R. Prasad, C. Jijina, A. Akhila, T. Johnson, S. Ajayan
Due to a surge in demand and cost, there is a requirement for alternative energy sources by devising strategies for the efficient production of biofuels. Immobilized microbial systems for the conversion of biomass to fuels have become progressively important. Cassava (Manihot esculentum) processing waste, a massive byproduct of starch processing is utilized in this work for bioethanol production. This study was an attempt to design and develop an experimental lab-scale Vertical Mass-Flow type Bioreactor (VMFB) demarcated into aerobic and anaerobic zones to produce bioethanol. The upper aerobic zone was meant for saccharification and the lower anaerobic zone for fermentation, the technique is called Simultaneous Saccharification and Fermentation (SSF). The feasibility of co-immobilizing saccharification strains (A. awamori and D. bruxellensis) and fermentation strains (Z. mobilis) for bioethanol production through SSF from cassava agro-waste were tested. Polyurethane foam was used in the aerobic reaction zone and calcium-alginate beads immobilized microorganisms in the anaerobic reaction zone were employed as carriers for the immobilization. The main objective of this study was to understand the usability of agricultural waste, especially cassava processing waste as raw material for bioethanol production, using SSF technology a concentration of 8 % w/w ethanol was obtained.
{"title":"Design of Experimental Lab Scale Vertical Mass Flow Type Bioreactor for Bioethanol Production by Co-Culture Strategy from Cassava Waste","authors":"R. Prasad, C. Jijina, A. Akhila, T. Johnson, S. Ajayan","doi":"10.3329/jsr.v15i1.59095","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.59095","url":null,"abstract":"Due to a surge in demand and cost, there is a requirement for alternative energy sources by devising strategies for the efficient production of biofuels. Immobilized microbial systems for the conversion of biomass to fuels have become progressively important. Cassava (Manihot esculentum) processing waste, a massive byproduct of starch processing is utilized in this work for bioethanol production. This study was an attempt to design and develop an experimental lab-scale Vertical Mass-Flow type Bioreactor (VMFB) demarcated into aerobic and anaerobic zones to produce bioethanol. The upper aerobic zone was meant for saccharification and the lower anaerobic zone for fermentation, the technique is called Simultaneous Saccharification and Fermentation (SSF). The feasibility of co-immobilizing saccharification strains (A. awamori and D. bruxellensis) and fermentation strains (Z. mobilis) for bioethanol production through SSF from cassava agro-waste were tested. Polyurethane foam was used in the aerobic reaction zone and calcium-alginate beads immobilized microorganisms in the anaerobic reaction zone were employed as carriers for the immobilization. The main objective of this study was to understand the usability of agricultural waste, especially cassava processing waste as raw material for bioethanol production, using SSF technology a concentration of 8 % w/w ethanol was obtained.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88731673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we considered Bianchi type-II space-time in the presence of a macroscopic body in the self-creation theory formulated by Barber. The relation between metric coefficient and state equation has helped present the exact cosmological model in theory. The features, stability, and some physical & kinematical properties of the obtained model are also discussed.
{"title":"Stability of Cosmological Model in Self-Creation Theory of Gravitation","authors":"A. S. Nimkar, S. Hadole","doi":"10.3329/jsr.v15i1.59676","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.59676","url":null,"abstract":"In the present paper, we considered Bianchi type-II space-time in the presence of a macroscopic body in the self-creation theory formulated by Barber. The relation between metric coefficient and state equation has helped present the exact cosmological model in theory. The features, stability, and some physical & kinematical properties of the obtained model are also discussed.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91328439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Since the innovative work of Terada and Akiyama, asymmetric reaction using chiral Brønsted acid has attracted great attention. Asymmetric aldol reactions are extensively studied in different organocatalysis. Brønsted acid-catalyzed aldol reaction may be carried out directly without modification of the substrates or Mukaiyama type aldol reaction using silyl enol ether as nucleophiles. The reaction may proceed through the formation of enol intermediate followed by the attack to the electrophile while Mukaiyama type aldol reactions may follow two mechanistic pathways- Brønsted acidic pathways where Brønsted acid directly activates the substrate or Lewis acid pathways where Brønsted acid acts as pre-catalyst. Here, the recent advancement of asymmetric aldol reactions using chiral Brønsted acid as a catalyst and the fate of the catalysts in the reaction has been discussed in this review. It is observed that some kinds of aldol reactions have rarely been studied and need more attention.
