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Scanning Electron Microscopy Of A Soil Fungus Gliocladium Roseum, David Jones, Derek Vaughan, William J. Mchardy
Scanning Electron Microscopy Of A Soil Fungus Gliocladium Roseum, David Jones, Derek Vaughan, William J. Mchardy
Scanning Microscopy
The paper describes the ultra-structural features of cryofixed and critical point-dried sporing cultures of a soil fungus Gliocladium roseum. Features described are Acrostalagmus-like conidiophores with spore masses in mucoid balls borne at the tips of branchlets and penicillate heads with conidia massed in rope-like formations. A particular feature of the aerial hyphae and conidiophores is the presence of blister-like swellings on their walls. These observations help to accurately characterize the organism in taxonomic studies.
The Diagnostic And Phylogenetic Significance Of Widened And Pronged Hamuli In Feathers, Tim G. Brom, Uri Frank
The Diagnostic And Phylogenetic Significance Of Widened And Pronged Hamuli In Feathers, Tim G. Brom, Uri Frank
Scanning Microscopy
The taxonomic distribution of widened and/or pronged hamuli (hooklets) on distal barbules in the pennaceous part of feathers was studied with light microscopy (LM) and scanning electron microscopy (SEM) in order to assess the diagnostic and phylogenetic significance of these structures. Comparison of the LM and SEM appearance of these structures indicates that "thickened" hamuli are artifacts, arising from the misinterpretation of rotated tape-like structures. Pronged hamuli, on the contrary, are non-artifacts. These structures have a much wider taxonomic distribution than was reported by earlier workers, and therefore do not seem to be useful for identifying feather fragments.
Effect Of Retinyl Acetate On Fibronectin And The Fibronectin Receptor Level In C3h/10t1/2 Mouse Embryo Fibroblast Cells During Transformation, Satoshi Suzuki
Effect Of Retinyl Acetate On Fibronectin And The Fibronectin Receptor Level In C3h/10t1/2 Mouse Embryo Fibroblast Cells During Transformation, Satoshi Suzuki
Biology
Fibronectin is involved in a variety of biological events such as cellular adhesion, cell growth, wound healing, and malignant transformation. In vitro, chemically or retrovirally transformed fibroblasts show a reduced ability to assemble a fibronectin-extracellular matrix. Very little is known about mechanisms of extracellular matrix assembly and the reduced assembly mechanism during cell transformation. This study was conducted to determine the importance of fibronectin integrity in tumor promotion. C3H/10T1/2 cells and several derivatives were utilized in this study. One such derivative used is the INIT/10T1/2 cell, which is a clone of methylcholanthrene-initiated C3H/10T1/2 cells and which has been inhibited from …
Synchronous Sporulation And Identification Of Two Secretory Proteins Associated With Sexual Reproduction Of Ascosphaera Proliperda, Meixiong Wu
Biology
Two secretory proteins associated with sexual reproduction m the bee pathogenic fungus Ascosphaera proliperda Skou were identified. In order to obtain sufficient quantities of homogeneous cells for this study, a minimal medium (MM) was developed to synchronously induce sporulation of A. proliperda. By culturing a mixture of sexually compatible mycelial fragments on this MM, a high degree of synchronous sporulation of the fungus was obtained. Monoclonal antibodies (McA) produced against secretory vesicles isolated from the synchronously sporulating cultures of A. proliperda were used to study antigens associated with sexual reproduction of this fungus. Two secretory proteins (SSF3 and SSE4) …
Red Beet Ca2+-Dependent Protein Kinases And Their Role In Syringomycin Action, Yuka S. Suzuki
Red Beet Ca2+-Dependent Protein Kinases And Their Role In Syringomycin Action, Yuka S. Suzuki
Biology
