Invariant Points Research Articles

Merizo: a rapid and accurate protein domain segmentation method using invariant point attention

The AlphaFold Protein Structure Database, containing predictions for over 200 million proteins, has been met with enthusiasm over its potential in enriching structural biological research and beyond. Currently, access to the database is precluded by an urgent need for tools that allow the efficient traversal, discovery, and documentation of its contents. Identifying domain regions in the database is a non-trivial endeavour and doing so will aid our understanding of protein structure and function, while facilitating drug discovery and comparative genomics. Here, we describe a deep learning method for domain segmentation called Merizo, which learns to cluster residues into domains in a bottom-up manner. Merizo is trained on CATH domains and fine-tuned on AlphaFold2 models via self-distillation, enabling it to be applied to both experimental and AlphaFold2 models. As proof of concept, we apply Merizo to the human proteome, identifying 40,818 putative domains that can be matched to CATH representative domains.

Thermodynamic phase equilibria containing sodium, potassium, magnesium, strontium and chloride in underground brine environment and evaporation and salt precipitation behavior of strontium chloride

The isothermal dissolution equilibrium method was employed to study the thermodynamic phase equilibria of the NaCl + KCl + MgCl2 + SrCl2 + H2O system at 298.2 K. The equilibrium solubilities and solid phase compositions of the quinary system at 298.2 K were determined by chemical analysis and X-ray diffraction, and the corresponding stable phase diagrams were drawn. The phase diagram of the quinary system has three invariant points, six solid phase crystallization fields and fifteen solubility curves. In the phase diagram, crystalline area of double salt KCl·MgCl2·6 H2O existed. Moreover, the Pitzer thermodynamic model was utilized to predict the phase equilibria of the quinary system at 298.2 K, and the predicted solubilities agreed well with the experimental values. The results demonstrate that the Pitzer model can accurately describe the thermodynamic properties in the quinary system at 298.2 K. Finally, based on the advantages of rich strontium in underground brine from Longnu Temple brine-bearing structure in Sichuan basin of China, the salt precipitation law of strontium chloride was studied.

Solid-liquid phase equilibrium and thermodynamic model of ternary system (NH4+ //SO42−, H2PO4−–H2O) from 313.15 to 343.15 K

A tremendous amount of wastewater containing ammonium salts, mainly NH4H2PO4 and (NH4)2SO4, has been produced in the production of cathode material of lithium iron phosphate (LFP). However, as an important basis for salt separation, the solid–liquid phase equilibrium (SLPE) of these two salts has been investigated by few studies. In this study, SLPE of the ternary system (NH4+ //SO42−, H2PO4−–H2O) from 313.15 K to 343.15 K at 101.2 kPa were investigated by isothermal dissolution method, and the corresponding physicochemical properties (density, viscosity, and pH) of saturated solution were measured. The phase diagram is composed of one invariant point, two univariant curves, and two single-salt crystallization fields for NH4H2PO4 and (NH4)2SO4. Comparing the phase diagrams from 263.15 K to 343.15 K, it is obvious that two single-salt crystallization fields shrink with increasing temperature. And the area reduction of NH4H2PO4 in two salts is more significant. When the temperature drops below 268.15 K, the ice crystallization field would appear. Neither single-salt solid solution, hydrous salt nor double salt was found in the whole temperature range. Furthermore, Pitzer model was successfully applied to describe the SLPE of the ternary system at temperatures from 273.15 K to 343.15 K. The lacking Pitzer-model parameters of mixed electrolytes (θSO4-H2PO4 and ψNH4-SO4-H2PO4) were calculated, and the temperature coefficients of model parameters and dissolution equilibrium constant were obtained. The importance of this study is that it supplies basic data and theoretical references for the separation and resource utilization of two ammonium salts from wastewater in the LFP batteries industry.

Analysis of phase equilibria in liquid chromium-manganese steels in the presence of calcium. Report 1. Phase diagrams of oxide systems.