{"title":"Recent Developments on Brønsted Acid Catalyzed Asymmetric Aldol Reactions and the Fate of the Catalysts","authors":"J. Das","doi":"10.3329/jsr.v15i1.59614","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.59614","url":null,"abstract":"Since the innovative work of Terada and Akiyama, asymmetric reaction using chiral Brønsted acid has attracted great attention. Asymmetric aldol reactions are extensively studied in different organocatalysis. Brønsted acid-catalyzed aldol reaction may be carried out directly without modification of the substrates or Mukaiyama type aldol reaction using silyl enol ether as nucleophiles. The reaction may proceed through the formation of enol intermediate followed by the attack to the electrophile while Mukaiyama type aldol reactions may follow two mechanistic pathways- Brønsted acidic pathways where Brønsted acid directly activates the substrate or Lewis acid pathways where Brønsted acid acts as pre-catalyst. Here, the recent advancement of asymmetric aldol reactions using chiral Brønsted acid as a catalyst and the fate of the catalysts in the reaction has been discussed in this review. It is observed that some kinds of aldol reactions have rarely been studied and need more attention.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87162866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Padma Rani, R. Puri, A. Qasim, P. Boora, D. Angmo
Berginia ligulata is medicinally significant and endangered plant of the western Himalayan Region. This plant is used to treat many diseases such as urinary problems and heart problems. By using leaf explant, an efficient and rapid micropropagation protocol was developed. In in-vitro propagation, MS medium was supplemented with benzyl amino purine (BAP), 1-naphthalene acetic acid (NAA) and indol-3-acetic acid (IAA) to induce multiple shoots from leaf explants. The most positive response for the formation of calluses was observed on MS media supplemented with MS medium + BAP(1 mg/L) + NAA(1 mg/L) followed by MS medium + BAP (0.5 mg/L) + NAA (1 mg/L) after 3 weeks. Maximum number of shoots were obtained on MS medium + BAP (2 mg/L) +IAA (2 mg/L). Maximum % shoot response was obtained on MS medium + Kn (2.5 mg/L) concentration. The maximum number of roots was observed on MS medium without growth regulators. These well-rooted plants were established in pots and acclimatized in the lab and transferred to field conditions. This process is useful to produce endangered plants on large scale.
{"title":"In vitro Micropropagation of Bergenia ligulata (Hook. f. & Thomson) Engl. through Leaf Explant","authors":"S. Padma Rani, R. Puri, A. Qasim, P. Boora, D. Angmo","doi":"10.3329/jsr.v15i1.59313","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.59313","url":null,"abstract":"Berginia ligulata is medicinally significant and endangered plant of the western Himalayan Region. This plant is used to treat many diseases such as urinary problems and heart problems. By using leaf explant, an efficient and rapid micropropagation protocol was developed. In in-vitro propagation, MS medium was supplemented with benzyl amino purine (BAP), 1-naphthalene acetic acid (NAA) and indol-3-acetic acid (IAA) to induce multiple shoots from leaf explants. The most positive response for the formation of calluses was observed on MS media supplemented with MS medium + BAP(1 mg/L) + NAA(1 mg/L) followed by MS medium + BAP (0.5 mg/L) + NAA (1 mg/L) after 3 weeks. Maximum number of shoots were obtained on MS medium + BAP (2 mg/L) +IAA (2 mg/L). Maximum % shoot response was obtained on MS medium + Kn (2.5 mg/L) concentration. The maximum number of roots was observed on MS medium without growth regulators. These well-rooted plants were established in pots and acclimatized in the lab and transferred to field conditions. This process is useful to produce endangered plants on large scale.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89523173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The point spread function (PSF) produced by a coherent optical system under the influence of defocus, coma, and primary spherical aberration (PSA) is examined in this work. This paper deals with asymmetric apodization and pupil engineering to control monochromatic aberrations. To reduce the influence of monochromatic aberrations on the diffracted PSF, this approach uses amplitude and phase apodization. Analytical investigations on intensity PSF are carried out with varying amounts of aberrations and degrees of amplitude and phase apodization. Computed central peak intensity and full width at half maxima (FWHM) and analyzed. The resolution of a diffraction-limited optical imaging system is improved by using an asymmetric optical filter that minimizes the effect of defocus.
