Solution Structure Research Articles

The structure-activity relationship for the ABA triblock siloxane surfactant in aqueous-ethanol system

It is challenging to improve the foam stability in high concentration ethanol solution. In this paper, well-defined polyether-modified siloxane surfactants were synthesized, and their structures were characterized through infrared spectroscopy and one- and two-dimensional Nuclear magnetic resonance (NMR) spectroscopy. Furthermore, the relationships of between their chemical structure, surface activity, and foam property in high concentration ethanol solution were investigated in detail. The results showed that the target surfactant exhibited an ABA-type structure. They can effectively reduce the surface tension and produce the excellent foam in 75 % ethanol. In particular, these surfactants with loner siloxane chain confer strong foaming power in 75 % solution. This ability with good surface activity in water-ethanol system suggests a wide range of potential applications in low surface tension solvent system.

New Findings on the Crystal Polymorphism of Imepitoin.

Scientific and industrial reasons dictate the study of the solid state of imepitoin, a highly safe and tolerable anticonvulsant drug used in the therapy of epileptic dogs that was approved in the Europe Union in 2013. Our investigations allowed us to discover the existence of a new polymorph of imepitoin, which finds itself in a monotropic relationship with the crystalline form (polymorph I) already known and present on the market. This form (polymorph II), obtained by crystallization from xylene, remains metastable under ambient conditions for at least 1 year. Both solid forms were characterized by thermal (DSC and TGA), spectroscopic (FT-IR and Raman), microscopic (SEM and HSM), and diffractometric techniques. The thermodynamic relationship between the two polymorphs (monotropic) is such that it is not possible to study the melting of polymorph II, not even by adopting appropriate experimental strategies. Our measurements highlighted that the melting peak of imepitoin actually also includes an onset of melt decomposition. The ab initio structure solution, obtained from synchrotron X-ray powder diffraction data collected at room temperature, allowed us to determine the crystal structure of the new polymorph (II). It crystallizes in the monoclinic crystal structure, P21/c space group (#14), with a = 14.8687(6) Å, b = 7.2434(2) Å, c = 12.5592(4) Å, β = 107.5586(8)°, V = 1289.61(8) Å3, and Z = 4.

Impact of molecular symmetry on crystallization pathways in highly supersaturated KH2PO4 solutions

Solute structure and its evolution in supersaturated aqueous solutions are key clues to understand Ostwald’s step rule. Here, we measure the structural evolution of solute molecules in highly supersaturated solutions of KH2PO4 (KDP) and NH4H2PO4 (ADP) using a combination of electrostatic levitation and synchrotron X-ray scattering. The measurement reveals the existence of a solution-solution transition in KDP solution, caused by changing molecular symmetries and structural evolution of the solution with supersaturation. Moreover, we find that the molecular symmetry of H2PO4- impacts on phase selection. These findings manifest that molecular symmetry and its structural evolution can govern the crystallization pathways in aqueous solutions, explaining the microscopic origin of Ostwald’s step rule.

