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28 pages, 1528 KiB  
Review
Is Human Chorionic Gonadotropin a Reliable Marker for Testicular Germ Cell Tumor? New Perspectives for a More Accurate Diagnosis
by Nunzio Marroncelli, Giulia Ambrosini, Andrea Errico, Sara Vinco, Elisa Dalla Pozza, Giulia Cogo, Ilaria Cristanini, Filippo Migliorini, Nicola Zampieri and Ilaria Dando
Cancers 2025, 17(14), 2409; https://doi.org/10.3390/cancers17142409 - 21 Jul 2025
Viewed by 320
Abstract
Testicular germ cell tumors (TGCTs) are the most common malignancies affecting young men between the ages of 14 and 44, accounting for about 95% of all testicular cancers. Despite being relatively rare compared to other cancers (~3.0 cases per 100,000 population, with high [...] Read more.
Testicular germ cell tumors (TGCTs) are the most common malignancies affecting young men between the ages of 14 and 44, accounting for about 95% of all testicular cancers. Despite being relatively rare compared to other cancers (~3.0 cases per 100,000 population, with high worldwide variability), TGCTs’ incidence is increasing, particularly in industrialized countries. The initial phase of TGCT diagnosis is performed by detecting in the blood the presence of three proteins, i.e., alpha-fetoprotein (AFP), lactate dehydrogenase (LDH), and human chorionic gonadotropin (hCG). Despite these proteins being defined as markers of TGCTs, they present limitations in specificity. Indeed, AFP is not elevated in pure seminomas; LDH serum levels can be elevated in other conditions, such as liver disease or tissue damage, and hCG can be elevated in both seminomas and non-seminomas, reducing its ability to differentiate between tumor types. However, the existence of hCG variants, characterized by distinct glycosylation profiles that are differentially expressed in TGCT types and subtypes, may increase the diagnostic and prognostic potential of this hormone. Furthermore, emerging molecular biomarkers, including miRNAs and tumor cells-related epigenetic status, may offer new promising alternatives to improve diagnostic accuracy. Nonetheless, standardized diagnostic protocols still need to be implemented. Finally, understanding the biological roles of hCG isoforms and their “canonical” (e.g., LHCGR) and “non-canonical” (e.g., TGF-βR) receptor interactions may help in understanding tumor biology and therapeutic targeting. Full article
(This article belongs to the Special Issue Insights from the Editorial Board Member)
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16 pages, 1780 KiB  
Perspective
BRCA2 Pre-mRNA Differential 5′ Splicing: A Rescue of Functional Protein Properties from Pathogenic Gene Variants and a Lifeline for Fanconi Anemia D1 Patients
by Roberto Paredes, Kiran Batta, Daniel H. Wiseman, Reham Gothbi, Vineet Dalal, Christine K. Schmidt, Reinhard Kalb, Stefan Meyer and Detlev Schindler
Int. J. Mol. Sci. 2025, 26(14), 6694; https://doi.org/10.3390/ijms26146694 - 12 Jul 2025
Viewed by 337
Abstract
Fanconi anemia (FA) is a DNA repair deficiency disorder associated with genomic and chromosomal instability and a high cancer risk. In a small percentage of cases, FA is caused by biallelic pathogenic variants (PVs) in the BRCA2/FANCD1 gene, defining the FA-D1 subtype. Experimental [...] Read more.