The metallurgical industry produces a wide range of chromium-manganese steels, deoxidized and modified with calcium. To determine the non-metallic inclusions (NI) that can form in the Fe–Ca–Cr–Mn–C–O system, it is necessary to study the double and triple phase diagrams included in the FeO–CaO–MnO–Cr2O3 system. Divalent chromium oxide, which is also included in the oxide melt in the Fe–Ca–Cr–Mn–C–O system, practically does not occur in the literature as a component of double or triple state diagrams; therefore, the activity of chromium(II) oxide was equated to its ion fraction and state diagrams with it were not considered in this work. The state diagrams of oxide systems FeO–CaO, FeO–MnO, FeO–Cr2O3, CaO–MnO, MnO–Cr2O3, and FeO–MnO–Cr2O3 were previously studied by the authors. In this work, the state diagrams of the CaO–Cr2O3, FeO–CaO–Cr2O3, FeO–CaO–MnO, and CaO–MnO–Cr2O3 systems are calculated and plotted. The mixing energies are selected to determine activities in solid (theory of regular ionic solutions) and liquid (theory of subregular ionic solutions) oxide solutions to calculate the coordinates of the liquidus and solidus lines of these state diagrams. The enthalpy (103.4 KJ/mol) and entropy (21.958 J/(mol•K)) of melt-ing of calcium chromite CaCr2O4 are specified. The invariant points of the state diagrams of the FeO–CaO–Cr2O3 and CaO–MnO–Cr2O3 systems have been determined. The study of double and triple phase diagrams belonging to the FeO–CaO–MnO–Cr2O3 system will make it possible to determine all possible NIs that can form in chromium-manganese steels in the presence of calcium under equilibrium conditions.

Non-variant phenomena in heterogeneous systems. New type of solubility diagrams points

The article gives a general classification of non-invariant points in phase equilibrium diagrams of all possible types. The complete topological isomorphism of the diagrams of fusibility, solubility, and liquid-vapor equilibria in various sets of variables is demonstrated. The stability of mono-variant equilibria near the non-variant points is investigated. Recurrent formulas for calculating the number of topological elements of phase diagrams are given. A previously undescribed type of non-invariant points and phase processes in the solubility diagrams is described and characterized. The last ones have no topological analogs in other types of diagrams. Thus, we have carried out, as far as is available to the authors, a complete classification of invariant points and invariant processes in phase equilibrium diagrams of an arbitrary type and with an arbitrary number of components.

Universality of Critical Dynamics with Finite Entanglement.

When a system is swept through a quantum critical point, the quantum Kibble-Zurek mechanism makes universal predictions for quantities such as the number and energy of excitations produced. This mechanism is now being used to obtain critical exponents on emerging quantum computers and emulators, which in some cases can be compared to matrix product state (MPS) numerical studies. However, the mechanism is modified when the divergence of entanglement entropy required for a faithful description of many quantum critical points is not fully captured by the experiment or classical calculation. In this Letter, we study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement, using conformally invariant critical points described approximately by a MPS as an example. We derive that the effect of finite entanglement on a Kibble-Zurek process is captured by a dimensionless scaling function of the ratio of two length scales, one determined dynamically and one by the entanglement restriction. Numerically we confirm first that dynamics at finite bond dimension χ is independent of the algorithm chosen, then obtain scaling collapses for sweeps in the transverse field Ising model and the three-state Potts model. Our result establishes the precise role played by entanglement in time-dependent critical phenomena and has direct implications for quantum state preparation and classical simulation of quantum states.

Investigation into the Nucleation of the p-Hydroxybenzoic Acid:Glutaric Acid 1:1 Cocrystal from Stoichiometric and Non-Stoichiometric Solutions.

The nucleation in the p-hydroxybenzoic acid:glutaric acid 1:1 cocrystal (PHBA:GLU) system has been investigated in stoichiometric and non-stoichiometric acetonitrile solutions by induction time experiments. Utilizing the ternary phase diagram, the supersaturated non-stoichiometric solutions were created with compositions along the invariant point boundary lines. In all cases, the PHBA:GLU cocrystal was the nucleating phase, even though the non-stoichiometric solutions were also supersaturated with respect to the pure solid phases. The nucleation of the cocrystal from the mixed solutions is found to be more difficult than the nucleation of the pure compounds from the respective pure solutions, as captured by lower pre-exponential factors (A). However, if the driving force is defined per reactant molecule instead of per heterodimer, the cocrystal nucleation difficulty is close to that of the more difficult-to-nucleate pure compound. The difference in nucleation difficulty of the cocrystal from stoichiometric and non-stoichiometric solutions was captured by differences in the interfacial energy, while the pre-exponential factor remained unchanged. Apart from the pure GLU system, the relation between the experimentally determined pre-exponential factors for the different systems correlates with calculated values using theoretical expressions for volume-diffusion and surface-integration control.

