Tensor Completion has numerous applications in digital image processing such as image recovery and video overlay. In this paper, we consider two new approaches to Tensor Completion. Efficient low-rank Tensor with Tensor train and Tensor ring for image recovery, some basic concepts about Tensor algebra and Completion problems are presented, after that Tensor Completion based on the Tensor train and Tensor ring are offered and implemented on some examples for image recovery with different observed ratios. The results of these implementations are compared and final results are proposed.

In this paper, we are going to analyze big data (embedded in the digital images) with new methods of Tensor Completion ((TC)). The determination of Tensor ranks and the type of decomposition are significant and essential matters. For defeating these problems, Bayesian CP-Factorization (BCPF) is applied to the Tensor Completion problem. The BCPF can optimize the type of ranks and decomposition for achieving the best results. In this paper, the hybrid method is proposed by integrating BCPF and general (TC). The Tensor Completion problem was briefly introduced. Then, based on our implementations, and related sources, the proposed Tensor-based Completion methods emphasize their strengths and weaknesses. Theoretical, practical, and applied theories have been discussed and two of them for analyzing big data have been selected, and applied to several examples of selected images. The results are extracted and compared to determine the method’, s efficiency and importance compared to each other. Finally, the future ways and the field of future activity are also presented.

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with Tensor data. Precisely, the goal of MDA  is to find mode-specific projections that optimally separate Tensor data from different classes. However, to solve this task, standard MDA methods use alternating optimization heuristics involving the computation of a succession of Tensor-matrix products. Such approaches are most of the time difficult to solve and not natural, highligthing the difficulty to formulate this problem in fully Tensor form. In this paper, we propose to solve multilinear discriminant analysis (MDA) by using the concept of transform domain (TD) recently proposed in [15]. We show here that moving MDA to this specific transform domain make its resolution easier and more natural. More precisely, each frontal face of the transformed Tensor is processed independently to build a separate optimization sub-problems easier to solve. Next, the obtained solutions are converted into projective Tensors by inverse transform. By considering a large number of experiments, we show the effectiveness of our approach with respect to existing MDA methods.

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discussed by the authors. We introduce a new class of geometric vector fields and prove some basic facts about them. We call these vector fields affinewise. By contraction of the symmetric curvature, we define two new curvatures which have direct relations to the notions of divergence, Laplacian, and the Ricci Tensor.

Tensors as vector fields structures and manifolds as great geometrical-topological structures have many applications in the fields of big data analysis. Types of norms, metrics, and scalable structures have been defined from various aspects. Nowadays, the hybrid methods between Tensorial algorithms and manifold learning (MaL) methods have been attracted some attention. In image and signal processing, from image recovery to face recognition, these methods have appeared very excellent. According to our experiments by MATLAB R2021a, the hybrid algorithms are powerful other than algorithms based on the efficient popular parameters.

Introduction: The aim of this study was to develop an optimized formulation for labeling a third-generation bisphosphonate, zoledronic acid with [99m(TC)] (TC) to achieve the best formulation in preparing an ideal skeletal radiotracer. Radiocomplex yield and purity, stability, biodistribution and imaging in normal rat were investigated. Methods: The samples containing different amounts of zoledronic acid, ascorbic acid and stannous chloride were prepared and labeled with [ 99m (TC)]technetium pertechnetate. TLC methods were used to determine the radiochemical purity. The stability was determined in saline and human serum solutions. Lipophilicity was calculated by measuring radio-complex that was divided between organic and aqueous phases. In vitro bone affinity was studied through hydroxyapatite binding assays. Considering the decomposition of radioactivity, biodistribution of radio-complex was assessed based on the percentage of injected activity per gram of organ (% IA/g). Results: [99m(TC)](TC)-zoledronic acid was prepared easily with high yield while 100 µ, g, 0. 34 µ, mol of zoledronic acid as a ligand and 100 µ, g, 0. 44 µ, mol SnCl2 as a reducing agent were used. Radiochemical purity of radio-complex was more than 99% with specific activity of 8050 MBq/µ, mol. The radio-complex showed rapid blood washout along with high bone uptake value (4. 53 ±,0. 14 % IA/g at 2 h post injection). Conclusion: Under optimized condition, [99m(TC)](TC)-zoledronic acid was prepared with high purity and stability together with high bone affinity and rapid blood clearance, make this radio-complex an ideal agent with great potential for skeletal imaging.

The ordinary Tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in each component. keeping this in mind, Linton and Banaschewski with Nelson defined and studied the Tensor product in an equational category and in a general (concrete) category K, respectively, using bimorphisms, that is, defined via the Hom-functor on K. Also, the so-called sesquilinear, or one and a half linear maps and the corresponding Tensor products generalize these notions for modules and vector spaces. In this paper, taking a concrete category K and an arbitrary subfunctor H of the functor U'=Hom o (Uop´U) rather than just the Hom-functor, where U is the underlying set functor on K, we generalize sesquilinearity to bivariation and study the related notions such as functional internal lifts, universal bivariants, Tensor products, and their interdependence.

Tension control bolts ((TC) bolts) are specialized fasteners mainly utilized in steel frame construction. They include a pre-assembled bolt, nut, and washer for simplified installation. In contrast to standard bolts, (TC) bolts have a domed head and a distinctive spline design that enables accurate tensioning during the installation process. This advancement has led to their growing popularity in the construction sector because of their effectiveness and dependability. In this article, examined this type of bolts, installation mechanism, their advantages over conventional high-strength structural bolts, challenges and considerations, durability comparison between traditional and (TC) bolts, design features, installation process, and also review the relevant standards associated with them.

Introduction: For renal scintigraphy, different radiopharmaceuticals like 99m(TC)-DMSA and 99m(TC)-EC can be used. Although these methods are accurate, some differences can be observed among them. These radiopharmaceuticals have different levels of reproducibility and repeatability. This study aimed to evaluate the level of inter and intra observer variability in 99m(TC)-DMSA scintigraphy. We also compared the renal function, measured with 99m(TC)-EC, with the one measured using 99m(TC)-DMSA scintigraphy to determine if 99m(TC)-EC can be used instead of 99m(TC)-DMSA in this regard.Methods: The sample volume consisted of 81 patients underwent both 99m(TC)-DMSA and 99m(TC)-EC in Imam Reza Health Center in 2008. These scans were interpreted by two observers. One of the observers interpreted the scans after one month for the second time. The data were analyzed with SPSS.Results: There was a close correlation between these two methods with respect to DRF (P = 0.51). Estimating intra observer variability showed close correlation between DMSA (r = 0.997) and EC (r = 0.996). The evaluation of inter observer variability also revealed high correlation between DMSA (r = 0.995) and EC (r = 0.996).Conclusion: Since the comparison between these two methods in measuring renal function showed the same results, 99m(TC)-EC can be used as a substitute for 99m(TC)-DMSA. In addition, (TC)-99m EC scintigraphy can be a reliable single-modality study to evaluate renal cortical defects, perfusion, and drainage of the urinary system and indirect evidence of vesicoureteric reflux with the added advantage of low radiation exposure to the patient. Also good reproducibility and repeatability were reported according to this study.