{"title":"Engineering of Aberrated PSF by Asymmetric Apodization with the Complex Shaded Aperture","authors":"M. Venkanna, N. Sabitha, D. K. Sagar","doi":"10.3329/jsr.v15i1.60366","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.60366","url":null,"abstract":"The point spread function (PSF) produced by a coherent optical system under the influence of defocus, coma, and primary spherical aberration (PSA) is examined in this work. This paper deals with asymmetric apodization and pupil engineering to control monochromatic aberrations. To reduce the influence of monochromatic aberrations on the diffracted PSF, this approach uses amplitude and phase apodization. Analytical investigations on intensity PSF are carried out with varying amounts of aberrations and degrees of amplitude and phase apodization. Computed central peak intensity and full width at half maxima (FWHM) and analyzed. The resolution of a diffraction-limited optical imaging system is improved by using an asymmetric optical filter that minimizes the effect of defocus.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89070198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thiosemicarbazones are class of compounds which are obtained by the condensation of thiosemicarbazide with carbonyl compounds. The transition metal complexes of thiosemicarbazones are widely considered due to their broad spectrum of biological activities such as antibacterial, antitumor and antifungal activities. In present research work a series of four novel Cu(II) aryl thiosemicarbazones complexes having the general composition [Cu(L1)2Cl2], [Cu(L2)2Cl2], [Cu(L3)2Cl2] and [Cu(L4)2Cl2]{where L1= 4-nitroacetophenone thiosemicarbazones (4NAT), L2 = 3-nitrobenzaldehyde thiosemicarbazone (3NBT), L3 = 4-hydroxybenzaldehyde thiosemicarbazone (4HBT) and L4 = 4-aminoacetophenone thiosemicarbazone (4AAT)} have been synthesized by the reaction of thiosemicarbazide with substituted aromatic aldehydes and ketones by conventional heating as well as microwave irradiations method followed by complexation with Cu(II) metal. The synthesized compounds have been characterised by elemental analysis, melting point determination, FTIR, UV-visible spectral analysis. Thiosemicarbazone ligands behave as bidentate ligand and forms octahedral complexes with Cu(II). The synthesized ligands and their new metal complexes have been screened in vitro for antibacterial activity against Escherichia coli, Staphylococcus aureus and Bacillus subtilis bacteria. The result shows that all the Cu(II) complexes are potent antibacterial agents against these bacteria.
{"title":"Microwave Assisted Synthesis, Characterisation and Biological Activities of Cu(II) Complexes of Few Thiosemicarbazones Ligands","authors":"K. Verma, N. Nirwan, R. Singh, N. Bhojak","doi":"10.3329/jsr.v15i1.60772","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.60772","url":null,"abstract":"Thiosemicarbazones are class of compounds which are obtained by the condensation of thiosemicarbazide with carbonyl compounds. The transition metal complexes of thiosemicarbazones are widely considered due to their broad spectrum of biological activities such as antibacterial, antitumor and antifungal activities. In present research work a series of four novel Cu(II) aryl thiosemicarbazones complexes having the general composition [Cu(L1)2Cl2], [Cu(L2)2Cl2], [Cu(L3)2Cl2] and [Cu(L4)2Cl2]{where L1= 4-nitroacetophenone thiosemicarbazones (4NAT), L2 = 3-nitrobenzaldehyde thiosemicarbazone (3NBT), L3 = 4-hydroxybenzaldehyde thiosemicarbazone (4HBT) and L4 = 4-aminoacetophenone thiosemicarbazone (4AAT)} have been synthesized by the reaction of thiosemicarbazide with substituted aromatic aldehydes and ketones by conventional heating as well as microwave irradiations method followed by complexation with Cu(II) metal. The synthesized compounds have been characterised by elemental analysis, melting point determination, FTIR, UV-visible spectral analysis. Thiosemicarbazone ligands behave as bidentate ligand and forms octahedral complexes with Cu(II). The synthesized ligands and their new metal complexes have been screened in vitro for antibacterial activity against Escherichia coli, Staphylococcus aureus and Bacillus subtilis bacteria. The result shows that all the Cu(II) complexes are potent antibacterial agents against these bacteria.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"67 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72480379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Garuba, I. T. Olabanji, O. M. Awogboro, G. Olahan, S. Atunwa, O. A. Ahmed, A. Aremu, M. Bolaji, A. A. Adegboye, S. Sabiu
