scholarly journals Weak Essential Fuzzy Submodules Of Fuzzy Modules

2020 ◽  
Vol 33 (4) ◽  
pp. 65
Author(s):  
Hassan K. Marhon ◽  
Hatam Y. Khalaf
Keyword(s):  
Homomorphic Image ◽  
Inverse Image

        Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

scholarly journals A homomorphism theorem for projective planes

1971 ◽  
Vol 4 (2) ◽  
pp. 155-158 ◽  
Author(s):  
Don Row
Keyword(s):  
Projective Plane ◽  
Homomorphic Image ◽  
Inverse Image ◽  
Projective Planes ◽  
Homomorphism Theorem ◽  
Central Collineations

We prove that a non-degenerate homomorphic image of a projective plane is determined to within isomorphism by the inverse image of any one point. An application gives conditions for the preservation of central collineations by a homomorphism.

scholarly journals Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 567 ◽  
Author(s):  
Hashem Bordbar ◽  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Homomorphic Image ◽  
Inverse Image ◽  
Closure Operation ◽  
Weak Closure ◽  
Closure Operations ◽  
Epimorphic Image

We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras φ : X → Y , we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping c l Y : I ( Y ) → I ( Y ) , we define a map c l Y ← on I ( X ) by A ↦ φ − 1 ( φ ( A ) c l Y ) . We prove that, if “ c l Y ” is a weak closure operation (respectively, semi-prime and meet) on I ( Y ) , then so is “ c l Y ← ” on I ( X ) . In addition, for mapping c l X : I ( X ) → I ( X ) , we define a map c l X → on I ( Y ) as follows: B ↦ φ ( φ − 1 ( B ) c l X ) . We show that, if “ c l X ” is a weak closure operation (respectively, semi-prime and meet) on I ( X ) , then so is “ c l X → ” on I ( Y ) .

scholarly journals A note on complex fuzzy subfield

2021 ◽  
Vol 21 (2) ◽  
pp. 1048
Author(s):  
Muhammad Gulzar ◽  
Fareeha Dilawar ◽  
Dilshad Alghazzawi ◽  
M. Haris Mateen
Keyword(s):  
Direct Product ◽  
Homomorphic Image ◽  
Inverse Image

In this paper, we introduce idea of complex fuzzy subfield and discuss its various algebraic aspects. We prove that every complex fuzzy subfield generate two fuzzy fields and shows that intersection of two complex fuzzy subfields is also complex fuzzy subfields. We also present the concept of level subsets of complex fuzzy subfield and shows that level subset of complex fuzzy subfield form subfield.  Furthermore, we extend this idea to define the notion of the direct product of two complex fuzzy subfields and also investigate the homomorphic image and inverse image of complex fuzzy subfield.

scholarly journals CUBIC Z-SUBALGEBRAS IN Z-ALGEBRAS

2021 ◽  
Vol 2070 (1) ◽  
pp. 012085
Author(s):  
S. Sowmiya ◽  
P. Jeyalakshmi
Keyword(s):  
Homomorphic Image ◽  
Cartesian Product ◽  
Inverse Image

Abstract In this article, the notions of Cubic Z-Subalgebras in Z-algebras is introduced and some of their properties are investigated. The Z-homomorphic image and inverse image of cubic Z-Subalgebras in Z-algebras is investigated. Also, the cartesian product of cubic Z-Subalgebras in Z-algebras is also discussed.

Dosimetry and optimization in digital radiography based on the contrast-detail resolution

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Wilson Otto Gomes Batista ◽  
Alexandre Gomes De Carvalho
Keyword(s):  
Image Quality ◽  
Inverse Image ◽  
Point Of View ◽  
Complete Analysis ◽  
Portable Devices ◽  
Evaluation Tool ◽  
Air Kerma ◽  
Direct Radiography ◽  
Definition Of ◽  
Entrance Surface Air Kerma

Contrast-detail (C-D) curves are useful in evaluating the radiographic image quality in a global way. The objective of the present study was to obtain the C-D curves and the inverse image quality figure. Both of these parameters were used as an evaluation tool for abdominal and chest imaging protocols. The C-D curves were obtained with the phantom CDRAD 2.0 in computerized radiography and the direct radiography systems (including portable devices). The protocols were 90 and 102 kV in the range of 2 to 20 mAs for the chest and 80 kV in the range of 10 to 80 mAs for the abdomen. The incident air kerma values were evaluated with a solid state sensor. The analysis of these C-D curves help to identify which technique would allow a lower value of the entrance surface air kerma, Ke, while maintaining the image quality from the point of view of C-D detectability. The results showed that the inverse image quality figure, IQFinv, varied little throughout the range of mAs, while the value of Ke varied linearly directly with the mAs values. Also, the complete analysis of the curves indicated that there was an increase in the definition of the details with increasing mAs. It can be concluded that, in the transition phase for the use of the new receptors, it is necessary to evaluate and adjust the practised protocols to ensure, at a minimum, the same levels of the image quality, taking into account the aspects of the radiation protection of the patient.

