diff --git a/Core/Data/Result/ConciseModel.cs b/Core/Data/Result/ConciseModel.cs
index a0fe553..2ed8503 100644
--- a/Core/Data/Result/ConciseModel.cs
+++ b/Core/Data/Result/ConciseModel.cs
@@ -59,7 +59,7 @@ public ConciseModel(string id, string title, string link = null, string descript
     /// Gets or sets the identifier.
     /// </summary>
     [JsonPropertyName("id")]
-    [Description("The identifier of the model.")]
+    [Description("The identifier of the item.")]
     public string Id
     {
         get => GetCurrentProperty<string>();
@@ -70,7 +70,7 @@ public string Id
     /// Gets or sets the title.
     /// </summary>
     [JsonPropertyName("title")]
-    [Description("The title of the model.")]
+    [Description("The title of the item.")]
     public string Title
     {
         get => GetCurrentProperty<string>();
@@ -82,7 +82,7 @@ public string Title
     /// </summary>
     [JsonPropertyName("desc")]
     [JsonIgnore(Condition = JsonIgnoreCondition.WhenWritingNull)]
-    [Description("The short description of the model.")]
+    [Description("The short description of the item.")]
     public string Description
     {
         get => GetCurrentProperty<string>();
@@ -102,9 +102,9 @@ public Uri ImageUri
     /// <summary>
     /// Gets or sets the image URI (thumbnail or avatar).
     /// </summary>
-    [JsonPropertyName("id")]
+    [JsonPropertyName("image")]
     [JsonIgnore(Condition = JsonIgnoreCondition.WhenWritingNull)]
-    [Description("The thumbnail or avatar URL of the model.")]
+    [Description("The thumbnail or avatar URL of the item.")]
     public string ImageUrl
     {
         get => ImageUri?.OriginalString;
@@ -116,7 +116,7 @@ public string ImageUrl
     /// </summary>
     [JsonPropertyName("url")]
     [JsonIgnore(Condition = JsonIgnoreCondition.WhenWritingNull)]
-    [Description("The URL to details page of the model.")]
+    [Description("The URL to details page of the item.")]
     public string Link
     {
         get => GetCurrentProperty<string>();
@@ -128,7 +128,8 @@ public string Link
     /// </summary>
     [JsonPropertyName("keywords")]
     [JsonIgnore(Condition = JsonIgnoreCondition.WhenWritingNull)]
-    [Description("The keywords of the model.")]
+    [Description("The keywords of the item.")]
+    [JsonConverter(typeof(JsonStringListConverter.SemicolonSeparatedConverter))]
     public ObservableCollection<string> Keywords
     {
         get => GetCurrentProperty<ObservableCollection<string>>();
@@ -216,7 +217,7 @@ public override string ToString()
 }
 
 /// <summary>
-/// The model with observable name and value.
+/// The model with observable key and value.
 /// </summary>
 /// <typeparam name="T">The type of the value.</typeparam>
 [DataContract]
@@ -232,16 +233,16 @@ public KeyValueObservableModel()
     /// <summary>
     /// Initializes a new instance of the KeyValueObservableModel class.
     /// </summary>
-    /// <param name="name">The name.</param>
+    /// <param name="key">The key.</param>
     /// <param name="value">The value.</param>
-    public KeyValueObservableModel(string name, T value)
+    public KeyValueObservableModel(string key, T value)
     {
-        Key = name;
+        Key = key;
         Value = value;
     }
 
