Rational differential operators and their kernels

A linear differential/integral operator is associated to a rational matrix in a natural way, and the behavior is defined to be the kernel of this operator. Conditions under which two rational matrices have the same behavior are derived.     

How to define the dual of a higher-dimensional linear system

The classical duality of linear systems is generalized to higher dimensions. Consequently, a new insight is given to the concepts of controllability and observability, and autonomy.     

Linear dynamical systems of higher genus

A class of linear systems which after ordinary linear systems are in a certain sense the simplest ones, is associated with every algebraic function field. From the standpoint developed in this paper ordinary linear systems are associated with the rational function field.     

First order representations of Fliess models

Fuhrmann’s state-space construction (in its generalized form) is used to obtain a general theory of first order representations of Fliess models defined over an arbitrary noetherian commutative ring. The case of arbitrary linear delay differential equations is involved.     

On some entire modular forms of weights 5 and 6 for the congruence group Г(in0)(4N)

Two entire modular forms of weight 5 and two of weight 6 for the congruence subgroup Γ₀ (4N)are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 10 and 12 variables.     

Sensitivity increase in molecular recognition by decrease of the sensing particle size and by increase of the receptor binding site--a case with chemomechanical polymers

For the first time it is shown that diminishing the particle size of a chemomechanical polymer leads to a dramatic sensitivity increase, with a large response triggered e.g. by action of external AMP; as illustrated with carbohydrate model complexes in solution, the necessary high binding affinity can be achieved by providing an excess of recognition units in one of the partners.     

On the Number of Representations of Positive Integers by a Direct Sum of Binary Quadratic Forms with Discriminant −23

Explicit exact formulas are obtained for the number of representations of positive integers by some direct sums of quadratic forms and      

On some entire modular forms of weights\tfrac{7}{2} and\tfrac{9}{2} for the congruence group Γ0(4N)for the congruence group Γ0(4N)

Entire modular forms of weights $\tfrac{7}{2}$ and $\tfrac{9}{2}$ for the congruence group Γ₀(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.