Positive definite and Gram tensor complementarity problems

Given a continuous function Open image in new window and Open image in new window , the non-linear complementarity problem \(\text{ NCP }(g,q)\) is to find a vector Open image in new window such that

$$\begin{aligned} x \ge 0,~~y:=g(x) +q\ge 0~~\text{ and }~~x^Ty=0. \end{aligned}$$

We say that g has the Globally Uniquely Solvable (\(\text{ GUS }\))-property if \(\text{ NCP }(g,q)\) has a unique solution for all Open image in new window and C-property if \(\mathrm{NCP}(g,q)\) has a convex solution set for all Open image in new window . In this paper, we find a class of non-linear functions that have the \(\text{ GUS }\)-property and C-property. These functions are constructed by some special tensors which are positive semidefinite. We call these tensors as Gram tensors.

     

Antibody drug conjugates: Development,characterization, and regulatory considerations

Previously, cancer chemotherapy was often accompanied by severe side effects. Antibody drug conjugates (ADCs) were introduced to address this treatment complication. ADCs are a potent category of bioconjugates and immunoconjugates designed as targeted therapy for the treatment of cancer. ADCs are complex molecules composed of an antibody linked via linker chemistry to a cytotoxic payload or drug. Therefore, biologic properties of the cell‐surface target antigen are important in designing an effective ADC as an anticancer agent. ADCs have the ability to discriminate between the healthy and diseased tissue, so that healthy cells are less effected and get maximum therapeutic benefit. This review describes the development, characterization, and regulatory consideration of ADCs, and it summarizes the approved products in the market and in clinical trials.     

Vacancy ordered phases in Al-Cu-Ni as quasiperiodic superlattice approximants

Vacancy ordered phases in the Al-Cu-Ni system have an arrangement of vacant and filled sites in the truncated Fibonacci sequence along the [111] direction. The length scales involved are commensurate and in the limit a quasiperiodic superlattice is obtained. The implication of having commensurate length scales and quasiperiodicity in conjunction is studied using the concept of average lattices and projection formalism.     

Tensor Complementarity Problems with Finite Solution Sets

Journal of Optimization Theory and Applications - In this paper, we first extend the concept of non-degenerate matrices to tensors and we then study the finiteness properties of the solution set of...