East West Math

SEVERAL ITERATIVE SCHEMES FOR THE SPLIT FEASIBILITY WITH MULTIPLE OUTPUT SETS AND APPLICATIONS

Nguyen Thi Quynh Anh — Mon, 22 Jun 2026 14:29:13 +0800

In this paper, for solving the split feasibility problem with multiple

output sets, defined by demiclosed strongly quasi-nonexpansive opera-

tors on Hilbert spaces, we propose some block-iterative schemes, using

the extrapolated Landweber-type operators. The strong convergence is

proved without the boundedly regular condition as well as the closedness

property of the range of the transformation operators, assumed recently

in the literature for the similar problems. We give a necessary and suf-

ficient condition which ensures that a kth iterate is a solution. We also

give an application of our results to solve the multiple-sets split feasibil-

ity problem (MSSFP) with multiple output level sets with computational

experiments for illustration.

AN OPERATOR APPROACH TO THREE q-HERMITE POLYNOMIALS IN THE SPIRIT OF CIGLER

Thomas Ernst — Mon, 22 Jun 2026 14:33:11 +0800

The purpose of this article is to define and then prove generating func-

tions, operational formulas, power series representations, recurrences, ta-

bles, vector forms, determinant expressions, alternative operator formu-

las, q-Nielsen and Rodriguez formulas for three q-Hermite polynomials.

Some of these polynomials have previously been investigated by Cigler,

Kirschenhofer and D´esarm´enien. Then we prove new q-orthogonality

relations by q-integrals with finite integral limits for one of these poly-

nomials. It turns out that a prerequisite, which is not suﬃcient, for this

is that the polynomial is of q-Appell form. Therefore, we briefly outline

q-Appell, and pseudo-q-Appell polynomials. We also investigate some

pseudo-q-Hermite polynomials, q-analogues of xν , whose orthogonality

with q-integration limits ±1 is equivalent to our q-orthogonality by a

simple change of variables in the q-integral.

LIE OPERATORS FOR TRUST DYNAMICS ON THE UNIT SPHERE IN COMPLEX NETWORKS

Dinh Que Tran — Mon, 22 Jun 2026 14:41:16 +0800

This paper is to introduce a geometric framework for trust modeling

in complex networks in which trust states are embedded as unit vectors in

a Hilbert space. Trust evolution is formulated as a continuous dynamical

system generated by Lie operators acting on the unit sphere, ensuring

norm preservation and stability of the representation. We show that

network interactions naturally induce skew-adjoint operators, leading to

flows that correspond to rotations on the trust sphere. This geometric

structure guarantees that trust propagation follows geodesic trajecto-

ries, providing both mathematical consistency and interpretability. The

proposed framework establishes a connection between graph-based inter-

actions, Lie algebraic dynamics, and geometric deep learning. It oﬀers a

principled foundation for modeling trust propagation with stability, in-

variance, and continuous-time dynamics in complex networked systems.

HILBERT OPERATOR–BASED TRUST COMPUTATION IN COMPLEX NETWORKS VIA TENSOR STATE REPRESENTATION

Dinh Que Tran — Mon, 22 Jun 2026 14:44:14 +0800

Trust evaluation plays a central role in complex networks or network-

drived systems such as social networks, collaborative systems, and online

communities. Traditional trust models rely on heuristic propagation rules

that do not fully exploit netwrok heterogeneous data. This paper pro-

poses a mathematical framework for trust computation based on Hilbert

space operators. The framework transforms user features of networks into

tensor representations, constructs trust states from these tensors, and

models trust propagation through bounded operators in Hilbert spaces.

A numerical example illustrates the complete pipeline from features to

trust scores.