The syringomycin stimulated protein phosphorylation of red beet plasma membranes was investigated. Rabbit antisera directed against N- and C-termini and the nucleotide binding site of the H+-ATPase detected the 100 kD polypeptide of this enzyme in the plasma membrane. Immunoprecipitation experiments revealed that the 100 kD polypeptide was phosphorylated, and syringomycin stimulated the phosphorylation in a Ca2+-dependent manner. Phosphoamino acids in the immunoprecipitates were phosphoserine and phosphothreonine. These findings are evidence that syringomycin stimulates the phosphorylation of the plasma membrane H+-ATPase. Okadaic acid, a phosphatase inhibitor, did not affect protein phosphorylation of syringomycin-treated and …
Acetylcholinesterase In Lygus Hesperus Knight (Hemiptera: Miridae): Enzymological And Molecular Properties, And Relationship To Insecticide Resistance, Kunyan Zhu
Biology
Acetylcholinesterase (AChE, EC 3.1.1.7) was purified from Lygus hesperus Knight by affinity chromatography following extraction by Triton X-100. The degree of purification ranged from 616- to 900-fold and the yield ranged from 42 to 56% (n = 5). The optimal pH and temperature for purified AChE were 7.5-8.0 and 35-40 °C, respectively, for hydrolyzing selected substrates. The efficiency for hydrolyzing various substrates was acetylthiocholine > acetyl-(β-methyl) thiocholine > propionylthiocholine > S-butyrylthiocholine. The inhibitor and substrate specificities, and substrate inhibition confirmed that the enzyme activity was due to AChE rather than butyrylcholinesterase. The susceptibility of AChE to inhibition by various organophosphrous compounds was mainly …
The Role Of Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase Activase In The Activation Of Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase, Yun Lan
Biology
A spectrophotometric assay for the activity of ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco) activase was developed. This assay was used to examine the effects of CO2 and the inactive-Rubisco:ribulose 1,5-bisphosphate complex (ER) concentrations on the rate of activase-catalyzed Rubisco activation reaction in a purified preparation. ER and CO2 in this reaction were consistent with two-substrate Michaelis Menton kinetics. The implications of these data and their relation to previously published data on the effects of ER and CO2 on activase are discussed. The spectrophotometric activase assay was also used to measure activase activity in extracts from spinach (Spinacea oleracea …
Esterases In Lygus Hesperus Knight (Hemiptera: Miridae) Associated With Insecticide Resistance, Gang Xu
Esterases In Lygus Hesperus Knight (Hemiptera: Miridae) Associated With Insecticide Resistance, Gang Xu
Biology
Populations of Lygus hesperus in areas where applications of the organophosphate insecticide, trichlorfon, had been used for control of this pest have elevated LC50 values when assessed by a contact bag bioassay. Biochemical investigation using ⍺-naphthyl acetate as an esterase substrate revealed that resistant populations contain a larger proportion of individuals with higher esterase activity. The same populations also had reduced acetylcholinesterase (AChE) sensitivity to inhibition by paraoxon. The population structure regarding resistance level could be easily visualized from the distribution patterns of esterase activity and AChE insensitivity, or its heterogeneity estimated by the slope of the bioassay line. …
Idaho River Systems Management Study Wetlands Report, United States Department Of The Interior, Bureau Of Reclamations
Idaho River Systems Management Study Wetlands Report, United States Department Of The Interior, Bureau Of Reclamations
Natural Resources-Planning, Management, and Conservation
The Bureau of Reclamation is cooperating with the Idaho Department of Water Resources and others in the formulation of a comprehensive water plan for the conservation, development, management, and use of waters within the state's river basins. The impact that wetlands may have on the use of water in the state is a major consideration.