Fanconi anemia (FA) is a DNA repair deficiency disorder associated with genomic and chromosomal instability and a high cancer risk. In a small percentage of cases, FA is caused by biallelic pathogenic variants (PVs) in the BRCA2/FANCD1 gene, defining the FA-D1 subtype. Experimental and epidemiologic data indicate that the complete absence of BRCA2 is incompatible with viability. Therefore, cells from individuals affected with FA caused by biallelic BRCA2 PVs must have a residual BRCA2 function. This activity may be maintained through hypomorphic missense mutations, translation termination–reinitiation associated with a translational stop mutation, or other non-canonical or uncommon translation initiation and elongation events. In some cases, however, residual BRCA2 function is provided by alternatively or aberrantly spliced BRCA2 transcripts. Here, we review and debate aspects of the contribution of splicing in the 5′ segment to BRCA2 functions in the context of PVs affecting this largely intrinsically disordered protein region, with a focus on recent findings in individuals with FA-D1. In this Perspective, we also discuss some of the broader biological implications and open questions that arise from considering 5′-terminal BRCA2 splicing in light of old and new findings from FA-D1 patients and beyond. Full article
(This article belongs to the Section Molecular Genetics and Genomics)
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21 pages, 5292 KiB  
Article
Downregulation of S6 Kinase and Hedgehog–Gli1 by Inhibition of Fatty Acid Synthase in AML with FLT3-ITD Mutation
by Maxim Kebenko, Ruimeng Zhuang, Konstantin Hoffer, Anna Worthmann, Stefan Horn, Malte Kriegs, Jan Vorwerk, Nikolas von Bubnoff, Cyrus Khandanpour, Niklas Gebauer, Sivahari Prasad Gorantla, Walter Fiedler, Carsten Bokemeyer and Manfred Jücker
Int. J. Mol. Sci. 2025, 26(12), 5721; https://doi.org/10.3390/ijms26125721 - 14 Jun 2025
Viewed by 554
Abstract
Acute myeloid leukemia (AML) is a heterogeneous hematological malignancy associated with a poor prognosis. Activating mutations in the FLT3 gene occur in approximately 30% of AML cases, with internal tandem duplications in the juxtamembrane domain (FLT3-ITD; 75%) and mutations in the tyrosine kinase [...] Read more.
Acute myeloid leukemia (AML) is a heterogeneous hematological malignancy associated with a poor prognosis. Activating mutations in the FLT3 gene occur in approximately 30% of AML cases, with internal tandem duplications in the juxtamembrane domain (FLT3-ITD; 75%) and mutations in the tyrosine kinase domain (FLT3-TKD; 25%). FLT3-ITD mutations are linked to poor prognosis and offer significant clinical predictive value, whereas the implications of FLT3-TKD mutations are less understood. The Hedgehog–Gli pathway is an established therapeutic target in AML, and emerging evidence suggests crosstalk between FLT3-ITD signaling and Gli expression regulation via non-canonical mechanisms. Post-translational modifications involving myristic and palmitic acids regulate various cellular processes, but their role in AML remains poorly defined. In this study, we investigated the role of fatty acid synthase (FASN), which synthesizes myristic and palmitic acids and catalyzes palmitoyl-acyltransferation, in regulating FLT3-ITD-Gli signaling. FASN knockdown using shRNA and the FASN inhibitor TVB-3166 was performed in FLT3-ITD-mutated AML cell lines (MOLM13, MV411) and Baf3-FLT3-ITD cells. The impact of FASN inhibition was assessed through Western blot and kinome profiling, while biological implications were evaluated by measuring cell viability and proliferation. FASN inhibition resulted in reduced levels of phospho-Akt (pAkt) and phospho-S6 kinase (pS6) and decreased expression of Hedgehog–Gli1, confirming non-canonical regulation of Gli by FLT3-ITD signaling. Combining TVB-3166 with the Gli inhibitor GANT61 significantly reduced the survival of MOLM13 and MV411 cells. Full article
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12 pages, 8458 KiB  
Case Report
Surgical Management of Intrathoracic Triton Tumors: Insights into Emerging Molecular and Epigenetic Mechanisms with a Case Series of Three Patients
by Alessandro Bonis, Alberto Busetto, Federica Pezzuto, Giulia Pagliarini, Vincenzo Verzeletti, Mario Pezzella, Giorgio Cannone, Eleonora Faccioli, Marco Mammana, Giovanni Maria Comacchio, Alessandro Rebusso, Marco Schiavon, Chiara Giraudo, Fiorella Calabrese, Andrea Dell’Amore, Samuele Nicotra, Angelo Paolo Dei Tos and Federico Rea
J. Mol. Pathol. 2025, 6(2), 10; https://doi.org/10.3390/jmp6020010 - 30 May 2025
Viewed by 817
Abstract
Malignant Triton Tumors (MTTs) are rare, high-grade malignant peripheral nerve sheath tumors (MPNSTs) frequently associated with Type 1 Neurofibromatosis (NF1). NF1, an autosomal dominant disorder, predisposes approximately 10% of affected individuals to developing MPNSTs, with 50% of these tumors occurring in NF1 patients, [...] Read more.
