Classification of certain integrable coupled potential KdV and modified KdV-type equations

2000 ◽  
Vol 41 (9) ◽  
pp. 6173-6185 ◽  
Author(s):  
Mikhail V. Foursov
Keyword(s):  
Kdv Type Equations

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

scholarly journals Some Connections between Classical and Nonclassical Symmetries of a Partial Differential Equation and Their Applications

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 524
Author(s):  
Chaolu Temuer ◽  
Laga Tong ◽  
George Bluman
Keyword(s):  
Sufficient Conditions ◽  
Partial Differential ◽  
Burgers Equations ◽  
Classical Symmetry ◽  
Nonclassical Symmetry ◽  
Kdv Type Equations ◽  
Nonclassical Symmetries ◽  
The Given

Essential connections between the classical symmetry and nonclassical symmetry of a partial differential equations (PDEs) are established. Through these connections, the sufficient conditions for the nonclassical symmetry of PDEs can be derived directly from the inconsistent conditions of the system determining equations of the classical symmetry of the PDE. Based on the connections, a new algorithm for determining the nonclassical symmetry of a PDEs is proposed. The algorithm make the determination of the nonclassical symmetry easier by adding compatibility extra equations obtained from system of determining equations of the classical symmetry to the system of determining equations of the nonclassical symmetry of the PDE. The findings of this study not only give an alternative method to determine the nonclassical symmetry of a PDE, but also can help for better understanding of the essential connections between classical and nonclassical symmetries of a PDE. Concurrently, the results obtained here enhance the efficiency of the existing algorithms for determining the nonclassical symmetry of a PDE. As applications of the given algorithm, a nonclassical symmetry classification of a class of generalized Burgers equations and the nonclassical symmetries of a KdV-type equations are given within a relatively easier way and some new nonclassical symmetries have been found for the Burgers equations.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

Interpreting HVEM of muscle-cell impulse networks

1992 ◽  
Vol 50 (1) ◽  
pp. 126-127
Author(s):  
Paul DeCosta ◽  
Kyugon Cho ◽  
Stephen Shemlon ◽  
Heesung Jun ◽  
Stanley M. Dunn
Keyword(s):  
Structural Analysis ◽  
Muscle Cell ◽  
Electron Micrographs ◽  
Relative Size ◽  
Automatic Classification ◽  
Nerve Fibers ◽  
Analysis Algorithm ◽  
Structural Networks

Introduction: The analysis and interpretation of electron micrographs of cells and tissues, often requires the accurate extraction of structural networks, which either provide immediate 2D or 3D information, or from which the desired information can be inferred. The images of these structures contain lines and/or curves whose orientation, lengths, and intersections characterize the overall network.Some examples exist of studies that have been done in the analysis of networks of natural structures. In, Sebok and Roemer determine the complexity of nerve structures in an EM formed slide. Here the number of nodes that exist in the image describes how dense nerve fibers are in a particular region of the skin. Hildith proposes a network structural analysis algorithm for the automatic classification of chromosome spreads (type, relative size and orientation).

Dual stain kit for the microscopic gram classification of ocular infection bacteria

1993 ◽  
Vol 51 ◽  
pp. 248-249
Author(s):  
Jacob S. Hanker ◽  
Dale N. Holdren ◽  
Kenneth L. Cohen ◽  
Beverly L. Giammara
Keyword(s):  
Contact Lenses ◽  
Ocular Infection ◽  
Gram Negative Bacteria ◽  
Gram Negative ◽  
Gram Staining ◽  
Ocular Infections ◽  
Different Types ◽  
Culture Positive ◽  
Increased Susceptibility

Keratitis and conjunctivitis (infections of the cornea or conjunctiva) are ocular infections caused by various bacteria, fungi, viruses or parasites; bacteria, however, are usually prominent. Systemic conditions such as alcoholism, diabetes, debilitating disease, AIDS and immunosuppressive therapy can lead to increased susceptibility but trauma and contact lens use are very important factors. Gram-negative bacteria are most frequently cultured in these situations and Pseudomonas aeruginosa is most usually isolated from culture-positive ulcers of patients using contact lenses. Smears for staining can be obtained with a special swab or spatula and Gram staining frequently guides choice of a therapeutic rinse prior to the report of the culture results upon which specific antibiotic therapy is based. In some cases staining of the direct smear may be diagnostic in situations where the culture will not grow. In these cases different types of stains occasionally assist in guiding therapy.