This report identifies opportunities that exist for private citizens, corporations, government agencies, and others to work together to slow the rate of wetland loss and to improve the quality of remaining wetlands. To work together effectively, these groups must reach an understanding of what comprises …
Molecular Basis For Extensin Size Heterogeneity In Two Maize Varieties, Jenifer M. Murphy
Molecular Basis For Extensin Size Heterogeneity In Two Maize Varieties, Jenifer M. Murphy
Biology
Extensin is a major cell wall structural protein found in both dicotyledonous and monocotyledonous plants that functions in cell wall support and putatively plays a role in plant defense. The purpose of this study was to demonstrate the molecular basis for the protein size heterogeneity of extensin from silk and pericarp tissues of two varieties of maize, Japanese Hulless Popcorn (JHL) and Golden X Bantam (GXB), a sweet corn. JHL and GXB differ in thickness of their pericarp. JHL pericarp is thicker and aids in water retention, which is important for popping. Extensin isolated from GXB has an apparent molecular …
A Molecular Analysis Of The Colonization Mechanisms Of The Beneficial Rhizobacterium, Pseudomonas Putida, Carol Robin Buell
A Molecular Analysis Of The Colonization Mechanisms Of The Beneficial Rhizobacterium, Pseudomonas Putida, Carol Robin Buell
Biology
Agglutinability in the beneficial fluorescent pseudomonad, Pseudomonas putida isolate Corvallis, with a plant root surface agglutinin is correlated with establishment of a bacterial population at the root-microbe interface. Agglutinability in P. putida Corvallis is conditioned in vitro by nutrient status and growth phase. Genetic analyses of the agglutination phenotype in P. putida indicate a locus, aggA, on a 2.7 kbp EcoRI-Hind III fragment is involved in manifestation of the agglutination phenotype and in adherence by the cells to bean root surfaces. Sequence analyses predict the presence of two potential open reading frames, ORFAGG1 and ORFAGG2, within the 2.7 kbp …
Epitopic Mapping Of Serogroup And Serotype Specific Proteins, Vp7 And Vp5, Among Five U.S. Bluetongue Viruses, Yi-Yuan Yang
Epitopic Mapping Of Serogroup And Serotype Specific Proteins, Vp7 And Vp5, Among Five U.S. Bluetongue Viruses, Yi-Yuan Yang
Biology
The identification of antigenic epitopes on VP7 and VP5, serogroup and serotype-specific antigens of bluetongue virus (BTV), respectively, was studied using the combination of polyclonal, monoclonal and oligoclonal antibodies and competitive blocking studies. This research is the first to identify the antigenic epitopes on proteins of any orbivirus. Two distinct antigenic determinants have been identified on VP7, the major inner capsid protein. One of the antigenic epitopes, consisting of eleven amino acid residues, was located between residues 339 and 349 at the carboxyl terminus of VP7. The location of this epitope was confirmed by specific inhibition of polyclonal antibody binding …
Mobilization Of Iron Enhances The Iron-Dependent Biochemical Reactivity Of Asbestos In Vitro And Contributes To The Cytotoxicity Of Asbestos In Cultured Cells, Loren Glen Lund
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Asbestos related research began approximately 60 years ago, yet, the mechanism(s) by which asbestos exerts its biological effects is not well understood. The hypothesis upon which this dissertation is based is that mobilization of iron from asbestos enhances the iron-dependent biochemical reactivity of asbestos in vitro and contributes to asbestos-dependent cytotoxicity. The specific aims for this hypothesis were, 1) to determine whether iron was responsible for the biochemical reactivity of asbestos in vitro and asbestos-induced cytotoxicity in cultured cells, and 2) to determine whether mobilization of iron from asbestos enhanced the reactions catalyzed by asbestos in vitro and contributes to …
Demographic Influences On Perceived Urgency Of Family Life Issues In Utah, Ted W. Warstadt
Demographic Influences On Perceived Urgency Of Family Life Issues In Utah, Ted W. Warstadt
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This study recognizes the need to identify and prioritize critical issues facing families. The literature review identifies and documents a number of critical issues facing families in American society. Survey questionnaires, which contained an abstract version of 33 previously identified issues, were sent to a sample of 2,000 people in Utah. The sample was randomly selected from resident listings in Utah telephone books. The survey asked respondents to rate each of 33 issues on a scale of 1 to 10, 1 being the least urgent and 10 being the most urgent. These issues include childhood, economic, health, and elderly concerns. …
