Some Remarks on the Proximal Point Algorithm

In this paper, we obtain some results on the boundedness and asymptotic behavior of the sequence generated by the proximal point algorithm without summability assumption on the error sequence. We also study the rate of convergence to minimum value of a proper, convex, and lower semicontinuous function. Finally, we consider the proximal point algorithm for solving equilibrium problems.     

Bifurcation analysis and nonlinear dynamics of a capacitive energy harvester in the vicinity of the primary and secondary resonances

Nonlinear Dynamics - The objective of the present study is to examine the effect of nonlinearity on the efficiency enhancement of a capacitive energy harvester. The model consists of a cantilever...     

Some Hadamard matrices of order 32 and their binary codes

It is known that all doubly‐even self‐dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly‐even self‐dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32. © 2004 Wiley Periodicals, Inc.     

Balancedly splittable Hadamard matrices

Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are presented. As an application, commutative association schemes of 4, 5, and 6 classes are constructed.     

New families of strongly regular graphs

We apply symmetric balanced generalized weighing matrices with zero diagonal to construct four parametrically new infinite families of strongly regular graphs. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 208–217, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10038     

Bush‐type Hadamard matrices and symmetric designs

Abstact: A symmetric 2‐(100, 45, 20) design is constructed that admits a tactical decomposition into 10 point and block classes of size 10 such that every point is in either 0 or 5 blocks from a given block class, and every block contains either 0 or 5 points from a given point class. This design yields a Bush‐type Hadamard matrix of order 100 that leads to two new infinite classes of symmetric designs with parameters and where m is an arbitrary positive integer. Similarly, a Bush‐type Hadamard matrix of order 36 is constructed and used for the construction of an infinite family of designs with parameters and a second infinite family of designs with parameters where m is any positive integer. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 72–78, 2001     

Ziziphus nummularia Attenuates the Malignant Phenotype of Human Pancreatic Cancer Cells: Role of ROS

Pancreatic cancer (PC) is the fourth leading cause of all cancer-related deaths. Despite major improvements in treating PC, low survival rate remains a major challenge, indicating the need for alternative approaches, including herbal medicine. Among medicinal plants is Ziziphus nummularia (family Rhamnaceae), which is a thorny shrub rich in bioactive molecules. Leaves of Ziziphus nummularia have been used to treat many pathological conditions, including cancer. However, their effects on human PC are still unknown. Here, we show that the treatment of human pancreatic ductal adenocarcinoma cells (Capan-2) with Ziziphus nummularia ethanolic extract (ZNE) (100–300 μg/mL) attenuated cell proliferation in a time- and concentration-dependent manner. Pretreatment with N-acetylcysteine, an ROS scavenger, attenuated the anti-proliferative effect of ZNE. In addition, ZNE significantly decreased the migratory and invasive capacity of Capan-2 with a concomitant downregulation of integrin α₂ and increased cell–cell aggregation. In addition, ZNE inhibited in ovo angiogenesis as well as reduced VEGF and nitric oxide levels. Furthermore, ZNE downregulated the ERK1/2 and NF-κB signaling pathways, which are known to drive tumorigenic and metastatic events. Taken together, our results suggest that ZNE can attenuate the malignant phenotype of Capan-2 by inhibiting hallmarks of PC. Our data also provide evidence for the potential anticancer effect of Ziziphus nummularia, which may represent a new resource of novel anticancer compounds, especially ones that can be utilized for the management of PC.     

On the Strong Convergence of Halpern Type Proximal Point Algorithm

The main result of this paper is to prove the strong convergence of the sequence generated by the proximal point algorithm of Halpern type to a zero of a maximal monotone operator under the suitable assumptions on the parameters and error. The results extend some of the previous results or give some different conditions for convergence of the sequence. It is also indicated that when the maximal monotone operator is the subdifferential of a convex, proper, and lower semicontinuous function, the results extend all previous results in the literature. We also prove the boundedness of the sequence generated by the algorithm with a weak coercivity condition defined in the paper and without any additional assumptions on the parameters.