Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

Transformation Semigroup of Alternating Nonnegative Integers

Set of integers, Zn is split into even-odd parts. The even part is arranged in ways, while the odd part fixes one point at a time to compliment the even part thereby forming the semigroup, AZn. Thus, -spaces are filled choosing maximum of two even points at a time. Green’s relations have formed important structures that enhance the algebraic study of transformation semigroups. The semigroup of Alternating Nonnegative Integers for n-even (AZn-even) is shown to have only two D-classes, and there are -classes for n≥4. The cardinality of L-classes is constant. Certain cardinalities and some other properties were derived. The coefficients of the zigzag triples obtained are 1, and . The second and third coefficients can be obtained by zigzag addition.

Advancement of human leukocyte antigen-partially matched related hematopoietic stem cell transplantation

Allogeneic hematopoietic stem cell transplantation(HSCT)is one of the most effective options for hematological malignancies,and human leukocyte antigen-partially matched related donors(PMRDs)are a valuable option for HSCT.Several protocols(with or without ex vivo T-cell depletion(TCD))have been established worldwide.TCD including CD34+positive selection and CD3/CD19 depletion has successfully overcome the human leukocyte antigen disparity.However,TCD is associated with prolonged immune deficiencies,increased risks of infectious complications,and high transplantation-related mortality.PMRD HSCT without ex vivo TCD is well developed,and numerous patients have benefitted from it.Here,we review the literature on PMRD HSCT.

Priority Setting in Health Care with Disease and Treatment Risks

This paper deals with the issue of priority setting in health care under uncertainties about the severity of the illness and the effectiveness of medical treatment. We examine the effect of a disease uncertainty(a treatment uncertainty) on the allocation of health care resources in the presence of a treatment risk(a disease risk) and identify preference conditions under which the social planner allocates more resources to higher risk population. We allow for the simultaneous presence of two risks and investigate the joint effect of two-source uncertainties on health care allocation when the two risks are either small or positively quadrant dependent. The effect of inequality aversion on health care allocation is also analyzed by introducing an equity weighting function. Our work extends the previous model of health care priority to two-risk framework and provides new insights into the problem of health care decision making under uncertainty.