An Embedded Ring Approach To The Vibrational Dynamics Of Disordered Two-Dimensional Materials, Timothy Edwin Doyle
An Embedded Ring Approach To The Vibrational Dynamics Of Disordered Two-Dimensional Materials, Timothy Edwin Doyle
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
A theoretical approach was developed to model the vibrational dynamics of amorphous, two-dimensional materials. The materials were modeled as continuous random networks (CRN's) comprising an assemblage of planar rings of diverse size. In-plane vibrational modes for symmetric 4-, 5-, 6-, 7-, and 8-membered rings were examined. Vibrational states of isolated rings were modified by coupling the rings to a continuous network to represent rings embedded in a CRN. An effective force constant was used to couple the ring vibrations to the network's collective motions. Potentials were approximated with the use of a central force model (bond-stretching force constant) and a …
A Cognitive Process Approach To Interpreting Performance On The Booklet Category Test And The Wisconsin Card Sorting Test, Phillip R. Wolfe
A Cognitive Process Approach To Interpreting Performance On The Booklet Category Test And The Wisconsin Card Sorting Test, Phillip R. Wolfe
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Modified administration techniques that relied on patient verbalization of reasoning on each item were devised. For the WCST, verbalized scores correlated highly with conventional scores. However, patterns of age, education, and IQ covariates for each scoring condition were very different, raising questions concerning what such verbalized scores measured. Further research based upon a prospective research design was suggested to address this question. Factor analysis of WCST scores for each scoring condition resulted in almost identical three-factor solutions in each case: (a) ineffective, perseverative responding; (b) nonperseverative number errors; and (c) Maintaining Set. A three-part hierarchy of response determinants for the …
Cognitive-Behavioral Treatment Of Adolescent Depression: Effects On Multiple Parameters, Steven E. Curtis
Cognitive-Behavioral Treatment Of Adolescent Depression: Effects On Multiple Parameters, Steven E. Curtis
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Clinical depression is the most frequently reported mental health problem for adolescents. Previously studied psychological treatment approaches for adolescent depression have recently been combined and packaged into a comprehensive psychoeducational intervention titled the Adolescent Coping With Depression Course (ACWDC). This study investigated whether treatment of clinically depressed adolescents using the ACWDC resulted in significant emotional, behavioral, and/or academic performance changes as reported by the adolescent, and observed by the parents and teachers.
Nineteen clinically depressed adolescents were identified by screening 876 students in a local high school, using a multistage screening procedure. All selected subjects met the DSM III-R criteria …
An Examination Of Operant-Respondent Interaction In The Development Of Tolerance To Ethanol, Brady Justin Phelps
An Examination Of Operant-Respondent Interaction In The Development Of Tolerance To Ethanol, Brady Justin Phelps
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
In four experiments, pigeons performed on schedules of food reinforcement across two different contexts. One context consisted of having the operant chamber fully illuminated, with increased noise levels, and reflective aluminum foil draped over the chamber sidewalls. This context was paired with oral injections of water. Another context consisting of having the chamber dark except for response keylight and at ambient noise levels was paired with oral injections of ethanol. Ethanol dosages were determined by using a dose that doubled the average variable-ratio postreinforcement pause. These procedures established the dark context as a conditioned stimulus capable of producing Pavlovian conditioned …
The Relationship Of Depression, Gender, And Sex Roles, Scott V. Cutler
The Relationship Of Depression, Gender, And Sex Roles, Scott V. Cutler
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The purpose of this study was to examine the relationship between gender and depression as a function of sex roles. Four hundred twenty subjects were recruited from two introductory psychology courses at Utah State University. Subjects completed the Bem Sex-Role Inventory (BSRI) and the Beck Depression Inventory (BDI).
A difference was found in the rate of depression between females and males that exceeds the generally accepted 2:1 ratio. There was a female to male ratio of approximately 4:1 in the group of subjects who indicated a high level of depression on the Beck Depression Inventory.
