mathematics
Let $U\subseteq R^{n}$ (res. $D\subset R^{n}$) be an open (res. a compact) subset, and let $L$ be an elliptic operator defined on $C^{2}(U, R)$ (res. $C^{2}(D, R)$). In the present paper, we are going to extend the maximum principle for the function $f \in C^{2}(U, R)$ (res. $f \in C^{2}(D, R)$) satisfying the equation $Lf=\varepsilon$, where $\varepsilon$ is a real everywhere nonzero continuous function on $U$ (res. $D$). Finally, we obtain some applications in mathematics and physics.
Notes On Product Semisymmetric Connection In A Locally Decomposable Riemannian Space, Miroslav Maksimovic, Mica Stankovic
Notes On Product Semisymmetric Connection In A Locally Decomposable Riemannian Space, Miroslav Maksimovic, Mica Stankovic
Turkish Journal of Mathematics
The purpose of this paper is to investigate the product semisymmetric connection in a locally decomposable Riemannian space. The curvature tensors of this connection were considered. Some properties of almost product structure, some properties of torsion tensor of product semisymmetric connection and some relations between curvature tensors and almost product structure are given. Also, the paper checks a special case of such connection when its generator is a gradient vector.
Widths And Entropy Of Sets Of Smooth Functions On Compact Homogeneous Manifolds, Alexander Kushpel, Kenan Taş, Jeremy Levesley
Widths And Entropy Of Sets Of Smooth Functions On Compact Homogeneous Manifolds, Alexander Kushpel, Kenan Taş, Jeremy Levesley
Turkish Journal of Mathematics
We develop a general method to calculate entropy and $n$-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold $% \mathbb{M}^{d}$. Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on $% \mathbb{M}^{d}$. This approach has been developed in the cycle of works [1, 2, 10-19]. The method's possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and $n$-widths of Sobolev's classes $W_{p}^{\gamma }\left( \mathbb{M}^{d}\right) $ and their generalisations in …
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
Turkish Journal of Mathematics
We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a $q$-geometric distribution of the second kind. Further, we find their $q$-binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.
Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov
Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov
Turkish Journal of Mathematics
he present paper studies the optimal control theory of second-order polyhedral delay discrete and delay differential inclusions with state constraints. We formulate the conditions of optimality for the problems with the second-order polyhedral delay discrete $(PD_d)$ and the delay differential $(PC_d)$ in terms of the Euler-Lagrange inclusions and the distinctive ''transversality'' conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.
Generalized Littlewood-Paley Functions On Product Spaces, Hussain Alqassem, Leslie Cheng, Yibiao Pan
Generalized Littlewood-Paley Functions On Product Spaces, Hussain Alqassem, Leslie Cheng, Yibiao Pan
Turkish Journal of Mathematics
We are interested in investigating the $L^{p}$ boundedness of the product of generalized Littlewood-Paley functions $S_{\Phi }^{(\lambda )}(f)$ arising from kernels satisfying only size and cancellation conditions. We obtain $L^{p}$ estimates of $S_{\Phi }^{(\lambda )}(f)$ for a sharp range of $p$ and under optimal conditions on $\Phi $. Using these estimates and an extrapolation argument, we obtain some new and improved results on generalized Littlewood-Paley functions on product spaces. As a consequence of our main results, we get two results, one of which answers a question posed by D. Fan and H. Wu and the other one answers a question …