scholarly journals L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

Impact on dose and image quality of a software-based scatter correction in mammography

2017 ◽  
Vol 59 (6) ◽  
pp. 649-656 ◽  
Author(s):  
Teresa Monserrat ◽  
Elena Prieto ◽  
Benigno Barbés ◽  
Luis Pina ◽  
Arlette Elizalde ◽  
...  
Keyword(s):  
Image Quality ◽  
Scatter Correction ◽  
Inverse Image ◽  
Clinical Image ◽  
Air Kerma ◽  
Average Glandular Dose ◽  
Standard Mode ◽  
Entrance Surface Air Kerma ◽  
Clinical Cases

Background In 2014, Siemens developed a new software-based scatter correction (Progressive Reconstruction Intelligently Minimizing Exposure [PRIME]), enabling grid-less digital mammography. Purpose To compare doses and image quality between PRIME (grid-less) and standard (with anti-scatter grid) modes. Material and Methods Contrast-to-noise ratio (CNR) was measured for various polymethylmethacrylate (PMMA) thicknesses and dose values provided by the mammograph were recorded. CDMAM phantom images were acquired for various PMMA thicknesses and inverse Image Quality Figure (IQFinv) was calculated. Values of incident entrance surface air kerma (ESAK) and average glandular dose (AGD) were obtained from the DICOM header for a total of 1088 pairs of clinical cases. Two experienced radiologists compared subjectively the image quality of a total of 149 pairs of clinical cases. Results CNR values were higher and doses were lower in PRIME mode for all thicknesses. IQFinv values in PRIME mode were lower for all thicknesses except for 40 mm of PMMA equivalent, in which IQFinv was slightly greater in PRIME mode. A mean reduction of 10% in ESAK and 12% in AGD in PRIME mode with respect to standard mode was obtained. The clinical image quality in PRIME and standard acquisitions resulted to be similar in most of the cases (84% for the first radiologist and 67% for the second one). Conclusion The use of PRIME software reduces, in average, the dose of radiation to the breast without affecting image quality. This reduction is greater for thinner and denser breasts.

scholarly journals A note on central group extensions

1973 ◽  
Vol 15 (4) ◽  
pp. 428-429 ◽  
Author(s):  
G. J. Hauptfleisch
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Free Group ◽  
Central Extension ◽  
Dihedral Group ◽  
Group Extension ◽  
Central Group ◽  
Group Extensions

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.

Revealing the nanodomain structure of silicon oxycarbide via preferential etching and pore analysis

2016 ◽  
Vol 09 (03) ◽  
pp. 1650043 ◽  
Author(s):  
Haolin Wu ◽  
Jie Yang ◽  
Haibiao Chen ◽  
Feng Pan
Keyword(s):  
Porous Structure ◽  
Gas Adsorption ◽  
Inverse Image ◽  
Silicon Oxycarbide ◽  
Experimental Results ◽  
Porous Network ◽  
Pore Analysis ◽  
Novel Approach ◽  
Nanodomain Structure ◽  
Nanocomposite Structures

Preferentially etching either carbon or silica from silicon oxycarbide (SiOC) created a porous network as an inverse image of the removed phase. The porous structure was analyzed by gas adsorption, and the experimental results verified the nanodomain structure of SiOC. This work demonstrated a novel approach for analyzing materials containing nanocomposite structures.

Image development in the framework of ξ –complex fuzzy morphisms

2021 ◽  
pp. 1-13
Author(s):  
Aneeza Imtiaz ◽  
Umer Shuaib ◽  
Abdul Razaq ◽  
Muhammad Gulistan
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Unit Disk ◽  
Homomorphic Image ◽  
Significant Role ◽  
Original Form ◽  
Mathematical Tool ◽  
Fuzzy Subgroups ◽  
Fundamental Theorems

The study of complex fuzzy sets defined over the meet operator (ξ –CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ –CFS and propose the notion of complex fuzzy subgroups defined over ξ –CFS (ξ –CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concepts of ξ –complex fuzzy homomorphism and ξ –complex fuzzy isomorphism between any two ξ –complex fuzzy subgroups and establish fundamental theorems of ξ –complex fuzzy morphisms. In addition, we effectively apply the idea of ξ –complex fuzzy homomorphism to refine the corrupted homomorphic image by eliminating its distortions in order to obtain its original form. Moreover, to view the true advantage of ξ –complex fuzzy homomorphism, we present a comparative analysis with the existing knowledge of complex fuzzy homomorphism which enables us to choose this particular approach to solve many decision-making problems.

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