Multiple Regression Analysis was computed …
Knowing Which Way Is Up: Sex Differences In Understanding Horizontality And Verticality, Gary A. Goodrich
Knowing Which Way Is Up: Sex Differences In Understanding Horizontality And Verticality, Gary A. Goodrich
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
In previous research men have been shown to obtain higher mean scores on tests of horizontality (H) and verticality (V) than do women. This study investigated the role of experiential factors in this gender difference. Undergraduate psychology students were randomly assigned to one of three treatment groups: training, enhanced training, and placebo. The pretest measure of verticality and horizontality (V/H), training, and posttest were administered via videotape. Major findings were: men obtained higher mean V/H scores than women; V and H scores correlated significantly; and training increased performance relative to a placebo, but enhanced training was not superior to standard …
The Impact Of Psychosocial Variables On Immune System Functioning In A Sample Of Hiv-Positive Males, Gary K. Richey
The Impact Of Psychosocial Variables On Immune System Functioning In A Sample Of Hiv-Positive Males, Gary K. Richey
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This study addressed the issue of the relationship between psychological well-being and immune function in a sample of HIV seropositive homosexual and bisexual males. A control group of HIV seronegative gay males was included. The study assessed the relationship between various psychological independent variables and immune system functioning over a 24-month time period for the seropositive subjects. Data on depression, coping style, psychosocial stress, and psychomatic symptoms were collected at baseline, as well as data on depression at 12 months and CD4 counts at 6-month intervals over a 2-year period. Preliminary analyses comparing HIV seropositive to HIV seronegative subjects showed …
Augmentation Of Natural Populations Of Entomophagous Insects Through The Use Of Secondary Food Sources, John Swallow
Augmentation Of Natural Populations Of Entomophagous Insects Through The Use Of Secondary Food Sources, John Swallow
Undergraduate Honors Capstone Projects
Local densities of predators, including ladybeetles, parasitoids, big-eyed bugs, and minute pirate bugs, increased with the application of artificial honeydew, consisted of sugar and wheast dissolved in water. Sugar, rather than wheast, was the active ingredient causing predators to aggregate, although wheast prolonged the effect of the sugar treatment for the ladybeetles. Furthermore, the artificial honeydew treatments had a marked effect for a period of one week. These results suggest a potentially important role of the use of synthetic honeydew as a means of pest control in an Integrated Pest Management system.
Parent-Adolescent Communication And Adolescents' Sexual Intentions, Julie A. Bullen
Parent-Adolescent Communication And Adolescents' Sexual Intentions, Julie A. Bullen
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This study investigated the quality and quantity of sexual communication between teens and parents in relation to the teens' sexual intentions. Perceptions about communication were examined of parents and adolescents of both genders separately. Both same- and cross-gender effects of parental communication on adolescent sexual intent ions were explored. Approximately 290 families (target teen and parent) were measured in pre- and posttests. Parents perceived higher quality communication with teens than teens did, but not necessarily more frequent sexual communication. As teens' perceptions of quality of communication with mother and father went up, teens' sexual intentions went down. The higher sons' …
Relationships Among Birds, Willows, And Native Ungulates In And Around Northern Yellowstone National Park, Sally Graves Jackson
Relationships Among Birds, Willows, And Native Ungulates In And Around Northern Yellowstone National Park, Sally Graves Jackson
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Although the impacts of livestock and human activities on riparian zones and associated wildlife have been well documented, little is known about the impacts that browsing by large native ungulates such as elk and moose may have. In the northern Yellowstone area, some willow stands experience intense browsing by elk and moose whereas others experience medium or very low amounts of browsing. The objectives of this study were (1) to compare the species and densities of birds among willow stands that have experienced different intensities of browsing by native ungulates, (2) to measure the relationship between five species of birds …
Pvs--To Die Or Not To Die? A Comprehensive Analysis Of The Persistent Vegetative State, Jonny Kelly
Pvs--To Die Or Not To Die? A Comprehensive Analysis Of The Persistent Vegetative State, Jonny Kelly
Undergraduate Honors Capstone Projects
Becky and Joy were returning home from the blind dates they had been on that night. Becky's cousin had introduced the two girls to his two buddies from college.