This study aimed at evaluating toxicological implications of aqueous P. ostreatus extract (POE) in male Wistar rats. POE was prepared in 1:10 (pulverized P. ostreatus : distilled water). In acute toxicity test, single oral dose of 2 mL/kg of POE was administered and observed for 28 days. The sub-chronic toxicity study was conducted by daily oral administration of graded doses (0.25, 0.50 and 0.75 mL/kg b.w) of the extract for 28 days. Clinical signs of toxicity, hematological, serum biochemical parameters and histopathological studies were subsequently evaluated. No treatment-related signs of toxicity or mortality in the animals were recorded in both toxicity tests. Rats administered with lowest dose of POE (25 mL/kg) had highest percentage weight gain. POE had no significant difference (P>0.05) on Red Blood Cell, White Blood Cell (WBC) and differential WBC, and serum biochemistry across all the treated groups when compared to the controls. The result of photomicrographs of stomach, spleen, heart, lung, kidney and liver showed a well outlined arrays of normal tissues in both acute and sub-chronic doses connoting that POE had no toxic effect on them. In view of these, POE may be concluded to be non-toxic within the tested doses and period of investigation.
{"title":"Haematological, Serum Biochemical and Histopathological Changes in Acute and Sub-Chronic Aqueous Extract of Oyster Mushroom in Male Wistar Rats","authors":"T. Garuba, I. T. Olabanji, O. M. Awogboro, G. Olahan, S. Atunwa, O. A. Ahmed, A. Aremu, M. Bolaji, A. A. Adegboye, S. Sabiu","doi":"10.3329/jsr.v15i1.59309","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.59309","url":null,"abstract":"This study aimed at evaluating toxicological implications of aqueous P. ostreatus extract (POE) in male Wistar rats. POE was prepared in 1:10 (pulverized P. ostreatus : distilled water). In acute toxicity test, single oral dose of 2 mL/kg of POE was administered and observed for 28 days. The sub-chronic toxicity study was conducted by daily oral administration of graded doses (0.25, 0.50 and 0.75 mL/kg b.w) of the extract for 28 days. Clinical signs of toxicity, hematological, serum biochemical parameters and histopathological studies were subsequently evaluated. No treatment-related signs of toxicity or mortality in the animals were recorded in both toxicity tests. Rats administered with lowest dose of POE (25 mL/kg) had highest percentage weight gain. POE had no significant difference (P>0.05) on Red Blood Cell, White Blood Cell (WBC) and differential WBC, and serum biochemistry across all the treated groups when compared to the controls. The result of photomicrographs of stomach, spleen, heart, lung, kidney and liver showed a well outlined arrays of normal tissues in both acute and sub-chronic doses connoting that POE had no toxic effect on them. In view of these, POE may be concluded to be non-toxic within the tested doses and period of investigation.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82342280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rewriting and executing codes violate the SOLID principle of object-oriented programming. Robotics being an emerging platform, it becomes hard to write the code from scratch. We focus on using what is already built in as a Robotics Component instead of writing something from scratch. The intention is to minimize development effort and produce the desired result on time without rewriting the software components. By allowing functionalities of different components to be brought into a single component, we are saving the time required for code conversion or replication of functionality written in one language to another. So an architecture with these properties seems ideal for integrating different components. Integration is one of the most fundamental problems in designing autonomous mobile robots, especially those interacting with people in real-life settings. This paper presents an approach to building complex systems from different robotics packages available as open source components (PLAYER, STAGE, GAZEBO, CARMEN). DBUS is a message-oriented protocol for communicating among processes running on the same desktop. SOA provides access to the services over the network and adds novelty to our application.