“Four words about kolomyika”: author’s experience of orchestration

Statement of the problem. Orchestration is one of the spheres of a composer’s professional activity, and its ways and principles are a special subject of scientific research. There are a sufficient number of examples, when the composer turns to the orchestration of self-own piano works (F. Liszt, C. Saint-Saëns, M. Ravel, H. Villa-Lobos, M. Skoryk and others), but the orchestration of violin works is not widespread phenomenon. The proposed work reveals the ways of orchestrating the four parts of the cycle “Seven words about the kolomyika” for solo violin, written by the author of the article. The main idea of the piece is interpretation of the kolomyika genre as a keeper of the genetic code of the Ukrainian people, through different levels of texture and structure solutions. Objectives, methods, and novelty of the research. Numerous works are devoted to orchestration, among them the guides by Adler, Casella & Mortari, Belkin, Klebanov and others. Another field of research is works on the theory of orchestration by Savchenko, Rakochi, Korobetska, Borodavkin, Kashyrtsev, Bohatyriov. However, the study of the ways and methods of translating a violin texture into an orchestral one has not yet attracted enough attention of musicologists-scientists and practicing musicians, and it is extremely difficult to find works on the orchestration of a violin texture, therefore, the presented work has an innovative focus. The purpose of the publication is to reveal the specifics of the orchestration of the violin texture using the example of the cycle “Four words about kolomyika” through the analysis of the use of orchestral principles and techniques in it. It was required the involvement of such research methods: genre-stylistic to identify the features of the kolomyika genre; structural-functional for researching the functions of instruments in the orchestral texture, the orchestration techniques, the form of the work; comparative one for considering the original violin source and the derived orchestral version; historical to light the context of the writing of the work. Results and conclusion. As a result of the research of the original source and its symphonic, timbre reinterpreted version, the next statements has been revealed. 1. The structural compositional analysis of the texture and form of the original source is of great importance for the creation of an orchestration of both one’s own and someone else’s work – the identification of potential harmony, bass voice, accompaniment, determination of the boundaries of the form, the character and tempo, which helps to understand the way of building timbre drama in the orchestral version. 2. The melody often in a “collapsed” form contains certain orchestral textural and timbre solutions. So, in many sections of the symphonic cycle, textural layers hidden in the initial melodic line are revealed – orchestral pedal, figurations, bass line, counterpoint, et cet. 3. The type, nature of the melody and the form of the piece determine the choice of timbre and orchestration techniques. The cycle uses such techniques of orchestral writing as underlining, the transfer of textural lines from one instrument to another, an orchestral crescendo, timbre mixes, the overlaying of textural layers of different instrumental groups, which creates a sonorous effect. 4. Each instrument of the wooden and brass groups corresponds to a certain line of the texture, is not duplicated in unison according to the “a2” principle, except for a few bars of the bassoons in the first part. This allows us to interpret the orchestra as a large ensemble, which to some extent is due to the neo-folkloric style of the piece. 5. The main idea of the piece in the symphonic version is manifested through the timbre reinterpretation of the theme, the multi-layered texture, the significant role of the woodwinds in the melodic lines and percussion to emphasize the rhythmic pattern and mark the boundaries of the form, as well as through the coloristic effects. The named ways of the piece working create the orchestral style that is a valuable component of composer’s creative activity.

Unified approach to the inverse median location problem under the sum and the max objectives applying ordered median function

ABSTRACT In this paper, we propose a unified approach to solving the inverse 1-median problem on trees under both the sum and max objectives by using the ordered median function. For the problem under the k-centrum cost function, we investigate the structure of an optimal solution and transform the problem into a univariate optimization problem where the parameter equals the k largest cost. We take advantage of the convexity of the objective function to efficiently find the optimal solution in O ( nlog ⁡ n ) time, where n is the number of vertices in the tree. For the problem under the centdian cost function, we parameterize it based on the maximum cost item and prove that the induced cost function is convex. We leverage this insight to develop a combinatorial algorithm that solves the corresponding problem in O ( nlog ⁡ n ) time.

Using multi‐criteria decision‐making methods in prioritizing structural flood control solutions: A case study from Iran

AbstractEffective management of flood risks requires the prioritization of appropriate flood control solutions. This study aims to prioritize structural flood control options using multi‐criteria decision‐making (MCDM) methods. Four MCDM methods, namely analytic hierarchy process, technique for order preference by similarity to ideal solution, multi‐criteria optimization and compromise solution, and Fuzzy‐VIKOR are employed to assess and rank the flood control options based on multiple criteria. Field surveys, interviews with local authorities and experts, and on‐site assessments of existing flood control structures constituted the primary data collection methods. The findings demonstrate the effectiveness of reservoir dams, retention basins, and levees as viable solutions. Conversely, flood control gates and the no‐project options were assigned lower priorities. The findings highlight the importance of considering multiple MCDM methods to account for variations in rankings. The study provides valuable insights into the decision‐making process for prioritizing flood control options in the study area. These findings can assist policymakers and stakeholders in effectively allocating resources and implementing appropriate structural flood control measures to mitigate flood risks.

Metastability of Protein Solution Structures in the Absence of a Solvent: Rugged Energy Landscape and Glass-like Behavior.