Development of a Hybrid Method for Multi-Stage End-to-End Recognition of Grocery Products in Shelf Images

Product recognition on grocery shelf images is a compelling task of object detection because of the similarity between products, the presence of the different scale of product sizes, and the high number of classes, in addition to constantly renewed packaging and added new products’ difficulty in data collection. The use of conventional methods alone is not enough to solve a number of retail problems such as planogram compliance, stock tracking on shelves, and customer support. The purpose of this study is to achieve significant results using the suggested multi-stage end-to-end process, including product detection, product classification, and refinement. The comparison of different methods is provided by a traditional computer vision approach, Aggregate Channel Features (ACF) and Single-Shot Detectors (SSD) are used in the product detection stage, and Speed-up Robust Features (SURF), Binary Robust Invariant Scalable Key points (BRISK), Oriented Features from Accelerated Segment Test (FAST), Rotated Binary Robust Independent Elementary Features (BRIEF) (ORB), and hybrids of these methods are used in the product classification stage. The experimental results used the entire Grocery Products dataset and its different subsets with a different number of products and images. The best performance was achieved with the use of SSD in the product detection stage and the hybrid use of SURF, BRISK, and ORB in the product classification stage, respectively. Additionally, the proposed approach performed comparably or better than existing models.

Equilibria of the ternary systems CsBr–LnBr3 (Ln = Gd, Dy)–H2O and the quaternary system CsBr–GdBr3–HBr (∼12.1 mass %)–H2O at T = 298.15 K and standard molar enthalpies of formation for new compounds

As part of a series of studies, this paper reports experimental phase equilibrium data for CsBr–GdBr3–H2O, CsBr–DyBr3–H2O and CsBr–GdBr3–HBr (∼12.1 mass %)–H2O systems at T = 298.15 K. The phase diagrams were constructed based on the measured data. In the phase diagrams of the ternary system CsBr–GdBr3–H2O and the quaternary system CsBr–GdBr3–HBr (∼12.1 mass %)–H2O,there are all two invariant points, and three crystallization regions corresponding to CsBr, Cs3GdBr6·10H2O, and GdBr3·6H2O, respectively.There are two invariant points and three crystallization regions corresponding to CsBr, Cs3Dy2Br9·16H2O and DyBr3·6H2Oin the system CsBr–DyBr3–H2O.The experimental solubility values of gadolinium bromide and dysprosium bromide at 298.15 K were 65.42 mass % and 65.94 mass %. The compounds Cs3GdBr6·10H2O and Cs3Dy2Br9·16H2O are incongruently soluble in water or a medium of ∼ 12.1 mass % HBr, and were characterized by XRD and TG-DTG techniques. The standard molar enthalpies of solution for Cs3GdBr6·10H2O, Cs3Dy2Br9·16H2O, GdBr3·nH2O (n = 6.00) and DyBr3·nH2O (n = 5.99) were obtainedby means of microcalorimetric measurement, the values found for standard molar enthalpies of formation of Cs3GdBr6·10H2O, Cs3Dy2Br9·16H2O, GdBr3·nH2O (n = 6.00) and DyBr3·nH2O (n = 5.99) were – (5104.8 ± 3.2) kJ·mol−1, – (7827.3 ± 3.6) kJ·mol−1, – (2726.0 ± 2.7) kJ·mol−1 and – (2734.5 ± 3.3) kJ·mol−1, respectively.

Formation of Fluorapatite in the Equilibrium System CaO–P2O5–HF–H2O at 298 K in a Nitrogen Atmosphere

The process of biomineralization of apatite in nature has been studied by scientists from various fields of science for more than a century. Unlike the volcanogenic, hydrothermal, and other types of igneous apatites, the genesis of which is entirely clear, the formation of phosphate ores of marine sedimentary origin is still debatable. Since phosphate concentrations in water bodies are too low for the spontaneous precipitation of solid phosphates, the study of different ways for their concentration is of particular interest. In this work, phase equilibria in the system CaO–P2O5–HF–H2O at 298 K, involving fluorapatite formation, have been studied. Fluorapatite is known to be the most common phosphate mineral and the main source of phosphorus on Earth, playing an important role in the mineralization process of dental tissues in vertebrates. The equilibrium in the system defined above was studied at a low mass fraction of the liquid phase components, i.e., in conditions close to natural. It has been shown that the compounds of variable composition with the fluorapatite structure containing HPO42− ions were formed in the acid region of this system. These compounds are formed at pH ≤ 7.0 and have invariant points with monetite, CaHPO4, and fluorite, CaF2. Stoichiometric fluorapatite was formed at the lowest concentrations of the liquid phase components in a neutral and weakly alkaline medium and had an invariant point with Ca(OH)2. The composition of the resulting equilibrium solid phases was found to be dependent on the Ca/P ratio of the initial components and pH of the equilibrium liquid phase. Fluorite CaF2 was present in each sample obtained in this study.