     /// <summary>
-    /// Gets or sets the name.
+    /// Gets or sets the key.
     /// </summary>
     [DataMember(Name = "key")]
     [JsonPropertyName("key")]
@@ -275,3 +276,64 @@ public object Tag
         set => SetCurrentProperty(value);
     }
 }
+
+/// <summary>
+/// The model with observable name and value.
+/// </summary>
+/// <typeparam name="T">The type of the value.</typeparam>
+[DataContract]
+public class NameValueObservableModel<T> : BaseObservableProperties
+{
+    /// <summary>
+    /// Initializes a new instance of the NameValueObservableModel class.
+    /// </summary>
+    public NameValueObservableModel()
+    {
+    }
+
+    /// <summary>
+    /// Initializes a new instance of the NameValueObservableModel class.
+    /// </summary>
+    /// <param name="name">The name.</param>
+    /// <param name="value">The value.</param>
+    public NameValueObservableModel(string name, T value)
+    {
+        Name = name;
+        Value = value;
+    }
+
+    /// <summary>
+    /// Gets or sets the name.
+    /// </summary>
+    [DataMember(Name = "name")]
+    [JsonPropertyName("name")]
+    [Description("The item name.")]
+    public string Name
+
+    {
+        get => GetCurrentProperty<string>();
+        set => SetCurrentProperty(value);
+    }
+
+    /// <summary>
+    /// Gets or sets the value.
+    /// </summary>
+    [DataMember(Name = "value")]
+    [JsonPropertyName("value")]
+    [Description("The value.")]
+    public T Value
+    {
+        get => GetCurrentProperty<T>();
+        set => SetCurrentProperty(value);
+    }
+
+    /// <summary>
+    /// Gets or sets the optional additional object.
+    /// </summary>
+    [JsonIgnore]
+    public object Tag
+    {
+        get => GetCurrentProperty<object>();
+        set => SetCurrentProperty(value);
+    }
+}
diff --git a/Core/Maths/Statistics/Average.cs b/Core/Maths/Statistics/Average.cs
index 82f3234..d565b08 100644
--- a/Core/Maths/Statistics/Average.cs
+++ b/Core/Maths/Statistics/Average.cs
@@ -1,14 +1,4 @@
-// --------------------------------------------------------------------------------------------------------------------
-// <copyright file="Arithmetic\Basic.cs" company="Nanchang Jinchen Software Co., Ltd.">
-//   Copyright (c) 2010 Nanchang Jinchen Software Co., Ltd. All rights reserved.
-// </copyright>
-// <summary>
-//   The basic arithmetic functions.
-// </summary>
-// <author>Kingcean Tuan</author>
-// --------------------------------------------------------------------------------------------------------------------
-
-using System;
+using System;
 using System.Collections.Generic;
 using System.Linq;
 using System.Text;
diff --git a/Core/Maths/Statistics/Difference.cs b/Core/Maths/Statistics/Difference.cs
new file mode 100644
index 0000000..b8c11bc
--- /dev/null
+++ b/Core/Maths/Statistics/Difference.cs
@@ -0,0 +1,124 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+
+namespace Trivial.Maths;
+
+/// <summary>
+/// The functions of probability theory and mathematical statistics.
+/// </summary>
+public static partial class StatisticalMethod
+{
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<double> Difference(IEnumerable<double> col)
+    {
+        if (col == null) yield break;
+        double? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<float> Difference(IEnumerable<float> col)
+    {
+        if (col == null) yield break;
+        float? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<decimal> Difference(IEnumerable<decimal> col)
+    {
+        if (col == null) yield break;
+        decimal? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<long> Difference(IEnumerable<long> col)
+    {
+        if (col == null) yield break;
+        long? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<int> Difference(IEnumerable<int> col)
+    {
+        if (col == null) yield break;
+        int? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<TimeSpan> Difference(IEnumerable<DateTime> col)
+    {
+        if (col == null) yield break;
+        DateTime? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+
+    /// <summary>
+    /// Gets a sequence about each item is different than before one of a specific numbers.
+    /// </summary>
+    /// <param name="col">The input numbers.</param>
+    /// <returns>The increasement of each item.</returns>
+    public static IEnumerable<TimeSpan> Difference(IEnumerable<TimeSpan> col)
+    {
+        if (col == null) yield break;
+        TimeSpan? test = null;
+        foreach (var item in col)
+        {
+            if (test.HasValue) yield return item - test.Value;
+            test = item;
+        }
+    }
+}
diff --git a/Core/Reflection/Lifecycle/ObservableProperties.cs b/Core/Reflection/Lifecycle/ObservableProperties.cs
index 9150e53..754b4ef 100644
--- a/Core/Reflection/Lifecycle/ObservableProperties.cs
+++ b/Core/Reflection/Lifecycle/ObservableProperties.cs
@@ -92,7 +92,7 @@ protected T GetCurrentProperty<T>(T defaultValue = default, [CallerMemberName] s
         if (string.IsNullOrWhiteSpace(key)) return defaultValue;
         try
         {
-            return cache.TryGetValue(key, out var v) ? (T)v : defaultValue;
+            return TryGetPropertyInternal(key, out var v) ? (T)v : defaultValue;
         }
         catch (InvalidCastException)
         {
@@ -146,7 +146,7 @@ protected T GetProperty<T>(string key, T defaultValue = default)
         if (string.IsNullOrWhiteSpace(key)) return defaultValue;
         try
         {
-            return cache.TryGetValue(key, out var v) && v is T t ? t : defaultValue;
+            return TryGetPropertyInternal(key, out var v) && v is T t ? t : defaultValue;
         }
         catch (InvalidOperationException)
         {
@@ -175,7 +175,7 @@ protected bool GetProperty<T>(string key, out T result)
     {
         try
         {
-            if (!string.IsNullOrWhiteSpace(key) && cache.TryGetValue(key, out var v) && v is T t)
+            if (!string.IsNullOrWhiteSpace(key) && TryGetPropertyInternal(key, out var v) && v is T t)
             {
                 result = t;
                 return true;
@@ -226,7 +226,7 @@ protected bool SetProperty(string key, object value)
     }
 