Native ion mobility/mass spectrometry is well-poised to structurally screen proteomes but characterizes protein structures in the absence of a solvent. This raises long-standing unanswered questions about the biological significance of protein structures identified through ion mobility/mass spectrometry. Using newly developed computational and experimental ion mobility/ion mobility/mass spectrometry methods, we investigate the unfolding of the protein ubiquitin in a solvent-free environment. Our data suggest that the folded, solvent-free ubiquitin observed by ion mobility/mass spectrometry exists in a largely native fold with an intact β-grasp motif and α-helix. The ensemble of folded, solvent-free ubiquitin ions can be partitioned into kinetically stable subpopulations that appear to correspond to the structural heterogeneity of ubiquitin in solution. Time-resolved ion mobility/ion mobility/mass spectrometry measurements show that folded, solvent-free ubiquitin exhibits a strongly stretched-exponential time dependence, which simulations trace to a rugged energy landscape with kinetic traps. Unfolding rate constants are estimated to be approximately 800 to 20,000 times smaller than in the presence of water, effectively quenching the unfolding process on the time scale of typical ion mobility/mass spectrometry measurements. Our proposed unfolding pathway of solvent-free ubiquitin shares substantial characteristics with that established for the presence of solvent, including a polarized transition state with significant native content in the N-terminal β-hairpin and α-helix. Our experimental and computational data suggest that (1) the energy landscape governing the motions of folded, solvent-free proteins is rugged in analogy to that of glassy systems; (2) large-scale protein motions may at least partially be determined by the amino acid sequence of a polypeptide chain; and (3) solvent facilitates, rather than controls, protein motions.

The Influence of Shear Connector Numbers on The Flexural Characteristics of Composite Geopolymer Reinforced Concrete Beams With Small Transverse Web Openings

Geopolymer concrete is a sustainable alternative to conventional Portland cement-based concrete, utilizes industrial by-products like fly ash and slag. Renowned for its reduced carbon footprint and exceptional durability, geopolymer concrete is gaining global recognition in eco-friendly construction practices. Steel composite reinforced geopolymer concrete beams combine the strength of steel with the sustainability of geopolymer concrete, offering a sturdy structural solution. This collaborative approach results in a composite material with excellent crack resistance and durability, harnessing the advantageous properties of both steel and geopolymer concrete. These beams present a promising option in construction by striking a balance between structural performance and environmental considerations through the incorporation of geopolymer technology. The focus of the current study is to investigate the impact of steel connectors on the flexural behavior of composite reinforced geopolymer concrete beams that have transverse web opening through experimental methods. The experimental program involves casting four geopolymer beams, with one being a traditional geopolymer-reinforced concrete beam (Control). The remaining three specimens are composite reinforced geopolymer concrete beams, each featuring a bottom 5 mm steel plate with six, twelve, and eighteen connectors near each support. The beams share common dimensions, with a total length of 1600mm, a height of 250mm, and a width of 180mm. The results showed that increasing the number of connectors near supports increased the resulted flexural behavior of beams. Such connectors increased the first crack load from 6.67% to 42.22% while the service load increased from 16.22% to 36.20%. the load carrying capacity was also increased from 12.00% to 24.80%. Finally, the mode of failure was moved from traditional tension failure to concrete crushing.

Benchmarking Guanidinium Organosulfonate Hydrogen-Bonded Frameworks for Structure Determination of Encapsulated Guests.

Single crystal X-ray diffraction (SCXRD) is arguably the most definitive method for molecular structure determination, but it is often challenged by compounds that are liquids or oils at room temperature or do not form crystals adequate for analysis. Our laboratory previously reported a simple, cost-effective, single-step crystallization method based on guanidinium organosulfonate (GS) hydrogen bonded frameworks for structure determination of a wide range of encapsulated guest molecules, including assignment of the absolute configuration of chiral centers. Herein, we expand on those results and report a head-to-head comparison of the GS method with adamantoid "molecular chaperones", which have been reported to be useful hosts for structure determination. Inclusion compounds limited to only two GS hosts are characterized by low R1 values and Flack parameters, infrequent disorder of the host and guest, and manageable disorder when it does exist. The structures of some target molecules that were not included or resolved using the adamantoid chaperones were successfully included and resolved by the GS hosts, and vice versa. Of the 32 guests attempted by the GS method, 31 inclusion compounds afforded successful guest structure solutions, a 97% success rate. The GS hosts and adamantoid chaperones are complementary with respect to guest inclusion, arguing that both should be employed in the arsenal of methods for structure determination. Furthermore, the low cost of organosulfonate host components promises an accessible route to molecular structure determination for a wide range of users.