Ultrastructural Classification of Pituary Adenomas

1990 ◽  
Vol 48 (3) ◽  
pp. 258-258
Author(s):  
S. Arumugam ◽  
Sarasa Bharati Arumugam
Keyword(s):  
Cytoplasmic Organelle ◽  
Null Cell ◽  
Cell Adenoma ◽  
Mixed Cell ◽  
Light Microscope Level ◽  
Null Cell Adenoma ◽  
Growth Hormone Cell ◽  
Ultrastructural Characteristics ◽  
Organelle Morphology

Adenoaas of the pituitary are no longer classified based on their tinctorial affinity to dyes. With the advent of the newer methods of sophisticated technology, it is now possible to classify. These depending upon the type of hormone secreted based either on histochemical techniques or on ultrastructural characteristics. The latter provides an insight into the cytoplasmic organelle morphology which offers a delightful feast to the eye as well.This paper presents the ultrastructural characters of the pituitary adenoma as seen in Madras. 171 adenomas (124 males and 47 females) were seen during 1972-1989, classified at the light microscope level as 159 chromophobe, 2 basophilic, 4 eosinophilic and 6 mixed adenomas.Ultrastructural examination showed that the sparsely granular prolactin cell adenoma is the commonest adenoma to be encountered closely followed by the growth hormone cell adenoma, null cell adenoma, the mixed cell adenoma and others.

Consistency in Latency Measurements and Interpretation of ABR Tracings

1997 ◽  
Vol 6 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Wayne O. Olsen ◽  
Terri L. Pratt ◽  
Christopher D. Bauch
Keyword(s):  
The Other

Multichannel ABR recordings for 30 otoneurologic patients were reviewed independently by three audiologists to assess interjudge consistency in determining absolute latencies and overall interpretation of ABR results. Four months later, the tracings were reviewed a second time to evaluate intrajudge consistency in interpretation of ABR waveforms. Interjudge agreement in marking latencies for waves I, III, and V within 0.2 ms was on the order of 90% or better. Intrajudge consistency was slightly higher. Only rarely did inter- or intrajudge differences in latency measurements exceed 0.3 ms. Agreement in overall interpretation of ABR results as "normal" or "abnormal" was unanimous for 90% of the patients. Across pairs of judges, the agreement for "normal" and "abnormal" classification of the ABR tracings was 97%. Intrajudge consistency for "normal" and "abnormal" categorization of the ABR results was 100% for one judge, 97% for the other two judges.

Classification of Infant Vocalizations by Untrained Listeners

2019 ◽  
Vol 62 (9) ◽  
pp. 3265-3275
Author(s):  
Heather L. Ramsdell-Hudock ◽  
Anne S. Warlaumont ◽  
Lindsey E. Foss ◽  
Candice Perry
Keyword(s):  
Formal Education ◽  
Additional Insight ◽  
Listener Responses ◽  
Infant Vocalization ◽  
Early Infant ◽  
Infant Vocalizations ◽  
Audio Recordings ◽  
Speech And Language Development ◽  
Insight Into

Purpose To better enable communication among researchers, clinicians, and caregivers, we aimed to assess how untrained listeners classify early infant vocalization types in comparison to terms currently used by researchers and clinicians. Method Listeners were caregivers with no prior formal education in speech and language development. A 1st group of listeners reported on clinician/researcher-classified vowel, squeal, growl, raspberry, whisper, laugh, and cry vocalizations obtained from archived video/audio recordings of 10 infants from 4 through 12 months of age. A list of commonly used terms was generated based on listener responses and the standard research terminology. A 2nd group of listeners was presented with the same vocalizations and asked to select terms from the list that they thought best described the sounds. Results Classifications of the vocalizations by listeners largely overlapped with published categorical descriptors and yielded additional insight into alternate terms commonly used. The biggest discrepancies were found for the vowel category. Conclusion Prior research has shown that caregivers are accurate in identifying canonical babbling, a major prelinguistic vocalization milestone occurring at about 6–7 months of age. This indicates that caregivers are also well attuned to even earlier emerging vocalization types. This supports the value of continuing basic and clinical research on the vocal types infants produce in the 1st months of life and on their potential diagnostic utility, and may also help improve communication between speech-language pathologists and families.

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