The problem of finding a rank-one solution to a system of linear matrix equations arises from many practical applications. Given a system of linear matrix equations, however, such a low-rank solution does not always exist. In this paper, we aim at developing some sufficient conditions for the existence of a rank-one solution to the system of homogeneous linear matrix equations (HLME) over the p...

We study several properties of a homotopy solution path associated with continuous nonlinear quasi-monotone complementarity problems. We use Poincare-Bohn’s homotopy invariance theorem of degree to derive an alternative theorem. Based on this result, a sufficient condition is established to assure the existence and boundedness of this homotopy solution path. Our results provide a theoretical ba...

We present the dual to Birkhoff’s variety theorem in terms of predicates over the carrier of a cofree coalgebra (i.e., in terms of “coequations”). We then discuss the dual to Birkhoff’s completeness theorem, showing how closure under deductive rules dualizes to yield two modal operators acting on coequations. We discuss the properties of these operators and show, given a familiar condition on t...

While it is clear that parenting behaviors impact adolescent adjustment in a number of ways (Steinberg, 2001), less is known about how parenting changes over time as children develop across adolescence. The current study has two goals: first, to examine longitudinal measurement invariance of a parenting behavior measure assessing acceptance, rejection, and consistent discipline by mother and fa...

The Children’s Depression Inventory is a self-report scale for screening depressive disorders in children and adolescents. The original model proposed by Kovacs has a hierarchical factor structure: Five first-order and a single second-order factors. This study used confirmatory factor analysis (CFA) to examine support for this model. It also examined measurement invariance of this model across ...

The test of relational reasoning (TORR) is designed to assess the ability to identify complex patterns within visuospatial stimuli. The TORR is designed for use in school and university settings, and therefore, its measurement invariance across diverse groups is critical. In this investigation, a large sample, representative of a major university on key demographic variables, was collected, and...

The purpose of this paper is to establish discrete versions of the well-known Lyapunov’s stability theorem and LaSalle’s invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and cont...

In many network applications and services, agents that share no secure channel in advance may still wish to communicate securely with each other. In such settings, one often settles for achieving security goals weaker than authentication, such as sender invariance. Informally, sender invariance means that all messages that seem to come from the same source actually do, where the source can perh...

A frequent motivation for the use of Scale Invariance in the bankruptcy literature is that it imposes that the outcome of a bankruptcy problem does not depend on the units of measurement. We show that this interpretation is not correct. Scale Invariance is an invariance condition that applies when all amounts are multiplied by a constant (without change of units). With this interpretation in mi...