Two-stage submodular maximization problem beyond nonnegative and monotone

We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.

Research on Design Optimization of Prefabricated Residential Houses Based on BIM Technology

Traditional and conventional methods of architectural and engineering design used for building informational modeling have a number of designs and updating and visualization issues which need to be addressed. In order to improve the design effect of prefabricated residential houses, this study proposes a design optimization method for prefabricated residential houses based on building information modeling (BIM) technology. BIM combines organized, multidisciplinary data to produce a digital representation of an asset across its development, starting from planning and design to building and operations. This study first analyzes the advantages of BIM technology and its applications in architectural design. It is further focused on the design of prefabricated houses, which are based on the optimization theory, modular function, modular design, and modular replacement. These are combined with the monomer architectural form, which is used in prefabricated houses design optimization of the assembly process. Furthermore, the article also focuses on the application of BIM technology in the design optimization of prefabricated residential houses, including the choice of implementation mode, accumulation of experience through the pilot, and the construction of an effective guarantee mechanism.

Convergence Results for Total Asymptotically Nonexpansive Monotone Mappings in Modular Function Spaces

In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space.

Increasing The Capacity of Headstega Based on Bitwise Operation

Headstega (Head steganography) is a noiseless steganography that used email headers as a cover for concealing messages. However, it has less embedding capacity and it raises suspicion. For overcoming the problem, bitwise operation is proposed. In the proposed method, the message was embedded into the cover by converting the message and the cover into binary representation based on a mapping table that was already known by the sender and the receiver. Furthermore, XOR bitwise operations were applied to the secret message and cover bits based on random numbers that were generated using a modular function. Moreover, the result was converted into characters that represent the secret message bits. After embedding the message into the cover, an email alias was generated to camouflage the secret message characters. Finally, the sender sends the embedded cover and the email alias to the recipient. Using the proposed method, the embedding capacity is 89% larger than using the original Headstega. For reducing the adversary’s suspicion, the existing email address was used instead of creating a new email address.

$rho$-Attractive Elements in Modular Function Spaces

In this paper, we introduce the notion of ρ-attractive elements in modular function spaces. A new class of mappings called ρ-k-nonspreading mappings is also introduced. Making a good use of the two notions, we first prove existence results and then some approximation results in the setup of modular function spaces. An example is presented to support the results proved herein.

VARIOUS EVALUATION IN PHYSICS AND MATHEMATICS FACULTIES OF GENERAL EDUCATIONAL SCIENCES

The article analyzes the integration of physics and mathematics in general secondary schools. KEY WORDS: continuity, optimized curriculum, quadratic equation, coordinate line, thermometer, surface, pressure, volume, density, parabola, exponential function, logarithmic function, modular function.

A Study of a Nonlinear Ordinary Differential Equation in Modular Function Spaces Endowed with a Graph

In this paper, we prove by means of a fixed-point theorem an existence result of the Cauchy problem associated to an ordinary differential equation in modular function spaces endowed with a reflexive convex digraph.

Multistep-type construction of fixed point for multivalued ρ-quasi-contractive-like maps in modular function spaces

PurposeIn this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that PρT, an associate multivalued map, is a ρ-contractive-like mapping.Design/methodology/approachThe concepts of relative ρ-stability and weak ρ-stability are introduced, and conditions in which these multistep iterations are relatively ρ-stable, weakly ρ-stable and ρ-stable are established for the newly introduced strong ρ-quasi-contractive-like class of maps.FindingsNoor type, Ishikawa type and Mann type iterative sequences are deduced as corollaries in this study.Originality/valueThe results obtained in this work are complementary to those proved in normed and metric spaces in the literature.