Measurements and predictions of phase equilibria in quinary system NaCl + KCl + MgCl2 + SrCl2 + H2O (saturated with NaCl) at 308.2 K

AbstractSichuan Basin of China is a typical underground brine enrichment area. In order to develop and utilize the brine resource, it is necessary to study the phase equilibria and phase diagram of brine systems. In this work, the phase equilibria of the quinary system NaCl + KCl + MgCl2 + SrCl2 + H2O (saturated with NaCl) at 308.2 K of the underground brines in Sichuan Basin are measured experimentally by isothermal dissolution equilibrium method. The phase diagram, water content diagram, and sodium chloride content change diagram of the quinary system with NaCl saturated are also drawn, respectively. The results show that the phase diagram of the quinary system contains three invariant points, seven isothermal solubility curves, and five solid crystal zones at 308.2 K. In the phase diagram, the KCl crystallization area is the largest, followed by SrCl2·6H2O, KCl·MgCl2·6H2O, and SrCl2·2H2O, while MgCl2·6H2O has the smallest crystallization area. Magnesium chloride in the quinary system has the largest solubility and has strong salting‐out effect on other salts. Furthermore, the unreported mixed ion interaction parameters θMg, Sr and ΨMg, Sr, Cl of Pitzer model are fitted, respectively. Consequently, the solubilities of the quinary system NaCl + KCl + MgCl2 + SrCl2 + H2O at 308.2 K are predicted using the Pitzer model, and the calculated phase diagram at 308.2 K is also plotted in detail. The predicted solubilities of the quinary system were in good agreement with the experimental solubilities. Finally, the study on the phase equilibrium of the quinary system can provide phase equilibrium data for the development and utilization of liquid mineral resources.

Solutions of Fractional Differential Inclusions and Stationary Points of Intuitionistic Fuzzy-Set-Valued Maps

One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point results of crisp mappings have been improved by using the symmetry of metrics. However, more than a handful of fixed-point theorems in symmetric spaces are yet to be investigated in fuzzy versions. In accordance with the aforementioned orientation, the idea of Presic-type intuitionistic fuzzy stationary point results is introduced in this study within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed herein to complement their corresponding concepts related to multi-valued and single-valued mappings. In the instance where the intuitionistic fuzzy-set-valued map is reduced to its crisp counterparts, our results complement and generalize a few well-known fixed-point theorems with symmetric structure, including the main results of Banach, Ciric, Presic, Rhoades, and some others in the comparable literature. A significant number of consequences of our results in the set-up of fuzzy-set- and crisp-set-valued as well as point-to-point-valued mappings are emphasized and discussed. One of our findings is utilized to assess situations from the perspective of an application for the existence of solutions to non-convex fractional differential inclusions involving Caputo fractional derivatives with nonlocal boundary conditions. Some nontrivial examples are constructed to support the assertions and usability of our main ideas.

An adaptive singularity avoidance method for five-axis toolpath generation with invariant cutter-contact points and bounded tool orientation variation based on the reduction of Jacobian condition number

To enhance the five-axis machine-tool performance, it is significant to avoid the singular configuration where the kinematic and dynamic performances degrade dramatically. Most existing methods aim at solving this issue by avoiding the singularity posture in the geometric manner. Different from them, this paper aims at avoiding the singular phenomenon by reducing the Jacobian-matrix condition number, and proposes an adaptive singularity avoidance toolpath generation method. This method adds a damping diagonal matrix into the computation of the pseudo-inverse Jacobian matrix to reduce its ill-condition extent during axial path generation, thus solving the singularity phenomenon. However, the adding of damping matrix gives arise to the toolpath error. To ensure the accuracy meanwhile, an adaptive law for determination of the damping matrix is presented to balance the singularity-avoiding effect and the path error, under the constraints of condition number and tool-orientation error-tolerance thresholds, as well as invariant cutter-contact points. Simulation and experimental tests verify that the proposed method can not only realize the singular avoidance without preliminary adjustment of the original toolpath, thus can be realized in real-time NC system, but also has better singular-avoiding performance and lower toolpath error when comparing with typical methods.