Sprinkler Irrigation-Pesticide Best Management Systems, A. Y. Ranjha, Richard C. Peralta, Robert W. Hill, A. M. Requena, Howard M. Deer, M. Ehteshami
Sprinkler Irrigation-Pesticide Best Management Systems, A. Y. Ranjha, Richard C. Peralta, Robert W. Hill, A. M. Requena, Howard M. Deer, M. Ehteshami
Civil and Environmental Engineering Faculty Publications
The relative reduction in potential groundwater contamination due to pesticides at several sites in Utah was determined by comparing alternative irrigation system designs, water management practices, and pesticides. Alternative sprinkler irrigation distribution coefficients were used to estimate irrigation application depths. The movement of pesticides through soils following sprinkler irrigations was simulated with a one-dimensional model. Pesticide contamination of groundwater can be reduced by careful selection of pesticides, using properly designed irrigation systems, and improved water management techniques. Procedures for selecting an appropriate sprinkler system design and pesticide are presented. KEYWORDS. Pesticides, Leaching, Sprinkler irrigation, Irrigation depth, Irrigation system design, Soil, …
Influence Of 2,5-Hexanedione, Acrylamide, Tri-O-Tolyl Phosphate, Leptophos And Methylmercury On Endogenous Levels Of Tryptophan, Serotonin And 5-Hydroxyindoleacetic Acid And Serotonin Turnover Rates In Rat Brain, Craig H. Farr
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Several industrial and environmental chemicals cause distal and/or central neuropathy among other diverse toxic effects. Spague-Dawley derived rats were fed doses of 2,5-hexanedione, acrylamide, tri-o-tolyl phosphate, Leptophos and methylmercury via gavage. The dose levels and administration periods were established in previous experiments designed to assess clinical neuropathy using rats trained to walk on a rotorod apparatus fitted with an electrode floor. After intravenous injections of 3H-Tryptophan, whole rat brain homogenates were analyzed using liquid scintillation and spectrofluorometric techniques for levels of tryptophan, serotonin and 5-hydroxyindoleacetic acid. Serotonin turnover rates were calculated using the specific activities of tryptophan and serotonin …
Influence Of Process Parameters In The Manufacture Of Cottage Cheese Curd From Ultrafiltered Skim Milk, Ronald Michael Raynes
Influence Of Process Parameters In The Manufacture Of Cottage Cheese Curd From Ultrafiltered Skim Milk, Ronald Michael Raynes
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
A processing procedure for the manufacture of directly acidified cottage cheese curd from 16% total solids ultrafiltered retentate was developed. The effects of preacidification of skim milk before ultrafiltration and heat treatment of retentate were investigated to improve the functional and sensory qualities of retentate curd.
Retentate directly acidified with phosphoric acid and glucono-delta-lactone to pH 4.7 formed a dense, rubbery curd that could not be handled well in a vat. A heat treatment of 71.1°C for 30 min applied to the retentate resulted in a curd with acceptable handling properties. However, this heat treatment caused the curd to shift …
Biosystematics Of Seven Species Of Stipa From Southwestern United States And Northern Mexico, Penelope S. Hoge
Biosystematics Of Seven Species Of Stipa From Southwestern United States And Northern Mexico, Penelope S. Hoge
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Two previously unidentified taxa of Stipa L. were evaluated morphologically, electrophoretically, and ecologically. The two 'new' taxa (tentatively referred to as "puzzlei" and "valdesii") were compared with five species from southwestern United States and northern Mexico (Stipa lobata Swallen, Stipa alta Swallen, Stipa scribneri Vasey, Stipa lettermanii Vasey, and Stipa nelsonii Scribner), all of which are considered to belong in the Achnatherum species-group. Anatomical and micromorphological features show that the 'new' taxa also belong in this species-group. Principal coordinate analyses of the morphological data showed that each of the seven taxa tended to occupy a …
Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu
Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This dissertation is both a literature survey and a presentation of new and independent results.
The survey gives an overview of disconjugacy and oscillation theory for linear differential and difference equations with an emphasis on comparing the theory of difference equations to the theory of differential equations. Second order scalar equations, higher order scalar equations, matrix equations (systems) and Hamiltonian systems are discussed. A chapter on three-term recurrences of systems is also included. Both similarities and differences between differential and difference equations are described.
The new and independent results are for Hamiltonian systems of difference equations. Those results include the …