Malignant Triton Tumors (MTTs) are rare, high-grade malignant peripheral nerve sheath tumors (MPNSTs) frequently associated with Type 1 Neurofibromatosis (NF1). NF1, an autosomal dominant disorder, predisposes approximately 10% of affected individuals to developing MPNSTs, with 50% of these tumors occurring in NF1 patients, while others arise sporadically or in association with radiation exposure. MTTs predominantly affect anatomical regions rich in large nerves, such as the limbs, spinal root, and cranial nerves. Mediastinal presentations are exceedingly rare, posing significant diagnostic and therapeutic challenges. Current treatment strategies include surgical resection, chemotherapy, radiotherapy, and lung-sparing procedures for metastatic disease. Molecular studies of MPNSTs have revealed that NF1 mutations lead to dysregulation of the RAS signalling pathway, while epigenetic alterations (e.g., SUZ12/EED mutations) further contribute to tumor progression. Dysregulated phylogenetically conserved pathways, including Wnt/beta-catenin and non-canonical SHH signalling, play a role in sarcoma progression and Schwann cell transformation. Recent advances in miRNA research highlight their involvement in tumor invasion and progression, with dysregulated miRNA expression and chromatin remodeling contributing to the pathogenesis of these neoplasms. However, the distinct molecular profiles for MTTs remain incompletely understood. Further investigation of the genetic and epigenetic landscape is essential for improving our understanding and identifying potential therapies. Herein, we present a single-center retrospective case series of three patients with an intrathoracic triton tumor treated at our University Hospital between 2000 and 2024, serving as a starting point for future insights into MPNST pathobiology. Full article
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27 pages, 4043 KiB  
Review
SARS-CoV-2 Spike Protein and Long COVID—Part 2: Understanding the Impact of Spike Protein and Cellular Receptor Interactions on the Pathophysiology of Long COVID Syndrome
by Bruno Pereira de Melo, Jhéssica Adriane Mello da Silva, Mariana Alves Rodrigues, Julys da Fonseca Palmeira, Angélica Amorim Amato, Gustavo Adolfo Argañaraz and Enrique Roberto Argañaraz
Viruses 2025, 17(5), 619; https://doi.org/10.3390/v17050619 - 25 Apr 2025
Viewed by 1568
Abstract
SARS-CoV-2 infection has had a significant impact on global health through both acute illness, referred to as coronavirus disease 2019 (COVID-19), and chronic conditions (long COVID or post-acute sequelae of COVID-19, PASC). Despite substantial advancements in preventing severe COVID-19 cases through vaccination, the [...] Read more.
SARS-CoV-2 infection has had a significant impact on global health through both acute illness, referred to as coronavirus disease 2019 (COVID-19), and chronic conditions (long COVID or post-acute sequelae of COVID-19, PASC). Despite substantial advancements in preventing severe COVID-19 cases through vaccination, the rise in the prevalence of long COVID syndrome and a notable degree of genomic mutation, primarily in the S protein, underscores the necessity for a deeper understanding of the underlying pathophysiological mechanisms related to the S protein of SARS-CoV-2. In this review, the latest part of this series, we investigate the potential pathophysiological molecular mechanisms triggered by the interaction between the spike protein and cellular receptors. Therefore, this review aims to provide a differential and focused view on the mechanisms potentially activated by the binding of the spike protein to canonical and non-canonical receptors for SARS-CoV-2, together with their possible interactions and effects on the pathogenesis of long COVID. Full article
(This article belongs to the Special Issue Viral RNA and Its Interaction with the Host)
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18 pages, 2532 KiB  
Review
Vitamin D: Beyond Traditional Roles—Insights into Its Biochemical Pathways and Physiological Impacts
by Vlad Mihai Voiculescu, Andreea Nelson Twakor, Nicole Jerpelea and Anca Pantea Stoian
Nutrients 2025, 17(5), 803; https://doi.org/10.3390/nu17050803 - 26 Feb 2025
Cited by 3 | Viewed by 4347
Abstract
Background: It is true that vitamin D did not earn its title as the “sunshine vitamin” for nothing. In recent years, however, there has been a shift in the perception surrounding vitamin D to a type of hormone that boasts countless bioactivities and [...] Read more.