Geometric-phase-based axicon lens for computational achromatic imaging.

Conventional optical imaging systems usually utilize several lenses within a precise assembly to eliminate chromatic aberration, which increases the difficulty of system integration. In recent years, with the rapid development of metasurfaces and liquid crystals (LCs), planar optical elements provide feasible solutions to realize flexible light manipulation and lightweight systems. However, there also exists chromatic aberration, which can be corrected but at the cost of a complex device design. Here, a geometric-phase-based axicon lens is utilized to correct chromatic aberration across a broadband wavelength with the assistance of a post-process algorithm. The axicon lens is fabricated through arranging orientations of liquid-crystal molecules with a standard photoalignment technique, and it produces an approximately invariant point spread function (PSF) at several discrete wavelengths, which is used as the prior information to extract the object in the blurred image. In the experiment, the reconstruction quality is significantly improved after the post-process algorithm. We expect our work to provide further development to reduce the dispersion with both the device design and the computational image technique.

Complex dynamics and initial state effects in a two-dimensional sine-bounded memristive map

Recently, discrete memristor maps can be directly constructed using discrete memristors. However, some discrete memristors with reciprocal polynomial memristances cannot be directly used to generate mapping models. To achieve an available memristive map, a simple and effective implementation scheme is proposed to construct a two-dimensional (2-D) sine-bounded memristive map (SBMM). The proposed map has line invariant point and its stability is extremely related to parameters and memristor initial state. The parameter-dependent complex dynamics, coexisting attractors with riddled attraction basin, and initial state-induced dynamics effect are disclosed using several numerical measures. SBMM has complex dynamics distributions with initial state effects and can generate chaotic and hyperchaotic attractors with riddled attraction basins. These chaotic/hyperchaotic sequences have excellent performance and can be applied to generate pseudorandom binary number generators (PBNGs). Besides, FPGA hardware implementation is performed, and the numerical results are verified by experiments.

Self-Similarity Principle and the General Theory of Fractal Elements: How to Fit a Random Curve with a Clearly Expressed Trend?

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and includes previously unknown but crucial adjustments. These new discoveries have the potential to significantly alter the preexisting theory and create new connections between it and its experimental support, particularly when it comes to measurements of the impedances of diverse metamaterials. It is now easy to demonstrate that any random curve with a clearly stated tendency in a specific range of scales is self-similar using the method involving reduction to three invariant points (Ymx, Ymn, and Ymin). This useful procedure indicates that the chosen random curve, even after being compressed a certain number of times, still resembles the original curve. Based on this common peculiarity, it is now possible to derive “a universal” fitting function that can be used in a variety of applied sciences, particularly those that deal with complex systems, to parametrize many initial curves when a model fitting function derived from a simple model is not present. This self-similarity principle-derived function demonstrates its effectiveness in data linked to photodiode noise and the smoothed integral curves produced from well-known transcendental numbers E and Pi, which are considered in the paper as an example.

Phase Equilibria for the Aqueous Quinary System Li+, Na+, K+, Mg2+//Cl––H2O Saturated with NaCl·2H2O at 258.15 K

The phase diagram can guide the comprehensive utilization of salt lake brine, particularly lithium extraction. In this paper, the study on phase equilibria of the quinary system Li+, Na+, K+, Mg2+//Cl––H2O saturated with NaCl·2H2O and its subsystem Li+, Na+, Mg2+//Cl––H2O at 258.15 K were carried out using the isothermal dissolution equilibrium method. Based on the experimental data, equilibrium diagrams for stable phases were plotted. For the equilibrium diagram of the quaternary system Li+, Na+, Mg2+//Cl––H2O at 258.15 K, there are two invariant points, five univariant curves, and four crystallization fields. The quinary system Li+, Na+, K+, Mg2+//Cl––H2O saturated with NaCl·2H2O at 258.15 K contains three invariant points, seven univariant curves, and five crystallization fields. Comparing the phase diagram of the system at 258.15 K to that at 298.15 K reveals that, except KCl, all crystallization zones have decreased, and LiCl·MgCl2·7H2O has the smallest crystallization zone compared to the other salts in the systems. This fundamental research could be valuable for promoting comprehensive utilization of the lithium-containing salt lake brine.

