Research problem

Introduction to Matrix Theory and Linear Algebra by Irving Reiner     

Research problem

This section appears from time to time. Contributions are invited, and should be submitted to Robert c.Thompson, Mathematics Department,University of California, Santa Barbara, CA 93106, USA.     

Research problem

This section appears in nearly every issue contributions are invited, and should be submitted to R.C. Thompson, Mathematics Department, University of California, Santa Barbara, CA 93106, U.S.A.     

Research problem

This section appears from time to time. Contributions are invited, and should be submitted to R C. Thompson, Mathematics Department. University of California, Santa Barbara, CA93106-3080, USA.     

Research problem

This section appears from time to time. Contributions are invited, and should be submitted to R C. Thompson, Mathematics Department. University of California, Santa Barbara, CA93106-3080, USA.     

Research problem the matrix numerical range

Every active mathematician has a storehouse of unresolved questions that he/she hopes someday to settle, but may never owing to changing interests, greener pastures elsewhere, or simply lack of a good idea. Since one mathematician's abandoned turf may be another's greener pasture, why not pose that unresolved question as a research problem? If it cannot be solved by anybody, the resulting publicity may confer luster on the proposer. and if it solved by somebody, the original proposer may be able to use the new ideas in further work. It's a winning stretegy to pose research problems, and a losing one not to since mathematics is a cooperative effort to reveal nature's truths     

Research problem: indefinite inner product normal matrices

Several open research problems are formulated concerning normal matrices with respect to indefinite inner products.     

Research problem: indefinite inner product normal matrices

Several open research problems are formulated concerning normal matrices with respect to indefinite inner products.     

Research problem: The completion number of a graph

Motivated by the remarkable connection between graph theory and matrix analysis, we associate to each graph a so-called completion number that might encode some aspects of this interplay. We show that this number is not trivial, and we ask for a graph-theoretic characterization of those graphs with a given completion number.     

Research on the vehicle routing problem with interval demands

In this paper, a vehicle routing problem with interval demands is investigated based on the motivation of dispatching vehicles to deliver perishable products in practice. A nonlinear interval-based programming method is used to build a model for the vehicle routing problem with interval demands, which assumes that demands of customers are uncertain but fall in given intervals and actual demand of a customer becomes known only when the vehicle visited the customer. A vehicle-coordinated strategy was designed to solve the service failure problem. A hybrid algorithm based on the artificial immune system is also proposed to solve the model for vehicle routing problem with interval demands. The validity of methods and sensitivity analysis are illustrated by conducting some numerical examples. We find that the tolerant possibility degree of interval number has significant impacts on the distances. The planned distance strictly increased, while the additional distance strictly decreased and the total distance after coordinated transport has a U-typed relationship with the tolerant possibility degree of interval number.