Background: It is true that vitamin D did not earn its title as the “sunshine vitamin” for nothing. In recent years, however, there has been a shift in the perception surrounding vitamin D to a type of hormone that boasts countless bioactivities and health advantages. Historically, vitamin D has been known to take care of skeletal integrity and the calcium–phosphorus balance in the body, but new scientific research displays a much larger spectrum of actions handled by this vitamin. Materials and Methods: A systematic literature search was performed using the following electronic databases: PubMed, Scopus, Web of Science, Embase, and Cochrane Library. Results: Many emerging new ideas, especially concerning alternative hormonal pathways and vitamin D analogs, are uniformly challenging the classic “one hormone–one receptor” hypothesis. To add more context to this, the vitamin D receptor (VDR) was previously assumed to be the only means through which the biologically active steroid 1,25-dihydroxyvitamin D3 could impact the body. Two other molecules apart from the active hormonal form of 1,25(OH)2D3 have gained interest in recent years, and these have reinvigorated research on D3 metabolism. These metabolites can interact with several other nuclear receptors (like related orphan receptor alpha—RORα, related orphan receptor gamma—RORγ, and aryl hydrocarbon receptor—AhR) and trigger various biological responses. Conclusions: This paper thus makes a case for placing vitamin D at the forefront of new holistic and dermatological health research by investigating the potential synergies between the canonical and noncanonical vitamin D pathways. This means that there are now plentiful new opportunities for manipulating and understanding the full spectrum of vitamin D actions, far beyond those related to minerals. Full article
(This article belongs to the Special Issue Assessment of Vitamin D Status and Intake in Human Health)
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13 pages, 5307 KiB  
Article
Localization of Potential Energy in Hydrogen Bonds of the ATXN2 Gene
by Mikhail Drobotenko, Oksana Lyasota, Stepan Dzhimak, Alexandr Svidlov, Mikhail Baryshev, Olga Leontyeva and Anna Dorohova
Int. J. Mol. Sci. 2025, 26(3), 933; https://doi.org/10.3390/ijms26030933 - 23 Jan 2025
Cited by 2 | Viewed by 780
Abstract
It is known that a number of neurodegenerative diseases, also called diseases of waiting, are associated with the expansion of the polyQ tract in the first exon of the ATXN2 gene. In the expanded polyQ tract, the probability of occurrence of non-canonical configurations [...] Read more.
It is known that a number of neurodegenerative diseases, also called diseases of waiting, are associated with the expansion of the polyQ tract in the first exon of the ATXN2 gene. In the expanded polyQ tract, the probability of occurrence of non-canonical configurations (hairpins, G-quadruplexes, etc.) is significantly higher than in the normal one. Obviously, for their formation, the occurrence of open states (OSs) is necessary. Calculations were made for these processes using the angular mechanical model of DNA. It has been established that the probability of the large OS zones genesis in a DNA segment depends not only on the “strength” of the nucleotide sequence but also on the factors determining the dynamics of DNA; localization of the energy in the DNA molecule and the potential energy of interaction between pairs of nitrogenous bases also depend on environmental parameters. The potential energy of hydrogen bonds does not remain constant, and oscillatory movements lead to its redistribution and localization. In this case, OSs effectively dissipate the energy of oscillations. Thus, mathematical modeling makes it possible to calculate the localization of mechanical energy, which is necessary for the OSs formation, and to predict the places of their origin, taking into account the mechanical oscillations of the DNA molecule. Full article
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22 pages, 333 KiB  
Article
Asymptotic and Oscillatory Properties for Even-Order Nonlinear Neutral Differential Equations with Damping Term
by Belal Batiha, Nawa Alshammari, Faten Aldosari, Fahd Masood and Omar Bazighifan
Symmetry 2025, 17(1), 87; https://doi.org/10.3390/sym17010087 - 8 Jan 2025
Cited by 6 | Viewed by 760
Abstract
This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relationship between the solutions of these equations and their associated [...] Read more.
This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relationship between the solutions of these equations and their associated functions. Leveraging the symmetry between positive and negative solutions simplifies the derivation of criteria that ensure the oscillation of all solutions. Using precise techniques such as the Riccati method and comparison methods, innovative criteria are developed that guarantee the oscillation of all the solutions of the studied equations. The study provides new conditions and effective analytical tools that contribute to deepening the theoretical understanding and expanding the practical applications of these systems. Based on solid scientific foundations and previous studies, the research concludes with the presentation of examples that illustrate the practical impact of the results, highlighting the theoretical value of research in the field of neutral differential equations. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)
17 pages, 289 KiB  
Article
Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior
by Belal Batiha, Nawa Alshammari, Faten Aldosari, Fahd Masood and Omar Bazighifan
Mathematics 2025, 13(1), 147; https://doi.org/10.3390/math13010147 - 2 Jan 2025
Cited by 5 | Viewed by 1037
Abstract
This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of [...] Read more.