{"title":"A SOA and DBUS-based Robotic Component Interaction","authors":"R. P. Srivastava, L. S. Umrao, R. Yadav","doi":"10.3329/jsr.v15i1.57545","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.57545","url":null,"abstract":"Rewriting and executing codes violate the SOLID principle of object-oriented programming. Robotics being an emerging platform, it becomes hard to write the code from scratch. We focus on using what is already built in as a Robotics Component instead of writing something from scratch. The intention is to minimize development effort and produce the desired result on time without rewriting the software components. By allowing functionalities of different components to be brought into a single component, we are saving the time required for code conversion or replication of functionality written in one language to another. So an architecture with these properties seems ideal for integrating different components. Integration is one of the most fundamental problems in designing autonomous mobile robots, especially those interacting with people in real-life settings. This paper presents an approach to building complex systems from different robotics packages available as open source components (PLAYER, STAGE, GAZEBO, CARMEN). DBUS is a message-oriented protocol for communicating among processes running on the same desktop. SOA provides access to the services over the network and adds novelty to our application.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82703885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study aims to show that four maps in a b-metric space that satisfy pairwise weak compatibility have common fixed points under certain conditions. In the main results of this paper, (CLR) property is employed, and common fixed points for four weakly compatible mappings are established. All our findings are backed up by befitting examples. Our results generalize and extend certain previous findings in the literature.
{"title":"An Affirmative Fixed Point Result on b-Metric Spaces using (CLR) Property","authors":"V. Rao, U. Dixit","doi":"10.3329/jsr.v15i1.59988","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.59988","url":null,"abstract":"This study aims to show that four maps in a b-metric space that satisfy pairwise weak compatibility have common fixed points under certain conditions. In the main results of this paper, (CLR) property is employed, and common fixed points for four weakly compatible mappings are established. All our findings are backed up by befitting examples. Our results generalize and extend certain previous findings in the literature.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90105304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the plane wave solutions of a free particle in three dimensions for Cubical and Spherical Symmetry have been considered. The coordinate space wave functions for the Cubical and Spherical Symmetry are obtained by solving the Schrdinger differential equation. The momentum space wave function is obtained by using the operator form of an observable in the case of Cubical Symmetry. For Spherical Symmetry, the same is obtained by taking the Fourier transform of the respective coordinate space wave function. The wave functions have been used to constitute probability densities in coordinate and momentum space for both the symmetries. Further, the Shannon information entropy has been computed both in coordinate and momentum space respectively for (L is the length of the side of the cubical box) values for Cubical Symmetry and for values in Spherical Symmetry keeping (k is the wave vector and p is the momentum of the free particle) constant. The values obtained for the Shannon information entropies are found to satisfy the Bialynicki-Birula and Myceilski (BBM) inequality at larger values () in case of Cubical Symmetry and for values of and in Spherical Symmetry.
{"title":"Shannon Information Entropy Sum of a Free Particle in Three Dimensions Using Cubical and Spherical Symmetry","authors":"S. Singh, A. Saha","doi":"10.3329/jsr.v15i1.60067","DOIUrl":"https://doi.org/10.3329/jsr.v15i1.60067","url":null,"abstract":"In this paper, the plane wave solutions of a free particle in three dimensions for Cubical and Spherical Symmetry have been considered. The coordinate space wave functions for the Cubical and Spherical Symmetry are obtained by solving the Schrdinger differential equation. The momentum space wave function is obtained by using the operator form of an observable in the case of Cubical Symmetry. For Spherical Symmetry, the same is obtained by taking the Fourier transform of the respective coordinate space wave function. The wave functions have been used to constitute probability densities in coordinate and momentum space for both the symmetries. Further, the Shannon information entropy has been computed both in coordinate and momentum space respectively for (L is the length of the side of the cubical box) values for Cubical Symmetry and for values in Spherical Symmetry keeping (k is the wave vector and p is the momentum of the free particle) constant. The values obtained for the Shannon information entropies are found to satisfy the Bialynicki-Birula and Myceilski (BBM) inequality at larger values () in case of Cubical Symmetry and for values of and in Spherical Symmetry.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72976596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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