On the optical wave structures to the fractional nonlinear integrable coupled Kuralay equation

This paper is mainly concerning the study of truncated M-fractional Kuralay equations that have applications in numerous fields, including nonlinear optics, ferromagnetic materials, signal processing, engineering fields and optical fibers. Due to its ability to clarify a wide range of sophisticated physical phenomena and reveal more dynamic structures of localized wave solutions, the Kuralay equation has captured a lot of attention in the research field. The newly designed integration methods, known as the modified Sardar subequation method and enhanced modified extended tanh expansion method are used as solving tools to validate the solutions. The goal of this study is to extract several kinds of optical solitons, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. Due to the many potential applications for superfast signal routing techniques and shorter light pulses in communications, the optical propagation of soliton in optical fibers is now a topic of significant interest. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. In addition, exponential, periodic, hyperbolic solutions are generated. The applied approaches are efficient in explaining fractional nonlinear partial differential equations by providing pre-existing solutions and also producing new solutions by combining results from multiple processes. Additionally, we plot the contour, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The results of this study show the effectiveness of the approaches adopted and help enhance comprehension of the nonlinear dynamical behavior of specific systems. We expect that a substantial amount of engineering model specialists will greatly benefit from our work. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

Ultrabroad distribution of multiple anelasticities in O-doped refractory multiprincipal element alloys

The Snoek anelastic internal friction (IF) peak due to stress-induced dipole ordering associated with interstitial atoms was well observed in IF curves of single-principal element alloys (SPEAs) as early as in the 1950s, however, its behavior remains elusive in multi-principal element alloys (MPEAs) to date. Here the temperature-dependent IF spectra of NbTiV0.5Zr refractory MPEAs with varying O contents were presented, and the analysis of these data indicates that for O-doped NbTiV0.5Zr MPEAs, the O addition triggers two anelastic IF peaks (the PO1 and PO2), corresponding to the O-Snoek-type relaxation in random solid solution (RSS) and local chemical ordering (LCO) structures, respectively. The half-peak width of the PO1 is 2–3 times broader than that for SPEAs, associated with the wide O migration energy barrier distribution in MPEAs. These phenomena show a striking contrast to the single and narrow Snoek-type peak observed for SPEAs. Our analysis further reveals an approximate linear correlation between the half-peak width of the Snoek-type peak and the mixing entropy. The introduction of O also shifts grain boundary relaxation peaks (PG) towards higher temperatures. Interestingly, high-temperature anomalous modulus changes were observed for the first time in TiV-based lightweight refractory MPEAs, which is suggested to be originated from the order reduction of the body-centered cubic (bcc) structure at elevated temperatures. Moreover, the 1 at.%O doped NbTiV0.5Zr MPEA with a favorable balance between the peak heights of the PO2 and PG, exhibits outstanding specific yield stress (SYS) among refractory MPEAs while maintaining an elongation as high as 20 %. This work provides not only a bridge between the anelastic behavior of SPEAs and MPEAs for upcoming studies and theories concerning bcc MPEAs with interstitial atoms, but contributes to the holistic design of bcc MPEAs with high strength and excellent ductility.

Environmental Health Predictions for Fire Resistant and Corrosion Protection Measures for Community Health Tourism Building Facilities Due to Climate Change

The recent expansion of green tourism building facilities and warehouse capacities entails the installation of integrated community health tourism facility for cultural events, safe mobility, sport activities, agricultural and veterinary activities at old heritage buildings for public health, environmental health, green circular economy promotion within safe structures, which operations increase the occurrence of compartment fires involving flammable dangerous substances i.e biogas from sanitary biomass treatment for renewable resources, electricity and heating. The aim of this research is to compare and analyze the fire resistant materials of structural members and design economic solutions made of different structural materials for natural hazards and climate change. Useful results are presented for sustainable design solutions at integrated community health tourism renew facilities at old heritage buildings, applying proper utilities. Then, are examined the possibility of reinforcing the beams with carbon fiber lamellae and proposed additional fire protection requirements. The examining results present useful solutions for stakeholders. The study outputs enable warehouse designers, operators, stakeholders, investors and safety experts to ensure safe building facilities. Finally, sanitary digital drawing utilities, monitoring schemes are demonstrated for safe green designs so as to protect the examining building facilities at foundations or roof top levels from flood events and high temperatures due to climate change and extreme weather events.

Bridging the Gap in Cryopreservation Mechanism: Unraveling the Interplay between Structure, Dynamics, and Thermodynamics in Cryoprotectant Aqueous Solutions.