Solid–Liquid Phase Equilibria of the Quaternary System NaCl–CaCl2–H3BO3–H2O at 323.15 K: Solubility Determination and Thermodynamic Model

The solid–liquid phase equilibria of brine systems containing boric acid are the theoretical basis for the development of boric acid from brine resources. The phase equilibria of the systems NaCl–CaCl2–H3BO3–H2O and CaCl2–H3BO3–H2O at 323.15 K were investigated by the isothermal solution method. The phase diagram for the ternary system is composed of one co-saturation point, two univariant solubility curves, and two singe-salt crystallization fields of CaCl2·2H2O and H3BO3. The dry-salt phase diagram for the quaternary system consists of one invariant point, three univariant solubility curves, and three single-salt crystallization fields for NaCl, CaCl2·2H2O, and H3BO3. In the phase diagrams of the quaternary system at 298.15 and 323.15 K, the areas of sodium chloride and calcium chloride salt regions are enlarged, whereas the area of the H3BO3 region is diminished significantly with the increase of temperature. Using the Pitzer model, the lacking Pitzer parameters for H3BO3 were obtained by fitting the solubilities in the CaCl2–H3BO3–H2O system. The calculated solubilities with the Pitzer model were in accord with the experimental data.

Parallel and anti-parallel helical surface states for topological semimetals

Weyl points, carrying a Z-type monopole charge C, have bulk-surface correspondence (BSC) associated with helical surface states (HSSs). When |C| >1, multi-HSSs can appear in a parallel manner. However, when a pair of Weyl points carrying C=pm 1 meet, a Dirac point carrying C = 0 can be obtained and the BSC vanishes. Nonetheless, a recent study in Zhang et al. (Phys Rev Res 4:033170, 2022) shows that a new BSC can survive for Dirac points when the system has time-reversal ({T})-glide ({G}) symmetry ({tilde{Theta }}=TG), i.e., anti-parallel double/quad-HSSs associated with a new Z_{2}-type monopole charge {Q} appear. In this paper, we systematically review and discuss both the parallel and anti-parallel multi-HSSs for Weyl and Dirac points, carrying two different kinds of monopole charges. Two material examples are offered to understand the whole configuration of multi-HSSs. One carries the Z-type monopole charge C, showing both local and global topology for three kinds of Weyl points, and it leads to parallel multi-HSSs. The other carries the Z_{2}-type monopole charge {Q}, only showing the global topology for {tilde{Theta }}-invariant Dirac points, and it is accompanied by anti-parallel multi-HSSs.

Investigation of Solid–Liquid Phase Equilibria of Mg2+, NH4+//Cl–, SO42–H2O at T = 303.15 K and P = 88.35 kPa

Nitrogen and magnesium compound fertilizer is an important and efficient fertilizer in the fertilizer industry. It can solve the problem of lack of sulfur, magnesium, and nitrogen in soil. MgCl2 can react with (NH4)2SO4 to produce Mg–N compound fertilizer. Therefore, the solid–liquid equilibrium data and physical properties (density and viscosity) of the quaternary system Mg2+, NH4+//Cl–, SO42––H2O and its ternary subsystems Mg2+, NH4+//Cl––H2O and Mg2+//Cl–, SO42––H2O at T = 303.15 K ± 0.05 K and P = 88.35 kPa were studied by an isothermal stripping equilibrium method. According to the experimental data, the phase diagram and physical property composition diagram of each system were drawn. The ternary subsystem Mg2+, NH4+//Cl––H2O contains two invariant points and three crystallization regions. The ternary system Mg2+//Cl–, SO42––H2O contains four invariant points and five crystallization regions. The quaternary system Mg2+, NH4+//Cl–, SO42––H2O contains seven invariant points and nine crystallization regions. MgCl2·NH4Cl·6H2O and MgSO4·(NH4)2SO4·6H2O exist in the quaternary system, and the quality of crops can be significantly improved by using the latter kind of complex salt. Therefore, this project is of great significance for the production of N–Mg compound fertilizers from magnesium resources in salt lake or other underground brines.