This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of solutions and their derivatives, paving the way for a deeper understanding of this complex behavior. The research is particularly significant as it extends the scope of previous studies by addressing more complex forms of neutral differential equations. Using the linearization technique, strict conditions are developed that exclude the existence of positive solutions, which allows the formulation of innovative criteria for determining the oscillatory behavior of the studied equations. This research highlights the theoretical and applied aspects of this mathematical phenomenon, which contributes to enhancing the scientific understanding of differential equations with neutral conditions. To demonstrate the effectiveness of the results, the research includes two illustrative examples that prove the validity and importance of the proposed methodology. This work represents a qualitative addition to the mathematical literature, as it lays new foundations and opens horizons for future studies in this vital field. Full article
19 pages, 527 KiB  
Article
Asymptotic and Oscillatory Analysis of Second-Order Differential Equations with Distributed Deviating Arguments
by Zuhur Alqahtani, Belgees Qaraad, Areej Almuneef and Higinio Ramos
Mathematics 2024, 12(22), 3542; https://doi.org/10.3390/math12223542 - 13 Nov 2024
Cited by 3 | Viewed by 881
Abstract
This paper focuses on studying the oscillatory properties of a distinctive class of second-order advanced differential equations with distributed deviating arguments in a noncanonical case. Utilizing the Riccati method and the comparison method with first-order equations, in addition to other analytical methods, we [...] Read more.
This paper focuses on studying the oscillatory properties of a distinctive class of second-order advanced differential equations with distributed deviating arguments in a noncanonical case. Utilizing the Riccati method and the comparison method with first-order equations, in addition to other analytical methods, we have established criteria to test whether the solutions of the studied equation exhibit oscillatory behavior. To verify the validity of the results we obtained and determine their applicability, we present some examples to confirm the strength and accuracy of our proposed criteria. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
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20 pages, 330 KiB  
Article
Third-Order Neutral Differential Equations with Non-Canonical Forms: Novel Oscillation Theorems
by Barakah Almarri, Belal Batiha, Omar Bazighifan and Fahd Masood
Axioms 2024, 13(11), 755; https://doi.org/10.3390/axioms13110755 - 31 Oct 2024
Cited by 7 | Viewed by 971
Abstract
This paper explores the asymptotic and oscillatory properties of a class of third-order neutral differential equations with multiple delays in a non-canonical form. The main objective is to simplify the non-canonical form by converting it to a canonical form, which reduces the complexity [...] Read more.
This paper explores the asymptotic and oscillatory properties of a class of third-order neutral differential equations with multiple delays in a non-canonical form. The main objective is to simplify the non-canonical form by converting it to a canonical form, which reduces the complexity of the possible cases of positive solutions and their derivatives from four cases in the non-canonical form to only two cases in the canonical form, which facilitates the process of inference and development of results. New criteria are provided that exclude the existence of positive solutions or Kneser-type solutions for this class of equations. New criteria that guarantee the oscillatory behavior of all solutions that satisfy the conditions imposed on the studied equation are also derived. This work makes a qualitative contribution to the development of previous studies in the field of neutral differential equations, as it provides new insights into the oscillatory behavior of neutral equations with multiple delays. To confirm the strength and effectiveness of the results, three examples are included that highlight the accuracy of the derived criteria and their practical applicability, which enhances the value of this research and expands the scope of its use in the field. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations)
10 pages, 457 KiB  
Article
The 17O/18O Ratio of Post-AGB Sources: Canonical and Non-Canonical Populations
by Javier Alcolea, Elisa Masa, Theo Khouri, Miguel Santander-García, Iván Gallardo Cava, Hans Olofsson, Carmen Sánchez Contreras, Valentín Bujarrabal, Wouter H. T. Vlemmings and Daniel Tafoya
Galaxies 2024, 12(6), 70; https://doi.org/10.3390/galaxies12060070 - 25 Oct 2024
Viewed by 939
Abstract
Stellar evolution models serve as tools to derive stellar parameters from elemental and isotopic abundance ratios. For low-to-intermediate mass evolved stars, C/O, 12C/13C, and 17O/18O ratios are proxies of the initial mass, a largely unknown parameter in [...] Read more.