Cryoprotectants play a crucial role in preserving biological material, ensuring their viability during storage and facilitating crucial applications such as the conservation of medical compounds, tissues, and organs for transplantation. However, the precise mechanism by which cryoprotectants modulate the thermodynamic properties of water to impede the formation and growth of ice crystals, thus preventing long-term damage, remains elusive. This is evident in the use of empirically optimized recipes for mixtures that typically contain DMSO, glycerol, and various sugar constituents. Here, we use terahertz calorimetry, Overhauser nuclear polarization, and molecular dynamics simulations to show that DMSO exhibits a robust structuring effect on water around its methyl groups, reaching a maximum at a DMSO mole fraction of XDMSO = 0.33. In contrast, glycerol exerts a smaller water-structuring effect, even at higher concentrations (Scheme 1). These results potentially suggest that the wrapped water around DMSO's methyl group, which can be evicted upon ligand binding, may render DMSO a more surface-active cryoprotectant than glycerol, while glycerol may participate more as a viscogen that acts on the entire sample. These findings shed light on the molecular intricacies of cryoprotectant solvation behavior and have potentially significant implications for optimizing cryopreservation protocols.

Experimental and Numerical Analyses of Timber–Steel Footbridges

In addition to traditional building materials, such as steel and concrete, wood has been gaining increasing prominence in recent years. In the past, the use of wood was limited due to its susceptibility to damage by fungi, insects, and temperature. These shortcomings were gradually eliminated as the quality of wood processing increased and thanks to modern high-quality insulating and protective materials. The return to the utilisation of this natural building material was also supported by the development of new wood-based materials, such as glued laminated wood, and new types of mechanical fasteners, as well as by the introduction of new design methods provided in the Eurocodes. Within this context, this paper focuses on using wood in transport infrastructure, especially as the basic material for footbridges and small road bridges. Combined timber–steel bridges emerge as a very effective type of superstructure in contemporary road bridges and footbridges, especially in areas with natural exposure. Usually, wood is used for the main bridge girders, while steel is preferred for bridge deck elements—stringers and cross-girders. The results of this parametric study offer optimal structural solutions for footbridges with spans of 12.0–24.0 m, reflecting satisfactory static and dynamic footbridge behaviour. Particular attention is paid to a problematic structural detail—the connection between the steel cross-girder and the timber main girder. Firstly, this connection’s characteristics were measured experimentally using nine laboratory samples made of two glued laminated timber blocks, simulating main girders connected with a hot-rolled steel cross-girder. The connection was prepared in three variants, with different heights of the end plates and different numbers of bolts. Subsequently, these characteristics were computed using two numerical FEM models. The first model was created using SCIA Engineer software with a combination of shell and beam finite elements. The second, more sophisticated model was created in the ANSYS software environment using 3D finite elements, allowing us to better take into account the plasticity and orthotropic properties of wood and the points of contact between the individual members. Finally, the experimental results produced by sample testing in the laboratory were compared to the outputs of FEM numerical studies.

A place to remain in the village. Dutch planning cultures and rural housing policies from 1945 onwards

ABSTRACT Historical consciousness leads to a deeper understanding of rural housing policies and helps to find structural solutions to the present-day situation. This statement is illustrated with a study on two villages in the Dutch province of Drenthe. Starting with a historical account of the post-war ‘top-down’ planning culture, the analysis moves further by assessing the change towards a ‘bottom-up’ planning culture. This culture fulfils the needs of those who living in villages better. However, old habits remain in place and hamper the new culture to become more mature. Historical consciousness helps administrators, civil servants, and actors from the local civil society to become aware of (in)effective behaviour. The concept of a new ‘bottom-up’ planning culture helps them to develop the formal and informal ways for the construction of housing further.

Modeling and analysis of Double-Double composite structures integrating piezoelectric materials

Multifunctional materials and structures are increasingly important for innovative structural solutions. This work aims to model such structures constituted by Double-Double composites and piezoelectric materials. Besides the homogenization trend of these laminates as the number of the replicating sub-laminates grows, other features include simple ply drop placement, and card sliding to potentially save weight. To control the mechanical response, piezoelectrics along with several types of stacking were considered. The first-order shear deformation theory implemented via the finite element method was used to assess the model, and a set of verification and parametric studies was developed, resulting in a good performance confirmation.