     /// <summary>
-    /// Test whether the new property to set is valid.
+    /// Tests whether the new property to set is valid.
     /// </summary>
     /// <param name="key">The property key.</param>
     /// <param name="value">The value of the property to set.</param>
@@ -234,6 +234,18 @@ protected bool SetProperty(string key, object value)
     protected virtual bool IsPropertyValid(string key, object value)
         => true;
 
+    /// <summary>
+    /// Occurs on request to get a specific value. This can be used to fill a default value.
+    /// </summary>
+    /// <param name="key">The property key.</param>
+    /// <param name="value">When this method returns, contains the value associated with the specified key, if the key is found; otherwise, the default value for the type of the value parameter. This parameter is passed uninitialized.</param>
+    /// <returns>true if need to set a default value; otherwise, false.</returns>
+    protected virtual bool FillNonExistProperty(string key, out object value)
+    {
+        value = default;
+        return false;
+    }
+
     /// <summary>
     /// Removes a property.
     /// </summary>
@@ -269,7 +281,7 @@ protected Type GetPropertyType(string key)
         if (string.IsNullOrWhiteSpace(key)) return null;
         try
         {
-            return cache.TryGetValue(key, out var v) ? v?.GetType() : null;
+            return TryGetPropertyInternal(key, out var v) ? v?.GetType() : null;
         }
         catch (ArgumentException)
         {
@@ -352,6 +364,21 @@ protected void CopyFrom(BaseObservableProperties props, bool skipIfExist = false
     protected IEnumerator<KeyValuePair<string, object>> EnumerateObject()
         => cache.GetEnumerator();
 