Stellar evolution models serve as tools to derive stellar parameters from elemental and isotopic abundance ratios. For low-to-intermediate mass evolved stars, C/O, 12C/13C, and 17O/18O ratios are proxies of the initial mass, a largely unknown parameter in post-AGB sources, yet fundamental to establish correlations with the main properties of their post-AGB envelopes, progressing in understanding their formation and evolution. In these sources, the C/O ratio can be constrained from the detection of C- or O-bearing species in addition to CO, while the 17O/18O ratio is straightforwardly determined from the C17O-to-C18O intensity ratio of rotational lines. However, the theory is at odds with the observations. We review the status of the question, including new accurate 17O/18O ratios for 11 targets (totaling 29). Comparing the results for the 17O/18O ratios and C-rich/O-rich chemical composition, we find that ∼45% of the cases are canonical, i.e., the observations align with standard model predictions. O-rich non-canonical sources, with 17O/18O ratios above the expected, can be explained by a premature interruption of their AGB evolution as a consequence of a quasi-explosive ejection of a large fraction of the initial mass. For non-canonical C-rich sources, with 17O/18O ratios below predictions, we suggest the possibility they are extrinsic C-rich stars. Full article
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16 pages, 315 KiB  
Article
Second-Order Neutral Differential Equations with a Sublinear Neutral Term: Examining the Oscillatory Behavior
by Ahmed Alemam, Asma Al-Jaser, Osama Moaaz, Fahd Masood and Hamdy El-Metwally
Axioms 2024, 13(10), 681; https://doi.org/10.3390/axioms13100681 - 1 Oct 2024
Cited by 4 | Viewed by 1296
Abstract
This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of several theorems, we investigate criteria for the oscillation of all solutions to the equations [...] Read more.
This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of several theorems, we investigate criteria for the oscillation of all solutions to the equations under study. By employing the Riccati technique in various ways, we derive results that expand the scope of previous research and enhance the cognitive understanding of this mathematical domain. Additionally, we provide three illustrative examples to demonstrate the validity and applicability of our findings. Full article
(This article belongs to the Special Issue Differential Equations and Related Topics, 2nd Edition)
24 pages, 1325 KiB  
Article
Non-Canonical Dark Energy Parameter Evolution in a Canonical Quintessence Cosmology
by Rodger I. Thompson
Universe 2024, 10(9), 356; https://doi.org/10.3390/universe10090356 - 5 Sep 2024
Cited by 3 | Viewed by 1125
Abstract
This study considers the specific case of a flat, minimally coupled to gravity, quintessence cosmology with a dark energy quartic polynomial potential that has the same mathematical form as the Higgs potential. Previous work on this case determined that the scalar field is [...] Read more.
This study considers the specific case of a flat, minimally coupled to gravity, quintessence cosmology with a dark energy quartic polynomial potential that has the same mathematical form as the Higgs potential. Previous work on this case determined that the scalar field is given by a simple expression of the Lambert W function in terms of the easily observable scale factor. This expression provides analytic equations for the evolution of cosmological dark energy parameters as a function of the scale factor for all points on the Lambert W function principal branch. The Lambert W function is zero at a scale factor of zero that marks the big bang. The evolutionary equations beyond the big bang describe a canonical universe that is similar to ΛCDM, making it an excellent dynamical template to compare with observational data. The portion of the W function principal before the big bang extends to the infinite pre-bang past. It describes a noncanonical universe with an initially very low mass density that contracts by rolling down the dark energy potential to a singularity, big bang, at the scale factor zero point. This provides a natural origin for the big bang. It also raises the possibility that the universe existed before the big bang and is far older, and that it was once far larger than its current size. The recent increasing interest in the possibility of a dynamical universe instead of ΛCDM makes the exploration of the nature of such universes particularly relevant. Full article
(This article belongs to the Special Issue Dark Energy and Dark Matter)
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19 pages, 473 KiB  
Article
Oscillatory Properties of Second-Order Differential Equations with Advanced Arguments in the Noncanonical Case
by Zuhur Alqahtani, Belgees Qaraad, Areej Almuneef and Faizah Alharbi
Symmetry 2024, 16(8), 1018; https://doi.org/10.3390/sym16081018 - 9 Aug 2024
Cited by 2 | Viewed by 1397
Abstract
This paper focuses on studying certain oscillatory properties of a new class of half-linear second-order differential equations with an advanced argument in a non-canonical case. By employing some new relations between the solution and its higher derivatives and taking into account the symmetry [...] Read more.
This paper focuses on studying certain oscillatory properties of a new class of half-linear second-order differential equations with an advanced argument in a non-canonical case. By employing some new relations between the solution and its higher derivatives and taking into account the symmetry of positive and negative solutions, we have introduced new criteria to test whether all solutions of the studied equation exhibit oscillatory behavior. Our study aims to expand and enhance previous results, helping to understand these properties in the specified context. The results obtained are confirmed and clarified through an example involving Euler-type equations. Full article
(This article belongs to the Special Issue Symmetry in Computational Mathematics and Biophysics)
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