Investigating the phase diagram-ionic conductivity isotherm relationship in aqueous solutions of common acids: hydrochloric, nitric, sulfuric and phosphoric acid

The relationship between phase diagram features around the solid–liquid equilibrium region and ionic conductivity in aqueous solutions is not well understood over the whole concentration range as is the case for acidic aqueous solutions. In this work, we have studied the ionic conductivity (κ) as a function of molar fraction (x) and temperature (T) for four acid/water solutions namely, monoprotic hydrochloric acid (HCl) and nitric acid (HNO3), diprotic sulfuric acid (H2SO4) and triprotic phosphoric acid (H3PO4) along with their binary phase diagrams. The connection between the main features of the phase diagrams and the trends in the ionic conductivity isotherms is established with a new insight on the two pertinent dominant conductivity mechanisms (hopping and vehicular). Ionic conductivity at different temperatures were collected from literature and fitted to reported isothermal (κ vs. x) and iso-compositional (κ vs. T) equations along with a novel semi-empirical equation (κ = f (x, T)) for diprotic and triprotic acids. This equation not only has the best fit for acids with different valency; but also contains four parameters, less than any other similar equation in literature. This work is one of few that advances the understanding of the intricate relationship between structure and ionic transport in various acidic aqueous solutions.

Mechanochemical Synthesis and Three-Dimensional Electron Diffraction Structure Solution of a Novel Cu-Based Protocatechuate Metal-Organic Framework.

Mechanochemical synthesis is a powerful approach to obtain new materials, limiting costs, and times. However, defected and submicrometrical-sized crystal products make critical their characterization through classical single-crystal X-ray diffraction. A valid alternative is represented by three-dimensional (3D) electron diffraction, in which a transmission electron microscope is used, like a diffractometer. This work matches a green water-based mechanochemical synthesis and 3D electron diffraction to obtain and characterize a Cu-based protocatechuate metal-organic framework (PC-MOF). Its structure has been fully refined through dynamical diffraction theory, and free water molecules could be detected in the channels of the framework. Thermal characterization, focused on the dehydration profile determination, leads to the formation of a novel high-temperature 2D coordination polymer, fully solved with 3D electron diffraction data. At last, the strong activity of the PC-MOF against cationic dyes like methylene blue has been reported.

Abundant dynamical solitary waves solutions of M -fractional Oskolkov model

This work uses a truncated M-fractional derivative variant of the Oskolkov model to investigate the dynamic behavior of solitary wavefronts. The methods used in this framework produce a variety of solitary waveforms, such as bright and dark solitons. A suitable choice of the free parameters is used to investigate the geometrical structures for the wave solutions, which are further characterized by stable bright periodic and soliton waves. The coefficient of the highest-order derivative and the effects of fractionality are shown in the figures. Moreover, the graphics are arranged to highlight the characteristics of novel soliton wave propagation. The findings of this research demonstrate that the fractional Oskolkov model may accommodate fundamental and higher-order soliton behaviors, each of which has unique characteristics. The fractional form of the several dynamical solitary waves seen in the study represents their practical ramifications. These waves can be seen as transmission waves via a Kelvin-Voigt fluid.

New Theorems Solving Fifth Degree Polynomial Equation in Complete Forms by Proposing New Five Roots Composed of Radical Expressions

This paper is presenting new theorems and formulas to solve fifth degree polynomial equation in general forms by proposing five formulary solutions that we can calculate nearly simultaneously. The proposed roots for fifth degree polynomial in this paper are composed of radical expressions distributed in a specific architecture that allows them to neutralize each other during multiplication by eliminating radicality and reducing degrees of terms. The proposed architecture for each solution of quantic polynomial is composed of at least six distributed terms, where each term is a multiplication of a pair of radical expressions, whereas multiplications among proposed terms is allowing the reduction of degrees in order to obtain a quartic form at maximum. Furthermore, the proposed architectures of radical roots in this paper are allowing also to solve polynomial equations with degrees higher than five by reducing their expressions. As a result, this paper is presenting two new theorems to solve quantic equation in general forms, where one theorem is eliminating the expression of fourth degree then reducing the whole fifth degree equation into a simplified form, whereas the other new theorem is solving the quantic equation without eliminating the expression of fourth degree. All proposed theorems in this paper are built on a scaling logic concretized by engineering the structure of solutions then calculating the precise formulas of roots for equations, which allow to calculate all roots nearly simultaneously and forward the used engineering methodology to solve polynomial equations with degrees higher than five.