+    /// <summary>
+    /// Tries to get property.
+    /// </summary>
+    /// <param name="key">The property key.</param>
+    /// <param name="value">When this method returns, contains the value associated with the specified key, if the key is found; otherwise, the default value for the type of the value parameter. This parameter is passed uninitialized.</param>
+    /// <returns>true if the cache contains an element with the specified key; otherwise, false.</returns>
+    private bool TryGetPropertyInternal(string key, out object value)
+    {
+        if (cache.TryGetValue(key, out value)) return true;
+        if (!FillNonExistProperty(key, out value)) return false;
+        cache[key] = value;
+        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(key));
+        return true;
+    }
+
     /// <summary>
     /// Sets the property.
     /// </summary>
diff --git a/Core/Text/Json/Converter.cs b/Core/Text/Json/Converter.cs
index ac18a89..5d11307 100644
--- a/Core/Text/Json/Converter.cs
+++ b/Core/Text/Json/Converter.cs
@@ -61,6 +61,32 @@ public sealed class SemicolonSeparatedConverter : JsonStringListConverter
         }
     }
 
+    /// <summary>
+    /// JSON string collection with enumeration comma separated.
+    /// </summary>
+    public sealed class EnumerationCommaSeparatedConverter : JsonStringListConverter
+    {
+        /// <summary>
+        /// Initializes a new instance of the EnumerationCommaSeparatedConverter class.
+        /// </summary>
+        public EnumerationCommaSeparatedConverter() : base('、')
+        {
+        }
+    }
+
+    /// <summary>
+    /// JSON string collection with semicolon separated.
+    /// </summary>
+    public sealed class ChineseSemicolonSeparatedConverter : JsonStringListConverter
+    {
+        /// <summary>
+        /// Initializes a new instance of the SemicolonSeparatedConverter class.
+        /// </summary>
+        public ChineseSemicolonSeparatedConverter() : base('；')
+        {
+        }
+    }
+
     /// <summary>
     /// JSON string collection with vertical bar separated.
     /// </summary>
@@ -126,7 +152,7 @@ public override IEnumerable<string> Read(ref Utf8JsonReader reader, Type typeToC
                 {
                     IEnumerable<string> arr = str.Split(chars, StringSplitOptions.RemoveEmptyEntries);
                     if (trim) arr = arr.Select(ele => ele.Trim()).Where(ele => ele.Length > 0);
-                    else col.AddRange(arr);
+                    col.AddRange(arr);
                 }
                 else
                 {
diff --git a/UnitTest/Reflection/SingletonUnitTest.cs b/UnitTest/Reflection/SingletonUnitTest.cs
index f299e7a..39fe169 100644
--- a/UnitTest/Reflection/SingletonUnitTest.cs
+++ b/UnitTest/Reflection/SingletonUnitTest.cs
@@ -7,6 +7,7 @@
 using System.Threading.Tasks;
 
 using Microsoft.VisualStudio.TestTools.UnitTesting;
+using Trivial.Data;
 using Trivial.Text;
 
 namespace Trivial.Reflection
@@ -44,7 +45,7 @@ public async Task TestSingletonKeeperAsync()
         public void TestObservableProperties()
         {
             var i = 0;
-            var obs = new NameValueObservableProperties<string>();
+            var obs = new NameValueObservableModel<string>();
             obs.PropertyChanged += (sender, obj) =>
             {
                 if (obj.PropertyName == "Value") i++;
@@ -57,8 +58,18 @@ public void TestObservableProperties()
             Assert.AreEqual(1, i);
             obs.Value = "uvwxyz";
             Assert.AreEqual(2, i);
+            var m = JsonSerializer.Deserialize<ConciseModel>("{ \"id\": \"9876543210\", \"keywords\": \"test;another\" }");
+            Assert.AreEqual("9876543210", m.Id);
+            Assert.IsNull(m.Title);
+            Assert.IsNotNull(m.Keywords);
+            Assert.AreEqual(2, m.Keywords.Count);
+            m = JsonSerializer.Deserialize<ConciseModel>("{ \"id\": \"9876543210\", \"keywords\": [\"test\", \"another\"] }");
+            Assert.AreEqual("9876543210", m.Id);
+            Assert.IsNull(m.Title);
+            Assert.IsNotNull(m.Keywords);
+            Assert.AreEqual(2, m.Keywords.Count);
         }
-        
+
         /// <summary>
         /// Tests factory.
         /// </summary>