Increment of the objective function and optimality criterion for one non-homogeneous network flow programming problem

For an linear non-homogeneous flow programming problem with additional constraints of general kind are obtained the increment of the objective function using properties of the problem and principles of decomposition of a support. Optimality conditions are received

Algorithms for construction of optimal and suboptimal solutions in network optimization problems

For a distributive flow programming optimization problem of a special structure direct and dual algorithms are constructed. These algorithms are based on a research of the theoretical and graph properties of the solution space bases. Optimality conditions are received, that allow to calculate a part of the components of the Lagrange vector. Algorithms that decompose calculation systems for pseudo-plans of the problem are presented. Suitable directions for change of the dual criterion function are constructed

Decomposition of the network support for one non-homogeneous network flow programming problem

We consider one extremal linear non-homogeneous problem of flow programming with additional constraints of general kind. We use the network properties of the non-homogeneous problem for the decomposition of a network support into trees and cyclic parts

Underdetermined linear systems in the sensor location problem

We consider underdetermined linear systems and characteristics of optimal solutions in the sensor location problem

Sensor Location Problem for a Multigraph

MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow volume and variable intensities of nodes for the whole multigraph. Research of the rank of the sparse matrix is based on the constructive theory of decomposition of sparse linear systems

Solution of large linear systems with embedded network structure for a non-homogeneous network flow programming problem

In the paper we consider the linear underdetermined system of a special type is considered. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a large sparse submatrix representing the embedded network structure. A direct method for finding solutions of the system is developed. The algorithm is based on the theoretic-graph specificities for the structure of the support and properties of the basis of a solution space of a homogeneous system. One of the key steps is decomposition of the system. A simple example is regarded at the end of the paper

A General Framework of Bound States in the Continuum in an Open Acoustic Resonator

Bound states in the continuum (BICs) provide a viable way of achieving high-Q resonances in both photonics and acoustics. In this work, we proposed a general method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a coupled acoustic waveguide-resonator system. We demonstrated that FW BICs can be achieved with arbitrary two degenerate resonances in a closed resonator regardless of whether they have the same or opposite parity. Moreover, their eigenmode profiles can be arbitrarily engineered by adjusting the position of attached waveguide. That suggests an effective way of continuous switching the nature of BIC from FW BIC to symmetry-protected BIC or accidental BICs. Also, such BICs are sustained in the coupled waveguide-resonator system with shapes such as rectangle, ellipse, and rhomboid. These interesting phenomena are well explained by the two-level effective non Hermitian Hamiltonian, where two strongly coupled degenerate modes play a major role in forming such FW BICs. Besides, we found that such an open system also supports accidental BICs in geometry space instead of momentum space via tuning the position of attached waveguide, which are attributed to the quenched coupling between the waveguide and eigenmodes of the closed cavity. Finally, we fabricated a series of 3D coupled-resonator-waveguide and experimentally verified the existence of FW BICs and accidental BICs by measuring the transmission spectra. Our results complement the current BIC library in acoustics and provide new routes for designing novel acoustic devices, such as in acoustic absorbers, filters and sensors.Comment: 20 pages, 6 figure